From 9fc3ba76a50668a214bd722ae55e43c753e9a01d Mon Sep 17 00:00:00 2001 From: Daniel Nezamabadi <55559979+dnezam@users.noreply.github.com> Date: Sat, 13 Apr 2024 10:25:48 +0200 Subject: [PATCH 01/13] Copy over files --- ...608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv | 31 + ..._8_7-gobra_ver_0608ac92.execution_time.png | Bin 0 -> 52965 bytes ...ac9-z3_ver_4_8_7-gobra_ver_0608ac92.qi.png | Bin 0 -> 76196 bytes .../first_half/first_half.gobra | 104 ++++ ...608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv | 31 + ..._8_7-gobra_ver_0608ac92.execution_time.png | Bin 0 -> 47947 bytes ...ac9-z3_ver_4_8_7-gobra_ver_0608ac92.qi.png | Bin 0 -> 78294 bytes .../full/full.gobra | 113 ++++ ...608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv | 31 + ..._8_7-gobra_ver_0608ac92.execution_time.png | Bin 0 -> 49472 bytes ...ac9-z3_ver_4_8_7-gobra_ver_0608ac92.qi.png | Bin 0 -> 76139 bytes .../last_half/last_half.gobra | 110 ++++ ...608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv | 31 + 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pqPrime.Elements() == pq.Elements() union mset[int]{y} +decreases len(pq) +pure func (pq PQueue) InsertCorrect(y int) Unit { + return match pq { + case Leaf{}: + Unit{} + case Node{?x, ?l, ?r}: + let pqPrime := pq.Insert(y) in + let min := y < x ? y : x in + let max := y < x ? x : y in + let newRight := r.Insert(max) in + let _ := asserting(pqPrime == Node{min, newRight, l}) in + let _ := asserting( + let L := len(l.Elements()) in + let R := len(r.Elements()) in + L == R || L == R + 1) in + r.InsertCorrect(max) + } +} + +ghost +decreases len(pq) +pure func (pq PQueue) Valid() bool { + return pq.IsBinaryHeap() && pq.IsBalanced() +} + +ghost +decreases len(pq) +pure func (pq PQueue) Insert(y int) PQueue { + return match pq { + case Leaf{}: + Node{y, Leaf{}, Leaf{}} + case Node{?x, ?left, ?right}: + y < x ? Node{y, right.Insert(x), left} : Node{x, right.Insert(y), left} + } +} + +ghost +decreases len(pq) +pure func (pq PQueue) Elements() mset[int] { + return match pq { + case Leaf{}: + mset[int]{} + case Node{?x, ?left, ?right}: + mset[int]{x} union left.Elements() union right.Elements() + } +} + +ghost +decreases len(pq) +pure func (pq PQueue) IsBalanced() (res bool) { + return match pq { + case Leaf{}: + true + case Node{_, ?left, ?right}: + left.IsBalanced() && right.IsBalanced() && + (let L := len(left.Elements()) in + let R := len(right.Elements()) in + L == R || L == R + 1) + } +} + +ghost +decreases len(pq) +pure func (pq PQueue) IsBinaryHeap() bool { + return match pq { + case Leaf{}: + true + case Node{?x, ?left, ?right}: + left.IsBinaryHeap() && right.IsBinaryHeap() && + (left == Leaf{} || x <= left.x) && + (right == Leaf{} || x <= right.x) + } +} + + +type Unit struct{} + +ghost +requires b +decreases +pure func asserting(b bool) Unit { + return Unit{} +} + +type PQueue = BraunTree + +type BraunTree adt { + Leaf {} + + Node { + x int + left BraunTree + right BraunTree + } +} diff --git a/evaluation/experiments/program_proofs_example_10_2/full/full-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv b/evaluation/experiments/program_proofs_example_10_2/full/full-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv new file mode 100644 index 0000000..ed17137 --- /dev/null +++ b/evaluation/experiments/program_proofs_example_10_2/full/full-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv @@ -0,0 +1,31 @@ +qi-k!601,qi-k!544,qi-k!578,qi-k!556,qi-quant-u-8,qi-quant-u-9,qi-$Multiset[Int]_prog.card_non_negative,qi-$Multiset[Int]_prog.card_empty,qi-quant-u-27,qi-quant-u-2,qi-quant-u-26,qi-quant-u-3,qi-quant-u-0,qi-quant-u-24,qi-quant-u-1,qi-quant-u-10,qi-quant-u-11,qi-quant-u-35,qi-quant-u-34,qi-quant-u-4,qi-quant-u-28,qi-quant-u-5,qi-quant-u-43,qi-quant-u-18,qi-quant-u-42,qi-quant-u-19,qi-quant-u-33,qi-quant-u-32,qi-quant-u-41,qi-quant-u-16,qi-quant-u-40,qi-quant-u-17,qi-quant-u-6,qi-quant-u-30,qi-quant-u-7,qi-quant-u-12,qi-quant-u-36,qi-quant-u-13,qi-$Multiset[Int]_prog.count_card,qi-$Multiset[Int]_prog.singleton_unionone,qi-$Multiset[Int]_prog.card_union,qi-$Multiset[Int]_prog.count_union,qi-$Multiset[Int]_prog.card_unionone,qi-$Multiset[Int]_prog.count_singleton,qi-$Multiset[Int]_prog.count_unionone,qi-$Multiset[Int]_prog.count_empty,qi-quant-u-22,qi-quant-u-45,qi-quant-u-23,qi-quant-u-44,qi-$Multiset[Int]_prog.equal_count,qi-$Multiset[Int]_prog.native_equality,qi-quant-u-14,qi-quant-u-38,qi-quant-u-15,qi-prog.getter_over_tuple2,qi-quant-u-20,qi-quant-u-21,qi-prog.integer_ax_dec,qi-k!560,qi-k!584,qi-k!590,qi-prog.integer_ax_bound,qi-quant-u-47,qi-quant-u-46,execution_time 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dictionary. +ghost +ensures IsEmpty(result) +decreases +pure func Empty() (result dict[int]int) { + return dict[int]int{} +} + +// Retrieves the value associated with the key, if present, as an option. +ghost +decreases +pure func Get(d dict[int]int, k int) option[int] { + return k in domain(d) ? some(d[k]) : none[int] +} + +// Keep all key-value pairs corresponding to the set of keys provided. +ghost +opaque +ensures forall x int :: {result[x]} (x in domain(d) && x in xs) ==> + (x in domain(result) && result[x] == d[x]) +ensures forall x int :: {x in domain(result)} x in domain(result) ==> + (x in domain(d) && x in xs) +ensures domain(result) == xs intersection domain(d) +decreases xs +pure func Restrict(d dict[int]int, xs set[int]) (result dict[int]int) { + return let ys := (xs intersection domain(d)) in + (sets_opaque.IsEmpty(ys) ? Empty() : + (let y := sets_opaque.Choose(ys) in + (let yr := sets_opaque.Remove(ys, y) in + (let _ := sets_opaque.IntersectLenUpper(xs, domain(d)) in + Restrict(d, yr)[y = d[y]])))) +} + +// Remove all key-value pairs corresponding to the set of keys provided. +ghost +decreases +pure func RemoveKeys(d dict[int]int, xs set[int]) (result dict[int]int) { + return Restrict(d, domain(d) setminus xs) +} + +// Remove a key-value pair. Returns d if k is not in the domain of d. +ghost +ensures len(result) <= len(d) +ensures k in domain(d) ==> len(result) == len(d) - 1 +ensures !(k in domain(d)) ==> len(result) == len(d) +decreases +pure func Remove(d dict[int]int, k int) (result dict[int]int) { + return let ys := (sets_opaque.Remove(domain(d), k)) in + let _ := util.Asserting(ys intersection domain(d) == ys) in + RemoveKeys(d, sets_opaque.SingletonSet(k)) +} + +// True iff k maps to the same value or is not in the domains of d1 and d2. +ghost +decreases +pure func IsEqualOnKey(d1, d2 dict[int]int, k int) bool { + return !(k in domain(d1) || k in domain(d2)) || + (k in domain(d1) && k in domain(d2) && d1[k] == d2[k]) +} + +// True iff if d1 is a subset of d2. +ghost +decreases +pure func IsSubset(d1, d2 dict[int]int) bool { + return domain(d1) subset domain(d2) && + forall k int :: {IsEqualOnKey(d1, d2, k)} {k in domain(d1)} (k in domain(d1)) ==> + IsEqualOnKey(d1, d2, k) +} + +// Union of two dictionaries. Does not require disjoint domains: on the intersection, +// values from the second dictionary are chosen. +ghost +opaque +ensures domain(result) == domain(d1) union domain(d2) +ensures forall k int :: {result[k]} (k in domain(d2)) ==> result[k] == d2[k] +ensures forall k int :: {result[k]} (!(k in domain(d2)) && k in domain(d1)) ==> + result[k] == d1[k] +decreases domain(d1) union domain(d2) +pure func Union(d1, d2 dict[int]int) (result dict[int]int) { + return let ks := domain(d1) union domain(d2) in + (sets_opaque.IsEmpty(ks) ? Empty() : + let k := sets_opaque.Choose(ks) in + let c1 := Remove(d1, k) in + let c2 := Remove(d2, k) in + let _ := sets_opaque.RemoveUnionLen(domain(d1), domain(d2), k) in + (k in domain(d2) ? Union(c1, c2)[k = d2[k]] : Union(c1, c2)[k = d1[k]])) +} + +// Dictionaries are disjoint iff their domains are disjoint. +ghost +decreases +pure func AreDisjoint(d1, d2 dict[int]int) bool { + return sets_opaque.AreDisjoint(domain(d1), domain(d2)) +} + +// The length of the union of two disjoint dictionaries is the sum of each of their lengths. +ghost +opaque +requires AreDisjoint(d1, d2) +ensures len(Union(d1, d2)) == len(d1) + len(d2) +decreases +pure func DisjointUnionLen(d1, d2 dict[int]int) util.Unit { + return util.Unit{} +} + +// True iff a dictionary is injective. +ghost +opaque +decreases +pure func IsInjective(d dict[int]int) bool { + return forall k1, k2 int :: {d[k1], d[k2]} (k1 != k2 && k1 in domain(d) && k2 in domain(d)) ==> + d[k1] != d[k2] +} + +// True iff a dictionary contains all valid keys. +ghost +opaque +decreases +pure func IsTotal(d dict[int]int) bool { + return forall k int :: {k in domain(d)} k in domain(d) +} + +// True iff a dictionary is monotonic. +ghost +opaque +decreases +pure func IsMonotonic(d dict[int]int) bool { + return forall k1, k2 int :: {d[k1], d[k2]} (k1 in domain(d) && k2 in domain(d) && k1 <= k2) ==> + d[k1] <= d[k2] +} + +// True iff a dictionary is monotonic. Only considers keys greater than or equal to start. +ghost +opaque +decreases +pure func IsMonotonicFrom(d dict[int]int, start int) bool { + return forall k1, k2 int :: {d[k1], d[k2]} (k1 in domain(d) && k2 in domain(d) && start <= k1 && k1 <= k2) ==> + d[k1] <= d[k2] +} + +// True iff a dictionary is monotonic. Only considers keys in the interval [start, end). +ghost +opaque +decreases +pure func IsMonotonicFromTo(d dict[int]int, start, end int) bool { + return forall k1, k2 int :: {d[k1], d[k2]} (k1 in domain(d) && + k2 in domain(d) && + start <= k1 && k1 <= k2 && k2 < end) ==> d[k1] <= d[k2] +} + +// True iff two dictionaries are equal in the interval [start, end). +ghost +opaque +decreases +pure func IsEqualInRange(d1, d2 dict[int]int, start, end int) bool { + return forall k int :: {d1[k], d2[k]} {k in domain(d1)} {k in domain(d2)}(start <= k && k < end) ==> + k in domain(d1) && k in domain(d2) && d1[k] == d2[k] +} + +// True iff d1 and d2 agree on all keys that their domains share. +ghost +decreases +pure func Agree(d1, d2 dict[int]int) bool { + return forall k int :: {d1[k], d2[k]} k in (domain(d1) intersection domain(d2)) ==> + d1[k] == d2[k] +} + +// The domain of a map after removing a key is equivalent to removing +// the key from the domain of the original map. +ghost +opaque +ensures domain(Remove(d, k)) == sets_opaque.Remove(domain(d), k) +decreases +pure func RemoveDomain(d dict[int]int, k int) util.Unit { + return util.Unit{} +} + +// The domain of the empty dictionary is the empty set. +ghost +opaque +requires IsEmpty(d) +ensures domain(d) == sets_opaque.Empty() +decreases +pure func EmptyDictEmptyDomain(d dict[int]int) util.Unit { + return util.Unit{} +} + +// The domain of a dictionary after inserting a key-value pair is equivalent to +// inserting the key into the original map's domain set. +ghost +opaque +ensures domain(d[k = v]) == sets_opaque.Add(domain(d), k) +decreases +pure func InsertDomain(d dict[int]int, k, v int) util.Unit { + return util.Unit{} +} + +// Inserting value at k in d results in a dictionary that maps k to v. +ghost +opaque +ensures d[k = v][k] == v +decreases +pure func UpdateSame(d dict[int]int, k, v int) util.Unit { + return util.Unit{} +} + +// Reassigning the corresponding value to a key does not change the dictionary. +ghost +opaque +requires k in domain(d) +requires v == d[k] +ensures d[k = v] == d +decreases +pure func UpdateEqual(d dict[int]int, k, v int) util.Unit { + return util.Unit{} +} + +// Inserting v at k2 does not change the value mapped to by any other keys in d. +ghost +opaque +requires k1 != k2 +ensures k2 in domain(d[k1 = v]) == k2 in domain(d) +ensures k2 in domain(d) ==> d[k1 = v][k2] == d[k2] +decreases +pure func UpdateDifferent(d dict[int]int, k1, k2, v int) util.Unit { + return util.Unit{} +} + +// Removing a key-value pair from a dictionary does not change the value mapped to +// by any other keys in the map. +ghost +opaque +requires k1 in domain(d) +requires k1 != k2 +ensures Remove(d, k2)[k1] == d[k1] +decreases +pure func RemoveDifferent(d dict[int]int, k1, k2 int) util.Unit { + return util.Unit{} +} + +// Two maps are equivalent if their domains are equivalent and every key in their +// domains map to the same value. +ghost +opaque +ensures (d1 == d2) == + (domain(d1) == domain(d2) && forall k int :: {d1[k], d2[k]} k in domain(d1) ==> d1[k] == d2[k]) +decreases +pure func ExtEqual(d1, d2 dict[int]int) util.Unit { + return util.Unit{} +} + +// The cardinality of a dictionary is non-negative. +ghost +opaque +ensures len(d) >= 0 +decreases +pure func NonNegativeLen(d dict[int]int) util.Unit { + return util.Unit{} +} + +// The cardinality of a dictionary is equal to the cardinality of its domain. +ghost +opaque +ensures len(d) == len(domain(d)) +decreases +pure func DomainLenEq(d dict[int]int) util.Unit { + return util.Unit{} +} + +// If two dictionaries are disjoint there is no key that is in both of their domains. +ghost +opaque +requires AreDisjoint(d1, d2) +ensures !(k in domain(d1) && k in domain(d2)) +decreases +pure func DisjointNoSharedKey(d1, d2 dict[int]int, k int) util.Unit { + return util.Unit{} +} + +// If two dictionaries are not disjoint, there exists a key that is in both of their domains. +ghost +opaque +requires !AreDisjoint(d1, d2) +ensures exists k int :: {k in domain(d1), k in domain(d2)} k in domain(d1) && k in domain(d2) +decreases +pure func NotDisjointSharedKey(d1, d2 dict[int]int) util.Unit { + return util.Unit{} +} + +// There is only one empty map. +ghost +opaque +requires IsEmpty(d) +ensures d == Empty() +decreases +pure func EmptyIsUnique(d dict[int]int) util.Unit { + return util.Unit{} +} + +// An empty dictionary contains no keys. +ghost +opaque +requires IsEmpty(d) +ensures !(k in domain(d)) +decreases +pure func NotInEmpty(d dict[int]int, k int) util.Unit { + return util.Unit{} +} + +// There exists a key in a non-empty dictionary. +ghost +opaque +requires !IsEmpty(d) +ensures exists k int :: {k in domain(d)} k in domain(d) +decreases +pure func NotEmptyKeyExists(d dict[int]int, k int) util.Unit { + return util.Unit{} +} + +// If a key is in d, d is not empty. +ghost +opaque +requires k in domain(d) +ensures !IsEmpty(d) +decreases +pure func KeyInDomainDictNotEmpty(d dict[int]int, k int) util.Unit { + return util.Unit{} +} + +// Inserting a new key increases the cardinality of the dictionary by 1. +// Updating the value of a key does not change the cardinality. +ghost +opaque +ensures k in domain(d) ==> len(d[k = v]) == len(d) +ensures !(k in domain(d)) ==> len(d[k = v]) == len(d) + 1 +decreases +pure func InsertUpdateLen(d dict[int]int, k, v int) util.Unit { + return util.Unit{} +} + +// If a value is in the range of a dictionary, there exists a corresponding key. +ghost +opaque +requires v in range(d) +ensures exists k int :: {k in domain(d)} k in domain(d) && d[k] == v +decreases +pure func ValueHasKey(d dict[int]int, v int) util.Unit { + return util.Unit{} +} + +// If a value is in the domain of a dictionary, the corresponding value is in its range. +ghost +opaque +requires k in domain(d) +ensures d[k] in range(d) +decreases +pure func KeyMapsToRange(d dict[int]int, k int) util.Unit { + return util.Unit{} +} + +// Returns a dictionary with the values at k1 and k2 swapped. +ghost +requires k1 in domain(d) && k2 in domain(d) +ensures domain(result) == domain(d) +ensures result[k1] == d[k2] && result[k2] == d[k1] +ensures forall k int :: {result[k]} (k in domain(d) && k != k1 && k != k2) ==> + result[k] == d[k] +decreases +pure func Swap(d dict[int]int, k1, k2 int) (result dict[int]int) { + return d[k1 = d[k2]][k2 = d[k1]] +} + +// Returns the set of keys from the given dictionary that map to the specified value. +ghost +opaque +ensures forall k int :: {k in result} (k in domain(d) && d[k] == v) == (k in result) +decreases len(d) +pure func Keys(d dict[int]int, v int) (result set[int]) { + return IsEmpty(d) ? sets_opaque.Empty() : + (let x := sets_opaque.Choose(domain(d)) in + (let subKeys := Keys(Remove(d, x), v) in + (d[x] == v ? sets_opaque.Add(subKeys, x) : subKeys))) + +} + +// Returns the number of occurences of the value in the dictionary. +ghost +decreases +pure func Occurrences(d dict[int]int, v int) int { + return len(Keys(d, v)) +} + +// Remove preserves the injectivity of a dictionary. +ghost +opaque +requires IsInjective(d) +ensures IsInjective(Remove(d, k)) +decreases +pure func RemovePreservesInjectivity(d dict[int]int, k int) util.Unit { + return let _ := reveal IsInjective(d) in + let _ := reveal IsInjective(Remove(d, k)) in + util.Unit{} +} + +// After removing a key, the corresponding value occurs one less time. +ghost +opaque +requires k in domain(d) +ensures Occurrences(Remove(d, k), d[k]) == Occurrences(d, d[k]) - 1 +decreases +pure func RemoveOccurrences(d dict[int]int, k int) util.Unit { + return let ks1 := reveal Keys(d, d[k]) in + let ks2 := reveal Keys(Remove(d, k), d[k]) in + util.Asserting(ks2 == sets_opaque.Remove(ks1, k)) +} + +// Adding a new key-value pair increases the occurrence of the value by one. +ghost +opaque +requires !(k in domain(d)) +ensures Occurrences(d[k = v], v) == Occurrences(d, v) + 1 +decreases +pure func AddOccurrences(d dict[int]int, k, v int) util.Unit { + return let ks1 := reveal Keys(d, v) in + let ks2 := reveal Keys(d[k = v], v) in + util.Asserting(ks2 == sets_opaque.Add(ks1, k)) +} + +// Updating a key to a new value results in an additional occurrences for the +// new value, and one less occurrence for the old value. +ghost +opaque +requires k in domain(d) +requires v != d[k] +ensures Occurrences(d[k = v], v) == Occurrences(d, v) + 1 +ensures Occurrences(d[k = v], d[k]) == Occurrences(d, d[k]) - 1 +decreases +pure func UpdateOccurrences(d dict[int]int, k, v int) util.Unit { + return let ks1v := reveal Keys(d, v) in + let ks2v := reveal Keys(d[k = v], v) in + let _ := util.Asserting(ks2v == sets_opaque.Add(ks1v, k)) in + let ks1dk := reveal Keys(d, d[k]) in + let ks2dk := reveal Keys(d[k = v], d[k]) in + util.Asserting(ks2dk == sets_opaque.Remove(ks1dk, k)) +} + +// v can occur at most once as a value in injective dictionaries. +ghost +opaque +requires IsInjective(d) +ensures Occurrences(d, v) <= 1 +decreases len(d) +pure func InjectiveOccurrences(d dict[int]int, v int) util.Unit { + return Occurrences(d, v) <= 1 ? util.Unit{} : + let x1 := sets_opaque.Choose(Keys(d, v)) in + let x2 := sets_opaque.Choose(sets_opaque.Remove(Keys(d, v), x1)) in + let _ := reveal IsInjective(d) in + util.Unit{} +} diff --git a/evaluation/experiments/standard_library/lemma_not_opaque/lemma_not_opaque-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv b/evaluation/experiments/standard_library/lemma_not_opaque/lemma_not_opaque-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv new file mode 100644 index 0000000..58d50ad --- /dev/null +++ b/evaluation/experiments/standard_library/lemma_not_opaque/lemma_not_opaque-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv @@ -0,0 +1,31 @@ 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Does not require e to be in xs. +ghost +ensures !(e in xs) ==> result == xs +ensures (e in xs) ==> (len(result) == len(xs) - 1) +ensures !(e in xs) ==> (len(result) == len(xs)) +decreases +pure func Remove(xs set[int], e int) (result set[int]) { + return xs setminus SingletonSet(e) +} + +// If xs is a subset of ys and both have the same cardinality, they are equal. +ghost +requires xs subset ys +requires len(xs) == len(ys) +ensures xs == ys +decreases +pure func SubsetEquality(xs, ys set[int]) util.Unit { + return util.Asserting(len(ys setminus xs) == len(ys) - len(xs)) +} + +// If xs is a subset of ys, then the cardinality of xs is less than or equal to the cardinality of ys. +// If xs is a strict subset of ys, then the cardinality of xs is less than the cardinality of ys. +ghost +decreases xs, ys +ensures xs subset ys ==> len(xs) <= len(ys) +ensures IsProperSubset(xs, ys) ==> len(xs) < len(ys) +pure func SubsetLen(xs, ys set[int]) util.Unit { + return (!(xs subset ys) || len(xs) == 0) ? util.Unit{} : + len(xs) == len(ys) ? + let _ := SubsetEquality(xs, ys) in + (let e := choose(xs) in + (SubsetLen(Remove(xs, e), Remove(ys, e)))) : + + let e:= choose(xs) in + (SubsetLen(Remove(xs, e), Remove(ys, e))) +} diff --git a/evaluation/experiments/standard_library/lemma_opaque/lemma_opaque-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv b/evaluation/experiments/standard_library/lemma_opaque/lemma_opaque-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv new file mode 100644 index 0000000..857658c --- /dev/null +++ b/evaluation/experiments/standard_library/lemma_opaque/lemma_opaque-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv @@ -0,0 +1,31 @@ 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Lemmas are turned opaque. +package lemma_opaque + +// ##(-I ./..) + +import "util" + +// A set is empty if it has cardinality 0. +ghost +decreases +pure func IsEmpty(xs set[int]) bool { + return len(xs) == 0 +} + +// A set is a singleton if it has cardinality 1. +ghost +decreases +pure func IsSingleton(xs set[int]) bool { + return len(xs) == 1 +} + +// Returns a singleton containing x. +ghost +ensures IsSingleton(result) +ensures e in result +decreases +pure func SingletonSet(e int) (result set[int]) { + return set[int]{e} +} + +// Returns whether xs is a proper subset of ys. +ghost +decreases +pure func IsProperSubset(xs, ys set[int]) bool { + return xs subset ys && xs != ys +} + +// Returns an element from a non-empty set. +ghost +requires !IsEmpty(xs) +ensures e in xs +ensures IsSingleton(xs) ==> xs == SingletonSet(e) +decreases +pure func choose(xs set[int]) (e int) + +// Remove e from xs. Does not require e to be in xs. +ghost +ensures !(e in xs) ==> result == xs +ensures (e in xs) ==> (len(result) == len(xs) - 1) +ensures !(e in xs) ==> (len(result) == len(xs)) +decreases +pure func Remove(xs set[int], e int) (result set[int]) { + return xs setminus SingletonSet(e) +} + +// If xs is a subset of ys and both have the same cardinality, they are equal. +ghost +opaque +requires xs subset ys +requires len(xs) == len(ys) +ensures xs == ys +decreases +pure func SubsetEquality(xs, ys set[int]) util.Unit { + return util.Asserting(len(ys setminus xs) == len(ys) - len(xs)) +} + +// If xs is a subset of ys, then the cardinality of xs is less than or equal to the cardinality of ys. +// If xs is a strict subset of ys, then the cardinality of xs is less than the cardinality of ys. +ghost +opaque +decreases xs, ys +ensures xs subset ys ==> len(xs) <= len(ys) +ensures IsProperSubset(xs, ys) ==> len(xs) < len(ys) +pure func SubsetLen(xs, ys set[int]) util.Unit { + return (!(xs subset ys) || len(xs) == 0) ? util.Unit{} : + len(xs) == len(ys) ? + let _ := SubsetEquality(xs, ys) in + (let e := choose(xs) in + (SubsetLen(Remove(xs, e), Remove(ys, e)))) : + + let e:= choose(xs) in + (SubsetLen(Remove(xs, e), Remove(ys, e))) +} diff --git a/evaluation/experiments/standard_library/sets_not_opaque/sets_not_opaque-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv b/evaluation/experiments/standard_library/sets_not_opaque/sets_not_opaque-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv new file mode 100644 index 0000000..4f812f5 --- /dev/null +++ b/evaluation/experiments/standard_library/sets_not_opaque/sets_not_opaque-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv @@ -0,0 +1,31 @@ +qi-k!881,qi-$Set[Int]_prog.in_singleton_set,qi-quant-u-0,qi-quant-u-110,qi-quant-u-1,qi-$Set[Int]_prog.singleton_set_cardinality,qi-$Set[Int]_prog.card_non_negative,qi-$Set[Int]_prog.empty_set_cardinality,qi-$Set[Int]_prog.in_singleton_set_equality,qi-$Set[Int]_prog.equality_definition,qi-$Set[Int]_prog.native_equality,qi-quant-u-2,qi-quant-u-115,qi-quant-u-113,qi-quant-u-3,qi-quant-u-112,qi-$Set[Int]_prog.in_right_in_union,qi-$Set[Int]_prog.in_left_in_union,qi-$Set[Int]_prog.in_union_in_one,qi-$Set[Int]_prog.cardinality_sums,qi-$Set[Int]_prog.in_intersection_in_both,qi-quant-u-4,qi-quant-u-117,qi-quant-u-5,qi-$Set[Int]_prog.not_in_difference,qi-$Set[Int]_prog.in_difference,qi-$Set[Int]_prog.cardinality_difference,qi-$Set[Int]_prog.in_empty_set,qi-$Set[Int]_prog.subset_definition,qi-k!643,qi-quant-u-6,qi-quant-u-119,qi-quant-u-7,qi-quant-u-127,qi-quant-u-8,qi-quant-u-126,qi-quant-u-20,qi-quant-u-9,qi-quant-u-121,qi-quant-u-21,qi-quant-u-147,qi-k!1885,qi-quant-u-10,qi-quant-u-130,qi-quant-u-128,qi-quant-u-129,qi-prog./home/daniel/practical-work/gobra-libs-eval/report/code/standard_library/sets_not_opaque/sets_not_opaque.gobra.vpr@428@12@430@56,qi-quant-u-137,qi-quant-u-12,qi-quant-u-136,qi-quant-u-13,qi-quant-u-132,qi-quant-u-18,qi-quant-u-145,qi-quant-u-19,qi-quant-u-144,qi-quant-u-16,qi-quant-u-143,qi-quant-u-17,qi-quant-u-141,qi-k!653,qi-quant-u-14,qi-quant-u-140,qi-quant-u-15,qi-quant-u-138,qi-quant-u-26,qi-quant-u-160,qi-quant-u-27,qi-quant-u-158,qi-quant-u-30,qi-quant-u-31,qi-quant-u-167,qi-quant-u-151,qi-quant-u-150,qi-quant-u-153,qi-quant-u-22,qi-quant-u-152,qi-quant-u-23,qi-$Set[Int]_prog.union_left_idempotency,qi-$Multiset[Int]_prog.count_card,qi-$Multiset[Int]_prog.card_non_negative,qi-$Multiset[Int]_prog.card_empty,qi-quant-u-72,qi-$Multiset[Int]_prog.singleton_unionone,qi-$Multiset[Int]_prog.card_union,qi-$Multiset[Int]_prog.count_union,qi-quant-u-73,qi-quant-u-251,qi-$Multiset[Int]_prog.card_unionone,qi-$Multiset[Int]_prog.count_empty,qi-$Multiset[Int]_prog.count_singleton,qi-$Multiset[Int]_prog.count_unionone,qi-k!4524,qi-k!4530,qi-prog./home/daniel/practical-work/gobra-libs-eval/report/code/standard_library/sets_not_opaque/sets_not_opaque.gobra.vpr@602@12@604@47,qi-$Set[Int]_prog.union_right_idempotency,qi-quant-u-24,qi-quant-u-156,qi-quant-u-155,qi-quant-u-25,qi-quant-u-154,qi-quant-u-88,qi-quant-u-89,qi-quant-u-284,qi-prog./home/daniel/practical-work/gobra-libs-eval/report/code/standard_library/sets_not_opaque/sets_not_opaque.gobra.vpr@486@6@489@41,qi-$Set[Int]_prog.intersection_right_idempotency,qi-$Set[Int]_prog.intersection_left_idempotency,qi-quant-u-162,qi-quant-u-161,qi-prog./home/daniel/practical-work/gobra-libs-eval/report/code/standard_library/sets_not_opaque/sets_not_opaque.gobra.vpr@219@13@221@54,qi-prog.getter_over_tuple2,qi-quant-u-44,qi-quant-u-45,qi-prog.set_ax_dec,qi-prog.set_ax_bound,qi-prog.integer_ax_dec,qi-prog.integer_ax_bound,execution_time 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set[int]) { + return Range(0, n) +} + +// Converts a set into a multiset where each element from the set has +// multiplicity 1 and any other element has multiplicity 0. +ghost +ensures forall i int :: {i # result} (i in s) ==> ((i # result) == 1) +ensures forall i int :: {i # result} (!(i in s)) ==> ((i # result) == 0) +decreases s +pure func ToMultiset(s set[int]) (result mset[int]) { + return IsEmpty(s) ? mset[int] {} : + let x := Choose(s) in + ((mset[int] {}) union (mset[int] {x})) union ToMultiset(Remove(s, x)) +} + +// Returns an element from a non-empty set. +ghost +requires !IsEmpty(xs) +ensures e in xs +ensures IsSingleton(xs) ==> xs == SingletonSet(e) +decreases +pure func Choose(xs set[int]) (e int) + +// Returns whether xs and ys are disjoint sets. +ghost +decreases +pure func AreDisjoint(xs, ys set[int]) bool { + return IsEmpty(xs intersection ys) +} + +// Definition of set equality. +ghost +ensures (xs == ys) == (forall e int :: {e in xs} {e in ys} ((e in xs) == (e in ys))) +decreases +pure func SetEquality(xs, ys set[int]) util.Unit { + return util.Unit{} +} + +// Definition of subset without quantifiers. +ghost +requires e in xs +requires xs subset ys +ensures e in ys +decreases +pure func InSubset(xs, ys set[int], e int) util.Unit { + return util.Unit{} +} + +// Subset relation is reflexive. +ghost +ensures xs subset xs +decreases +pure func SubsetIsReflexive(xs set[int]) util.Unit { + return util.Unit{} +} + +// Subset relation is transitive. +ghost +requires xs subset ys +requires ys subset zs +ensures xs subset zs +decreases +pure func SubsetIsTransitive(xs, ys, zs set[int]) util.Unit { + return util.Unit{} +} + +// If xs is a subset of ys and both have the same cardinality, they are equal. +ghost +requires xs subset ys +requires len(xs) == len(ys) +ensures xs == ys +decreases +pure func SubsetEquality(xs, ys set[int]) util.Unit { + return util.Asserting(len(ys setminus xs) == len(ys) - len(xs)) +} + +// Returns whether xs is a proper subset of ys. +ghost +decreases +pure func IsProperSubset(xs, ys set[int]) bool { + return xs subset ys && xs != ys +} + +// If e is in the union of xs and ys, then it must be in xs or ys. +ghost +ensures (e in (xs union ys)) == ((e in xs) || (e in ys)) +decreases +pure func InUnionInOne(xs, ys set[int], e int) util.Unit { + return util.Unit{} +} + +// Union is commutative. +ghost +ensures (xs union ys) == (ys union xs) +decreases +pure func UnionIsCommutative(xs, ys set[int]) util.Unit { + return util.Unit{} +} + +// Union is idempotent. +ghost +ensures (xs union ys) union ys == xs union ys +ensures xs union (xs union ys) == xs union ys +decreases +pure func UnionIsIdempotent(xs, ys set[int]) util.Unit { + return util.Unit{} +} + +// Add x to xs. +ghost +// Need this post-condition first to ensure the properties about the length. +ensures (e in xs) ==> result == xs +ensures (e in xs) ==> (len(result) == len(xs)) +ensures !(e in xs) ==> (len(result) == len(xs) + 1) +ensures e in result +decreases +pure func Add(xs set[int], e int) (result set[int]) { + return xs union SingletonSet(e) +} + +// If a is in xs union {b}, then a is equal to b, or a was already in xs. +ghost +ensures (a in Add(xs, b)) == ((a == b) || a in xs) +decreases +pure func InAdd(xs set[int], a, b int) util.Unit { + return util.Unit{} +} + +// If a is in xs, then a will remain in xs no matter what we add to it. +ghost +requires a in xs +ensures a in Add(xs, b) +decreases +pure func InvarianceInAdd(xs set[int], a, b int) util.Unit { + return util.Unit{} +} + +// Remove e from xs. Does not require e to be in xs. +ghost +ensures !(e in xs) ==> result == xs +ensures (e in xs) ==> (len(result) == len(xs) - 1) +ensures !(e in xs) ==> (len(result) == len(xs)) +decreases +pure func Remove(xs set[int], e int) (result set[int]) { + return xs setminus SingletonSet(e) +} + +// Intersection is commutative. +ghost +ensures (xs intersection ys) == (ys intersection xs) +decreases +pure func IntersectionIsCommutative(xs, ys set[int]) util.Unit { + return util.Unit{} +} + +// Intersection is idempotent. +ghost +ensures (xs intersection ys) intersection ys == (xs intersection ys) +ensures xs intersection (xs intersection ys) == (xs intersection ys) +decreases +pure func IntersectionIsIdempotent(xs, ys set[int]) util.Unit { + return util.Unit{} +} + +// If e is in the difference xs - ys, then e must be in xs but not in ys. +ghost +ensures (e in (xs setminus ys)) == ((e in xs) && !(e in ys)) +decreases +pure func InDifference(xs, ys set[int], e int) util.Unit { + return util.Unit{} +} + +// If ys contains e, then the difference xs - ys does not contain e. +ghost +requires e in ys +ensures !(e in (xs setminus ys)) +decreases +pure func NotInDifference(xs, ys set[int], e int) util.Unit { + return util.Unit{} +} + +// If e is in the intersection of xs and ys, then e must be both in xs and ys. +ghost +ensures e in (xs intersection ys) == ((e in xs) && (e in ys)) +decreases +pure func InIntersectionInBoth(xs, ys set[int], e int) util.Unit { + return util.Unit{} +} + +// If xs and ys are disjoint, adding and then removing one from the other +// yields the original set. +ghost +requires AreDisjoint(xs, ys) +ensures (xs union ys) setminus xs == ys +ensures (xs union ys) setminus ys == xs +decreases +pure func DisjointUnionDifference(xs, ys set[int]) util.Unit { + return util.Unit{} +} + +// If e is in xs, removing and adding it back yields the original set. +ghost +requires e in xs +ensures Add(Remove(xs, e), e) == xs +decreases +pure func AddRemove(xs set[int], e int) util.Unit { + return util.Unit{} +} + +// If we remove e from the set xs, it doesn't matter whether we have added e +// to it before. +ghost +ensures Remove(Add(xs, e), e) == Remove(xs, e) +decreases +pure func RemoveAdd(xs set[int], e int) util.Unit { + return util.Unit{} +} + +// xs - {e} is a subset of xs. +ghost +ensures Remove(xs, e) subset xs +decreases +pure func SubsetRemove(xs set[int], e int) util.Unit { + return util.Unit{} +} + +// xs and ys are subsets of the union of xs and ys. +ghost +ensures xs subset (xs union ys) +ensures ys subset (xs union ys) +decreases +pure func SubsetUnion(xs, ys set[int]) util.Unit { + return util.Unit{} +} + +// The intersection of xs and ys are subsets of xs, and ys. +ghost +ensures (xs intersection ys) subset xs +ensures (xs intersection ys) subset ys +decreases +pure func SubsetIntersection(xs, ys set[int]) util.Unit { + return util.Unit{} +} + +// The difference xs - ys is a subset of xs. +ghost +ensures (xs setminus ys) subset xs +decreases +pure func SubsetDifference(xs, ys set[int]) util.Unit { + return util.Unit{} +} + +// The cardinality of a set is non-negative. +ghost +ensures len(xs) >= 0 +decreases +pure func NonNegativeLen(xs set[int]) util.Unit { + return util.Unit{} +} + +// If xs is a subset of ys, then the cardinality of xs is less than or equal to the cardinality of ys. +// If xs is a strict subset of ys, then the cardinality of xs is less than the cardinality of ys. +ghost +decreases xs, ys +ensures xs subset ys ==> len(xs) <= len(ys) +ensures IsProperSubset(xs, ys) ==> len(xs) < len(ys) +pure func SubsetLen(xs, ys set[int]) util.Unit { + return (!(xs subset ys) || len(xs) == 0) ? util.Unit{} : + len(xs) == len(ys) ? + let _ := SubsetEquality(xs, ys) in + (let e := Choose(xs) in + (SubsetLen(Remove(xs, e), Remove(ys, e)))) : + + let e:= Choose(xs) in + (SubsetLen(Remove(xs, e), Remove(ys, e))) +} + +// The cardinality of a union of two sets is greater than or equal to the cardinality of +// either individual set. +ghost +ensures len(xs union ys) >= len(xs) +ensures len(xs union ys) >= len(ys) +decreases ys +pure func UnionLenLower(xs, ys set[int]) util.Unit { + return IsEmpty(ys) ? util.Unit{} : + let y := Choose(ys) in + (let yr := Remove(ys, y) in + (y in xs ? + (let xr := Remove(xs, y) in + (let _ := util.Asserting(xr union yr == Remove(xs union ys, y)) in UnionLenLower(xr, yr))) : + (let _ := util.Asserting(xs union yr == Remove(xs union ys, y)) in UnionLenLower(xs, yr)))) +} + +// The cardinality of a union of two sets is less than or equal to the cardinality of +// both individual sets combined. +ghost +ensures len(xs union ys) <= len(xs) + len(ys) +decreases +pure func UnionLenUpper(xs, ys set[int]) util.Unit { + return util.Unit{} +} + +// The cardinality of the intersection of xs and ys is less than or equal to the +// cardinality of xs. +ghost +ensures len(xs intersection ys) <= len(xs) +decreases xs +pure func IntersectLenUpper(xs, ys set[int]) util.Unit { + return IsEmpty(xs) ? util.Unit{} : + let x := Choose(xs) in + (let _ := util.Asserting((Remove(xs, x)) intersection ys == Remove((xs intersection ys), x)) in + (IntersectLenUpper(Remove(xs, x), ys))) +} + +// The cardinality of the difference xs - ys is less than or equal to the cardinality of xs. +ghost +ensures len(xs setminus ys) <= len(xs) +decreases +pure func DifferenceLenUpper(xs, ys set[int]) util.Unit { + return util.Unit{} +} + +ghost +ensures len(xs union ys) == len(xs) + len(ys) - len(xs intersection ys) +decreases +pure func UnionLenEq(xs, ys set[int]) util.Unit { + return util.Unit{} +} + +ghost +ensures len(xs setminus ys) == len(xs) - len(xs intersection ys) +ensures len(xs setminus ys) + len(ys setminus xs) + len(xs intersection ys) == len(xs union ys) +decreases +pure func DifferenceLenEq(xs, ys set[int]) util.Unit { + return util.Unit{} +} + +// If e is in xs, adding it to xs doesn't change the cardinality. +// If e is not in xs, adding it to xs increases the cardinality by 1. +ghost +ensures (e in xs) ==> (len(Add(xs, e)) == len(xs)) +ensures !(e in xs) ==> (len(Add(xs, e)) == len(xs) + 1) +decreases +pure func AddLen(xs set[int], e int) util.Unit { + return util.Unit{} +} + +// If e is in xs, removing it from xs reduces the cardinality by 1. +// If e is not in xs, removing it from xs doesn't change the cardinality. +ghost +ensures (e in xs) ==> (len(Remove(xs, e)) == len(xs) - 1) +ensures !(e in xs) ==> (len(Remove(xs, e)) == len(xs)) +decreases +pure func RemoveLen(xs set[int], e int) util.Unit { + return util.Unit{} +} + +// Remove is right distributive over union. +ghost +ensures Remove(xs union ys, e) == Remove(xs, e) union Remove(ys, e) +decreases +pure func RemoveUnion(xs, ys set[int], e int) util.Unit { + return util.Unit{} +} + +// If e is in (xs union ys), removing it from both sets reduces the cardinality by 1. +ghost +requires e in (xs union ys) +ensures len(Remove(xs, e) union Remove(ys, e)) == len(xs union ys) - 1 +decreases +pure func RemoveUnionLen(xs, ys set[int], e int) util.Unit { + return RemoveUnion(xs, ys, e) +} + +// If xs and ys are disjoint, the cardinality of their union is equal to the +// sum of the cardinality of xs, and the cardinality of ys. +ghost +requires AreDisjoint(xs, ys) +ensures len(xs union ys) == len(xs) + len(ys) +decreases +pure func DisjointUnionLen(xs, ys set[int]) util.Unit { + return util.Unit{} +} + +// If xs solely contains integers in the range [a, b), then its size is +// bounded by b - a. +ghost +requires forall i int :: { i in xs } i in xs ==> (a <= i && i < b) +requires a <= b +ensures len(xs) <= b - a +decreases +pure func BoundedSetLen(xs set[int], a, b int) util.Unit { + return SubsetLen(xs, Range(a, b)) +} diff --git a/evaluation/experiments/standard_library/sets_opaque/sets_opaque-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv b/evaluation/experiments/standard_library/sets_opaque/sets_opaque-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv new file mode 100644 index 0000000..7c9ffd9 --- /dev/null +++ b/evaluation/experiments/standard_library/sets_opaque/sets_opaque-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv @@ -0,0 +1,31 @@ +qi-k!881,qi-$Set[Int]_prog.in_singleton_set,qi-quant-u-0,qi-quant-u-110,qi-quant-u-1,qi-$Set[Int]_prog.singleton_set_cardinality,qi-$Set[Int]_prog.card_non_negative,qi-$Set[Int]_prog.empty_set_cardinality,qi-$Set[Int]_prog.in_singleton_set_equality,qi-$Set[Int]_prog.equality_definition,qi-$Set[Int]_prog.native_equality,qi-quant-u-2,qi-quant-u-115,qi-quant-u-113,qi-quant-u-3,qi-quant-u-112,qi-$Set[Int]_prog.not_in_difference,qi-$Set[Int]_prog.in_difference,qi-$Set[Int]_prog.cardinality_difference,qi-$Set[Int]_prog.cardinality_sums,qi-$Set[Int]_prog.in_intersection_in_both,qi-$Set[Int]_prog.in_left_in_union,qi-$Set[Int]_prog.in_right_in_union,qi-$Set[Int]_prog.in_union_in_one,qi-$Set[Int]_prog.in_empty_set,qi-quant-u-4,qi-quant-u-117,qi-quant-u-5,qi-$Set[Int]_prog.subset_definition,qi-k!643,qi-quant-u-6,qi-quant-u-119,qi-quant-u-7,qi-quant-u-126,qi-quant-u-8,qi-quant-u-125,qi-quant-u-9,qi-quant-u-121,qi-quant-u-133,qi-quant-u-10,qi-quant-u-132,qi-quant-u-24,qi-quant-u-11,qi-quant-u-127,qi-quant-u-25,qi-quant-u-153,qi-k!2008,qi-quant-u-12,qi-quant-u-136,qi-quant-u-134,qi-quant-u-135,qi-prog./home/daniel/practical-work/gobra-libs-eval/report/code/standard_library/sets_opaque/sets_opaque.gobra.vpr@448@12@450@56,qi-quant-u-18,qi-quant-u-145,qi-quant-u-19,qi-quant-u-17,qi-quant-u-141,qi-quant-u-14,qi-quant-u-140,qi-quant-u-15,qi-quant-u-138,qi-quant-u-160,qi-quant-u-27,qi-quant-u-158,qi-quant-u-148,qi-quant-u-20,qi-quant-u-147,qi-quant-u-21,qi-$Set[Int]_prog.union_left_idempotency,qi-quant-u-150,qi-quant-u-23,qi-quant-u-149,qi-$Set[Int]_prog.intersection_right_idempotency,qi-$Set[Int]_prog.intersection_left_idempotency,qi-quant-u-157,qi-quant-u-156,qi-prog./home/daniel/practical-work/gobra-libs-eval/report/code/standard_library/sets_opaque/sets_opaque.gobra.vpr@222@13@224@54,qi-k!653,qi-quant-u-69,qi-quant-u-241,qi-quant-u-79,qi-quant-u-262,qi-$Multiset[Int]_prog.count_card,qi-$Multiset[Int]_prog.card_non_negative,qi-$Multiset[Int]_prog.card_empty,qi-quant-u-92,qi-$Multiset[Int]_prog.singleton_unionone,qi-$Multiset[Int]_prog.card_union,qi-$Multiset[Int]_prog.count_union,qi-quant-u-93,qi-quant-u-293,qi-$Multiset[Int]_prog.card_unionone,qi-$Multiset[Int]_prog.count_empty,qi-$Multiset[Int]_prog.count_singleton,qi-$Multiset[Int]_prog.count_unionone,qi-k!5521,qi-k!5527,qi-prog./home/daniel/practical-work/gobra-libs-eval/report/code/standard_library/sets_opaque/sets_opaque.gobra.vpr@637@12@639@47,qi-$Set[Int]_prog.union_right_idempotency,qi-prog./home/daniel/practical-work/gobra-libs-eval/report/code/standard_library/sets_opaque/sets_opaque.gobra.vpr@511@6@514@41,qi-prog.getter_over_tuple2,qi-quant-u-40,qi-quant-u-41,qi-prog.set_ax_dec,qi-prog.set_ax_bound,qi-prog.integer_ax_dec,qi-prog.integer_ax_bound,execution_time 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element from the set has +// multiplicity 1 and any other element has multiplicity 0. +ghost +ensures forall i int :: {i # result} (i in s) ==> ((i # result) == 1) +ensures forall i int :: {i # result} (!(i in s)) ==> ((i # result) == 0) +decreases s +pure func ToMultiset(s set[int]) (result mset[int]) { + return IsEmpty(s) ? mset[int] {} : + let x := Choose(s) in + ((mset[int] {}) union (mset[int] {x})) union ToMultiset(Remove(s, x)) +} + +// Returns an element from a non-empty set. +ghost +requires !IsEmpty(xs) +ensures e in xs +ensures IsSingleton(xs) ==> xs == SingletonSet(e) +decreases +pure func Choose(xs set[int]) (e int) + +// Returns whether xs and ys are disjoint sets. +ghost +decreases +pure func AreDisjoint(xs, ys set[int]) bool { + return IsEmpty(xs intersection ys) +} + +// Definition of set equality. +ghost +opaque +ensures (xs == ys) == (forall e int :: {e in xs} {e in ys} ((e in xs) == (e in ys))) +decreases +pure func SetEquality(xs, ys set[int]) util.Unit { + return util.Unit{} +} + +// Definition of subset without quantifiers. +ghost +opaque +requires e in xs +requires xs subset ys +ensures e in ys +decreases +pure func InSubset(xs, ys set[int], e int) util.Unit { + return util.Unit{} +} + +// Subset relation is reflexive. +ghost +opaque +ensures xs subset xs +decreases +pure func SubsetIsReflexive(xs set[int]) util.Unit { + return util.Unit{} +} + +// Subset relation is transitive. +ghost +opaque +requires xs subset ys +requires ys subset zs +ensures xs subset zs +decreases +pure func SubsetIsTransitive(xs, ys, zs set[int]) util.Unit { + return util.Unit{} +} + +// If xs is a subset of ys and both have the same cardinality, they are equal. +ghost +opaque +requires xs subset ys +requires len(xs) == len(ys) +ensures xs == ys +decreases +pure func SubsetEquality(xs, ys set[int]) util.Unit { + return util.Asserting(len(ys setminus xs) == len(ys) - len(xs)) +} + +// Returns whether xs is a proper subset of ys. +ghost +decreases +pure func IsProperSubset(xs, ys set[int]) bool { + return xs subset ys && xs != ys +} + +// If e is in the union of xs and ys, then it must be in xs or ys. +ghost +opaque +ensures (e in (xs union ys)) == ((e in xs) || (e in ys)) +decreases +pure func InUnionInOne(xs, ys set[int], e int) util.Unit { + return util.Unit{} +} + +// Union is commutative. +ghost +opaque +ensures (xs union ys) == (ys union xs) +decreases +pure func UnionIsCommutative(xs, ys set[int]) util.Unit { + return util.Unit{} +} + +// Union is idempotent. +ghost +opaque +ensures (xs union ys) union ys == xs union ys +ensures xs union (xs union ys) == xs union ys +decreases +pure func UnionIsIdempotent(xs, ys set[int]) util.Unit { + return util.Unit{} +} + +// Add x to xs. +ghost +// Need this post-condition first to ensure the properties about the length. +ensures (e in xs) ==> result == xs +ensures (e in xs) ==> (len(result) == len(xs)) +ensures !(e in xs) ==> (len(result) == len(xs) + 1) +ensures e in result +decreases +pure func Add(xs set[int], e int) (result set[int]) { + return xs union SingletonSet(e) +} + +// If a is in xs union {b}, then a is equal to b, or a was already in xs. +ghost +opaque +ensures (a in Add(xs, b)) == ((a == b) || a in xs) +decreases +pure func InAdd(xs set[int], a, b int) util.Unit { + return util.Unit{} +} + +// If a is in xs, then a will remain in xs no matter what we add to it. +ghost +opaque +requires a in xs +ensures a in Add(xs, b) +decreases +pure func InvarianceInAdd(xs set[int], a, b int) util.Unit { + return util.Unit{} +} + +// Remove e from xs. Does not require e to be in xs. +ghost +ensures !(e in xs) ==> result == xs +ensures (e in xs) ==> (len(result) == len(xs) - 1) +ensures !(e in xs) ==> (len(result) == len(xs)) +decreases +pure func Remove(xs set[int], e int) (result set[int]) { + return xs setminus SingletonSet(e) +} + +// Intersection is commutative. +ghost +opaque +ensures (xs intersection ys) == (ys intersection xs) +decreases +pure func IntersectionIsCommutative(xs, ys set[int]) util.Unit { + return util.Unit{} +} + +// Intersection is idempotent. +ghost +opaque +ensures (xs intersection ys) intersection ys == (xs intersection ys) +ensures xs intersection (xs intersection ys) == (xs intersection ys) +decreases +pure func IntersectionIsIdempotent(xs, ys set[int]) util.Unit { + return util.Unit{} +} + +// If e is in the difference xs - ys, then e must be in xs but not in ys. +ghost +opaque +ensures (e in (xs setminus ys)) == ((e in xs) && !(e in ys)) +decreases +pure func InDifference(xs, ys set[int], e int) util.Unit { + return util.Unit{} +} + +// If ys contains e, then the difference xs - ys does not contain e. +ghost +opaque +requires e in ys +ensures !(e in (xs setminus ys)) +decreases +pure func NotInDifference(xs, ys set[int], e int) util.Unit { + return util.Unit{} +} + +// If e is in the intersection of xs and ys, then e must be both in xs and ys. +ghost +opaque +ensures e in (xs intersection ys) == ((e in xs) && (e in ys)) +decreases +pure func InIntersectionInBoth(xs, ys set[int], e int) util.Unit { + return util.Unit{} +} + +// If xs and ys are disjoint, adding and then removing one from the other +// yields the original set. +ghost +opaque +requires AreDisjoint(xs, ys) +ensures (xs union ys) setminus xs == ys +ensures (xs union ys) setminus ys == xs +decreases +pure func DisjointUnionDifference(xs, ys set[int]) util.Unit { + return util.Unit{} +} + +// If e is in xs, removing and adding it back yields the original set. +ghost +opaque +requires e in xs +ensures Add(Remove(xs, e), e) == xs +decreases +pure func AddRemove(xs set[int], e int) util.Unit { + return util.Unit{} +} + +// If we remove e from the set xs, it doesn't matter whether we have added e +// to it before. +ghost +opaque +ensures Remove(Add(xs, e), e) == Remove(xs, e) +decreases +pure func RemoveAdd(xs set[int], e int) util.Unit { + return util.Unit{} +} + +// xs - {e} is a subset of xs. +ghost +opaque +ensures Remove(xs, e) subset xs +decreases +pure func SubsetRemove(xs set[int], e int) util.Unit { + return util.Unit{} +} + +// xs and ys are subsets of the union of xs and ys. +ghost +opaque +ensures xs subset (xs union ys) +ensures ys subset (xs union ys) +decreases +pure func SubsetUnion(xs, ys set[int]) util.Unit { + return util.Unit{} +} + +// The intersection of xs and ys are subsets of xs, and ys. +ghost +opaque +ensures (xs intersection ys) subset xs +ensures (xs intersection ys) subset ys +decreases +pure func SubsetIntersection(xs, ys set[int]) util.Unit { + return util.Unit{} +} + +// The difference xs - ys is a subset of xs. +ghost +opaque +ensures (xs setminus ys) subset xs +decreases +pure func SubsetDifference(xs, ys set[int]) util.Unit { + return util.Unit{} +} + +// The cardinality of a set is non-negative. +ghost +opaque +ensures len(xs) >= 0 +decreases +pure func NonNegativeLen(xs set[int]) util.Unit { + return util.Unit{} +} + +// If xs is a subset of ys, then the cardinality of xs is less than or equal to the cardinality of ys. +// If xs is a strict subset of ys, then the cardinality of xs is less than the cardinality of ys. +ghost +opaque +decreases xs, ys +ensures xs subset ys ==> len(xs) <= len(ys) +ensures IsProperSubset(xs, ys) ==> len(xs) < len(ys) +pure func SubsetLen(xs, ys set[int]) util.Unit { + return (!(xs subset ys) || len(xs) == 0) ? util.Unit{} : + len(xs) == len(ys) ? + let _ := SubsetEquality(xs, ys) in + (let e := Choose(xs) in + (SubsetLen(Remove(xs, e), Remove(ys, e)))) : + + let e:= Choose(xs) in + (SubsetLen(Remove(xs, e), Remove(ys, e))) +} + +// The cardinality of a union of two sets is greater than or equal to the cardinality of +// either individual set. +ghost +opaque +ensures len(xs union ys) >= len(xs) +ensures len(xs union ys) >= len(ys) +decreases ys +pure func UnionLenLower(xs, ys set[int]) util.Unit { + return IsEmpty(ys) ? util.Unit{} : + let y := Choose(ys) in + (let yr := Remove(ys, y) in + (y in xs ? + (let xr := Remove(xs, y) in + (let _ := util.Asserting(xr union yr == Remove(xs union ys, y)) in UnionLenLower(xr, yr))) : + (let _ := util.Asserting(xs union yr == Remove(xs union ys, y)) in UnionLenLower(xs, yr)))) +} + +// The cardinality of a union of two sets is less than or equal to the cardinality of +// both individual sets combined. +ghost +opaque +ensures len(xs union ys) <= len(xs) + len(ys) +decreases +pure func UnionLenUpper(xs, ys set[int]) util.Unit { + return util.Unit{} +} + +// The cardinality of the intersection of xs and ys is less than or equal to the +// cardinality of xs. +ghost +opaque +ensures len(xs intersection ys) <= len(xs) +decreases xs +pure func IntersectLenUpper(xs, ys set[int]) util.Unit { + return IsEmpty(xs) ? util.Unit{} : + let x := Choose(xs) in + (let _ := util.Asserting((Remove(xs, x)) intersection ys == Remove((xs intersection ys), x)) in + (IntersectLenUpper(Remove(xs, x), ys))) +} + +// The cardinality of the difference xs - ys is less than or equal to the cardinality of xs. +ghost +opaque +ensures len(xs setminus ys) <= len(xs) +decreases +pure func DifferenceLenUpper(xs, ys set[int]) util.Unit { + return util.Unit{} +} + +ghost +opaque +ensures len(xs union ys) == len(xs) + len(ys) - len(xs intersection ys) +decreases +pure func UnionLenEq(xs, ys set[int]) util.Unit { + return util.Unit{} +} + +ghost +opaque +ensures len(xs setminus ys) == len(xs) - len(xs intersection ys) +ensures len(xs setminus ys) + len(ys setminus xs) + len(xs intersection ys) == len(xs union ys) +decreases +pure func DifferenceLenEq(xs, ys set[int]) util.Unit { + return util.Unit{} +} + +// If e is in xs, adding it to xs doesn't change the cardinality. +// If e is not in xs, adding it to xs increases the cardinality by 1. +ghost +opaque +ensures (e in xs) ==> (len(Add(xs, e)) == len(xs)) +ensures !(e in xs) ==> (len(Add(xs, e)) == len(xs) + 1) +decreases +pure func AddLen(xs set[int], e int) util.Unit { + return util.Unit{} +} + +// If e is in xs, removing it from xs reduces the cardinality by 1. +// If e is not in xs, removing it from xs doesn't change the cardinality. +ghost +opaque +ensures (e in xs) ==> (len(Remove(xs, e)) == len(xs) - 1) +ensures !(e in xs) ==> (len(Remove(xs, e)) == len(xs)) +decreases +pure func RemoveLen(xs set[int], e int) util.Unit { + return util.Unit{} +} + +// Remove is right distributive over union. +ghost +opaque +ensures Remove(xs union ys, e) == Remove(xs, e) union Remove(ys, e) +decreases +pure func RemoveUnion(xs, ys set[int], e int) util.Unit { + return util.Unit{} +} + +// If e is in (xs union ys), removing it from both sets reduces the cardinality by 1. +ghost +opaque +requires e in (xs union ys) +ensures len(Remove(xs, e) union Remove(ys, e)) == len(xs union ys) - 1 +decreases +pure func RemoveUnionLen(xs, ys set[int], e int) util.Unit { + return RemoveUnion(xs, ys, e) +} + +// If xs and ys are disjoint, the cardinality of their union is equal to the +// sum of the cardinality of xs, and the cardinality of ys. +ghost +opaque +requires AreDisjoint(xs, ys) +ensures len(xs union ys) == len(xs) + len(ys) +decreases +pure func DisjointUnionLen(xs, ys set[int]) util.Unit { + return util.Unit{} +} + +// If xs solely contains integers in the range [a, b), then its size is +// bounded by b - a. +ghost +opaque +requires forall i int :: { i in xs } i in xs ==> (a <= i && i < b) +requires a <= b +ensures len(xs) <= b - a +decreases +pure func BoundedSetLen(xs set[int], a, b int) util.Unit { + return SubsetLen(xs, Range(a, b)) +} diff --git 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We prove the assertions "manually" using the standard +// library. We do not use DifferenceLenEq. +package no_diffleneq + +// We copy an abstract version of the required lemmas in the standard library +// to here. Otherwise, Gobra would try to verify these lemmas again, which +// would not work whenever we disable set axiomatization. + +type Unit struct{} + +ghost +ensures len(xs setminus ys) == len(xs) - len(xs intersection ys) +//ensures len(xs setminus ys) + len(ys setminus xs) + len(xs intersection ys) == len(xs union ys) +decreases +pure func DifferenceLenEq(xs, ys set[int]) Unit + +ghost +ensures len(xs union ys) == len(xs) + len(ys) - len(xs intersection ys) +decreases +pure func UnionLenEq(xs, ys set[int]) Unit + +ghost +ensures len(xs union ys) <= len(xs) + len(ys) +decreases +pure func UnionLenUpper(xs, ys set[int]) Unit + +ghost +decreases +func synthetic(a, b, c, d, e, f set[int]) { + // Sprinkle in unions and intersections; maybe will lead to more + // instantiations of quantifiers like in_intersection_in_both or + // in_left_in_union + u0 := a union b + i0 := a intersection b + u1 := c union d + i1 := c intersection d + u2 := e union f + i2 := e intersection f + + // Assert what we would learn from DifferenceLenEq, UnionLenUpper + // and UnionLenEq. + // It appears that both of the following sections are needed to generate + // a lot of quantifier instantiations with some variance. + + // DifferenceLenEq + i3 := u0 intersection i0 + m0 := u0 setminus i0 + + i4 := m0 intersection i1 + m1 := m0 setminus i1 + //DifferenceLenEq(m0, i1) + assert len(m1) == len(m0) - len(i4) + + i5 := m1 intersection u2 + m2 := m1 setminus u2 + //DifferenceLenEq(m1, u2) + assert len(m2) == len(m1) - len(i5) + + // UnionLenEq, UnionLenUpper + UnionLenEq(a, b) + UnionLenUpper(a, b) + if len(i0) == 0 { + assert len(u0) == len(a) + len(b) + } else { + assert len(u0) < len(a) + len(b) + } + + UnionLenEq(c, d) + UnionLenUpper(c, d) + if len(i1) == 0 { + assert len(u1) == len(c) + len(d) + } else { + assert len(u1) < len(c) + len(d) + } + + UnionLenEq(e, f) + UnionLenUpper(e, f) + if len(i2) == 0 { + assert len(u2) == len(e) + len(f) + } else { + assert len(u2) < len(e) + len(f) + } +} diff --git a/evaluation/experiments/synthetic_set/no_diffleneq_unionlenupper/no_diffleneq_unionlenupper-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv b/evaluation/experiments/synthetic_set/no_diffleneq_unionlenupper/no_diffleneq_unionlenupper-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv new file mode 100644 index 0000000..91a9573 --- /dev/null +++ b/evaluation/experiments/synthetic_set/no_diffleneq_unionlenupper/no_diffleneq_unionlenupper-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv @@ -0,0 +1,31 @@ +qi-k!456,qi-prog.getter_over_tuple2,qi-quant-u-2,qi-quant-u-3,qi-$Set[Int]_prog.equality_definition,qi-$Set[Int]_prog.native_equality,qi-$Set[Int]_prog.cardinality_sums,qi-$Set[Int]_prog.card_non_negative,qi-$Set[Int]_prog.empty_set_cardinality,qi-$Set[Int]_prog.cardinality_difference,qi-$Set[Int]_prog.in_intersection_in_both,qi-$Set[Int]_prog.not_in_difference,qi-$Set[Int]_prog.in_right_in_union,qi-$Set[Int]_prog.in_left_in_union,qi-$Set[Int]_prog.in_difference,qi-$Set[Int]_prog.in_union_in_one,qi-quant-u-4,qi-quant-u-5,qi-quant-u-10,qi-k!369,qi-$Set[Int]_prog.in_empty_set,execution_time +1,3,2,1,18,18,27,60,60,38,1894,596,740,791,498,405,7,7,7,104,108,9.44849443435669 +1,3,2,1,18,18,27,60,60,38,1659,513,630,685,421,343,7,7,7,96,96,9.497825860977173 +1,3,2,1,18,18,27,60,60,38,1725,539,654,706,429,362,7,7,7,93,93,9.6283700466156 +1,3,2,1,18,18,27,60,60,38,1778,562,693,737,466,379,7,7,7,103,104,9.390675067901611 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We prove the assertions "manually" using the standard +// library. We do not use DifferenceLenEq nor UnionLenUpper. +package no_diffleneq_unionlenupper + +// We copy an abstract version of the required lemmas in the standard library +// to here. Otherwise, Gobra would try to verify these lemmas again, which +// would not work whenever we disable set axiomatization. + +type Unit struct{} + +ghost +ensures len(xs setminus ys) == len(xs) - len(xs intersection ys) +//ensures len(xs setminus ys) + len(ys setminus xs) + len(xs intersection ys) == len(xs union ys) +decreases +pure func DifferenceLenEq(xs, ys set[int]) Unit + +ghost +ensures len(xs union ys) == len(xs) + len(ys) - len(xs intersection ys) +decreases +pure func UnionLenEq(xs, ys set[int]) Unit + +ghost +ensures len(xs union ys) <= len(xs) + len(ys) +decreases +pure func UnionLenUpper(xs, ys set[int]) Unit + +ghost +decreases +func synthetic(a, b, c, d, e, f set[int]) { + // Sprinkle in unions and intersections; maybe will lead to more + // instantiations of quantifiers like in_intersection_in_both or + // in_left_in_union + u0 := a union b + i0 := a intersection b + u1 := c union d + i1 := c intersection d + u2 := e union f + i2 := e intersection f + + // Assert what we would learn from DifferenceLenEq, UnionLenUpper + // and UnionLenEq. + // It appears that both of the following sections are needed to generate + // a lot of quantifier instantiations with some variance. + + // DifferenceLenEq + i3 := u0 intersection i0 + m0 := u0 setminus i0 + + i4 := m0 intersection i1 + m1 := m0 setminus i1 + //DifferenceLenEq(m0, i1) + assert len(m1) == len(m0) - len(i4) + + i5 := m1 intersection u2 + m2 := m1 setminus u2 + //DifferenceLenEq(m1, u2) + assert len(m2) == len(m1) - len(i5) + + // UnionLenEq, UnionLenUpper + UnionLenEq(a, b) + //UnionLenUpper(a, b) + if len(i0) == 0 { + assert len(u0) == len(a) + len(b) + } else { + assert len(u0) < len(a) + len(b) + } + + UnionLenEq(c, d) + //UnionLenUpper(c, d) + if len(i1) == 0 { + assert len(u1) == len(c) + len(d) + } else { + assert len(u1) < len(c) + len(d) + } + + UnionLenEq(e, f) + //UnionLenUpper(e, f) + if len(i2) == 0 { + assert len(u2) == len(e) + len(f) + } else { + assert len(u2) < len(e) + len(f) + } +} diff --git a/evaluation/experiments/synthetic_set/not_assisted/not_assisted-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv b/evaluation/experiments/synthetic_set/not_assisted/not_assisted-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv new file mode 100644 index 0000000..98b10ba --- /dev/null +++ b/evaluation/experiments/synthetic_set/not_assisted/not_assisted-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv @@ -0,0 +1,31 @@ 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b/evaluation/experiments/synthetic_set/weak_diffleneq/weak_diffleneq.gobra new file mode 100644 index 0000000..aabef97 --- /dev/null +++ b/evaluation/experiments/synthetic_set/weak_diffleneq/weak_diffleneq.gobra @@ -0,0 +1,85 @@ +// Contains a function to synthetically push the quantifier instantiations +// to the hundreds. We prove the assertions "manually" using the standard +// library. Additionally, we weaken DifferenceLenEq to only include +// the relevant postcondition. +package weak_diffleneq + +// We copy an abstract version of the required lemmas in the standard library +// to here. Otherwise, Gobra would try to verify these lemmas again, which +// would not work whenever we disable set axiomatization. + +type Unit struct{} + +ghost +ensures len(xs setminus ys) == len(xs) - len(xs intersection ys) +//ensures len(xs setminus ys) + len(ys setminus xs) + len(xs intersection ys) == len(xs union ys) +decreases +pure func DifferenceLenEq(xs, ys set[int]) Unit + +ghost +ensures len(xs union ys) == len(xs) + len(ys) - len(xs intersection ys) +decreases +pure func UnionLenEq(xs, ys set[int]) Unit + +ghost +ensures len(xs union ys) <= len(xs) + len(ys) +decreases +pure func UnionLenUpper(xs, ys set[int]) Unit + +ghost +decreases +func synthetic(a, b, c, d, e, f set[int]) { + // Sprinkle in unions and intersections; maybe will lead to more + // instantiations of quantifiers like in_intersection_in_both or + // in_left_in_union + u0 := a union b + i0 := a intersection b + u1 := c union d + i1 := c intersection d + u2 := e union f + i2 := e intersection f + + // Assert what we would learn from DifferenceLenEq, UnionLenUpper + // and UnionLenEq. + // It appears that both of the following sections are needed to generate + // a lot of quantifier instantiations with some variance. + + // DifferenceLenEq + i3 := u0 intersection i0 + m0 := u0 setminus i0 + + i4 := m0 intersection i1 + m1 := m0 setminus i1 + DifferenceLenEq(m0, i1) + assert len(m1) == len(m0) - len(i4) + + i5 := m1 intersection u2 + m2 := m1 setminus u2 + DifferenceLenEq(m1, u2) + assert len(m2) == len(m1) - len(i5) + + // UnionLenEq, UnionLenUpper + UnionLenEq(a, b) + UnionLenUpper(a, b) + if len(i0) == 0 { + assert len(u0) == len(a) + len(b) + } else { + assert len(u0) < len(a) + len(b) + } + + UnionLenEq(c, d) + UnionLenUpper(c, d) + if len(i1) == 0 { + assert len(u1) == len(c) + len(d) + } else { + assert len(u1) < len(c) + len(d) + } + + UnionLenEq(e, f) + UnionLenUpper(e, f) + if len(i2) == 0 { + assert len(u2) == len(e) + len(f) + } else { + assert len(u2) < len(e) + len(f) + } +} diff --git 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Note that single plots are stored in the same directory +as the csv by default. Combined plots, or plots where `--name` was passed +are stored in the current working directory. + +The following commands were executed from the `combined_plots` directory. + +# Using opaque +- standard_library_lemma_opaque: `python ../scripts/plot.py ../experiments/standard_library/lemma_not_opaque/lemma_not_opaque-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv ../experiments/standard_library/lemma_opaque/lemma_opaque-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv --top 2 --name standard_library_lemma_opaque --qi_size 8 4 --variants "Default" "opaque"` +- standard_library_sets_opaque: `python ../scripts/plot.py ../experiments/standard_library/sets_not_opaque/sets_not_opaque-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv ../experiments/standard_library/sets_opaque/sets_opaque-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv --top 3 --qi_size 8 4 --name standard_library_sets_opaque --start_at_zero_qi --variants "Default" "opaque"` +- standard_library_dicts_opaque: `python ../scripts/plot.py ../experiments/standard_library/dicts_not_opaque/dicts_not_opaque-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv ../experiments/standard_library/dicts_opaque/dicts_opaque-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv --name standard_library_dicts_opaque --top 3 --qi_size 8 4 --variants "Default" opaque` + +# Manual Proofs +- synthetic_not_assisted_single: `python ../scripts/plot.py ../experiments/synthetic_set/not_assisted/not_assisted-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv --name synthetic_not_assisted_single --top 6` +- synthetic_compare_noaxioms: `python ../scripts/plot.py ../experiments/synthetic_set/not_assisted/not_assisted-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv ../experiments/synthetic_set/fully_assisted/fully_assisted-rand-no_set_axiom-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv --name synthetic_compare_noaxioms --variants Automatic Manual` + +# Assisting the Verifier +- synthetic_assisted_compare: `python ../scripts/plot.py --name synthetic_assisted_compare ../experiments/synthetic_set/fully_assisted/fully_assisted-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv ../experiments/synthetic_set/weak_diffleneq/weak_diffleneq-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv ../experiments/synthetic_set/no_diffleneq/no_diffleneq-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv ../experiments/synthetic_set/no_diffleneq_unionlenupper/no_diffleneq_unionlenupper-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv ../experiments/synthetic_set/not_assisted/not_assisted-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv --qi_size 8 4 --execution_time_size 7 4 --top 3 --variants "Fully Assisted" "Weak Eq" "No Eq" "No Eq/Upper" "Unassisted"` +- programproofs_first_half: `python ../scripts/plot.py ../experiments/program_proofs_example_10_2/first_half/first_half-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv --name programproofs_first_half --top 5 --qi_size 8 4` +- programproofs_assisted_compare_all: `python ../scripts/plot.py ../experiments/program_proofs_example_10_2/full/full-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv ../experiments/program_proofs_example_10_2/first_half/first_half-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv ../experiments/program_proofs_example_10_2/last_half/last_half-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv ../experiments/program_proofs_example_10_2/minimal/minimal-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv --name programproofs_assisted_compare_all --variants "Full" "First Half" "Last Half" "Minimal" --qi_size 12 20` +- programproofs_assisted_compare_no_first_half: `python ../scripts/plot.py ../experiments/program_proofs_example_10_2/full/full-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv ../experiments/program_proofs_example_10_2/last_half/last_half-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv ../experiments/program_proofs_example_10_2/minimal/minimal-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv --name programproofs_assisted_compare_no_first_half --variants "Full" "Last Half" "Minimal" --top 3 --filter --qi_size 8 4` diff --git a/evaluation/scripts/plot.py b/evaluation/scripts/plot.py new file mode 100644 index 0000000..832fe8e --- /dev/null +++ b/evaluation/scripts/plot.py @@ -0,0 +1,245 @@ +"""Module for plotting the results of profile.py.""" + +import argparse +import pandas as pd +import numpy as np +import seaborn as sns +import matplotlib.pyplot as plt + +from util import file_path + + +def parse_args(): + """Parse command line arguments.""" + parser = argparse.ArgumentParser(formatter_class=argparse.ArgumentDefaultsHelpFormatter) + parser.add_argument("csv_path", type=program_path, nargs="+", help="CSV files to be analyzed") + parser.add_argument("--filter_anonymous", action="store_true", required=False, + help="filter out anonymous quantifier instantiations like quant-u-17 and k!512.") + parser.add_argument("--name", type=str, required=False, + help="Prefix for the output files.") + parser.add_argument("--top", type=int, required=False, + help="Plot only the top n quantifiers") + parser.add_argument("--variants", type=str, nargs="+", required=False, + help="Names of the variants in the plot (only works with multiple CSV files).") + parser.add_argument("--qi_size", type=int, nargs=2, required=False, default=[6, 4], + help="Size of the quantifier instantiation plot (width height)") + parser.add_argument("--execution_time_size", type=int, nargs=2, required=False, default=[6, 4], + help="Size of the execution time plot (width height)") + parser.add_argument("--start_at_zero_qi", action="store_true", required=False, + help="Start the axis for the number of quantifier instantiations at zero.") + parser.add_argument("--start_at_zero_execution_time", action="store_true", required=False, + help="Start the axis for execution time at zero.") + + return parser.parse_args() + + +def main(): + """Main function of the plotter.""" + # Parse arguments + args = parse_args() + + if (args.variants is not None) and (len(args.csv_path) != len(args.variants)): + raise argparse.ArgumentTypeError(f"Number of variants must match the number of CSV files") + + if len(args.csv_path) == 1: + plot(args, args.csv_path[0]) + else: + plot_multiple(args, args.csv_path) + + +def plot(args, csv_path): + """Plot a single CSV file.""" + if args.name is None: + args.name = csv_path.with_suffix("") + + # Read CSV file using pandas. + df = pd.read_csv(csv_path) + + # Remove "qi-" from column names that start with it. + df.columns = df.columns.str.replace('qi-', '') + + # Remove columns that start with "quant-u" or "k!". + if args.filter_anonymous: + df = df.filter(regex='^(?!quant-u|k!).*$', axis=1) + + # Split the DataFrame into two DataFrames: one with only the 'execution_time' column and one with all other columns. + execution_time_df = df[['execution_time']] + qi_df = df.drop(columns=['execution_time']) + + # Determine Top Quantifiers if needed + if args.top is not None: + top_quantifiers = qi_df.median(numeric_only=True).nlargest(args.top).index + qi_df = qi_df.loc[:, list(top_quantifiers)] + + qi_df = qi_df.sort_values(by=qi_df.index[0], ascending=False, axis=1) + + sns.set_theme(rc={'figure.figsize': args.qi_size}) + + # Generate plot for quantifier instantiations. + plt.figure() # Create a new figure + + if len(df) == 1: + sns.barplot(qi_df, orient='h') + else: + sns.boxplot(qi_df, orient='h') + + if args.start_at_zero_qi: + plt.xlim(0, None) + + plt.tight_layout() + plt.savefig((str(args.name) + ".qi.pdf"), dpi=600) + plt.close() + + # Generate plot for execution time if we have more than one measurement + sns.set_theme(rc={'figure.figsize': args.execution_time_size}) + if len(df) > 1: + plt.figure() + + # Calculate median, quartiles, and IQR + median = execution_time_df['execution_time'].median() + quartile1 = execution_time_df['execution_time'].quantile(0.25) + quartile3 = execution_time_df['execution_time'].quantile(0.75) + iqr = quartile3 - quartile1 + + # Identify outliers + outliers = execution_time_df[(execution_time_df < (quartile1 - 1.5 * iqr)) | + (execution_time_df > (quartile3 + 1.5 * iqr))] + + # Plot histogram + sns.histplot(execution_time_df) + + # Overlay the median and quartiles using Matplotlib + plt.axvline(median, color='red', linestyle='--', label='Median') + plt.axvline(quartile1, color='green', linestyle='--', label='1st Quartile (Q1)') + plt.axvline(quartile3, color='green', linestyle='--', label='3rd Quartile (Q3)') + + # Plot the outliers as individual points + plt.scatter(outliers['execution_time'], np.zeros(len(outliers)), color='orange', s=30, label='Outliers') + + plt.title('Histogram of Execution Times with Quartiles and Median') + + if args.start_at_zero_execution_time: + plt.xlim(0, None) + + plt.xlabel('Execution Time (seconds)', labelpad=15) + plt.ylabel('Frequency', labelpad=15) + plt.legend() + plt.savefig((str(args.name) + ".execution_time.pdf"), dpi=600) + plt.close() + + +def plot_multiple(args, csv_paths): + """Plot multiple CSV files on the same graph.""" + # Default value for variant name + if args.variants is None: + args.variants = [csv_path.stem.split("-")[0] for csv_path in csv_paths] + + # Load csv files and set the variant name + # Note that zip won't ignore extra elements in the longer list since they have the same length (checked in main) + dfs = [] + for csv_path, variant in zip(csv_paths, args.variants): + df = pd.read_csv(csv_path) + df['Variant'] = variant + dfs.append(df) + + # Remove "qi-" from column names that start with it. + for df in dfs: + df.columns = df.columns.str.replace('qi-', '') + + if args.filter_anonymous: + # Remove columns that start with "quant-u" or "k!". + dfs = [df.filter(regex='^(?!quant-u|k!).*$', axis=1) for df in dfs] + + # Split the DataFrames into two DataFrames: one with only the 'execution_time' column and one with all other + # columns. + execution_time_dfs = [df[['execution_time']] for df in dfs] + qi_dfs = [df.drop(columns=['execution_time']) for df in dfs] + + if args.top is not None: + # Determine Top Quantifiers for Each DataFrame + top_quantifiers_sets = [] + for df in qi_dfs: + top_quantifiers = df.median(numeric_only=True).nlargest(args.top).index + top_quantifiers_sets.append(set(top_quantifiers)) + + # Take the Union of Top Quantifiers + union_top_quantifiers = set.union(*top_quantifiers_sets) + + # Filter Each DataFrame on the Union of Top Quantifiers + qi_dfs_filtered = [] + for df in qi_dfs: + # Keep 'Variant' column and any quantifier in the union of top quantifiers + columns_to_keep = ['Variant'] + list(union_top_quantifiers.intersection(df.columns)) + qi_dfs_filtered.append(df.loc[:, columns_to_keep]) + + # Now qi_dfs_filtered contains the DataFrames filtered to include only the union of top quantifiers + qi_dfs = qi_dfs_filtered + + # Sort each DataFrame in qi_dfs by the median number of instantiations + sorted_qi_dfs = [] + for df in qi_dfs: + # Calculate the median of each column + medians = df.median(numeric_only=True).sort_values(ascending=False) + # Sort the DataFrame based on the calculated medians + sorted_df = df.loc[:, df.columns.intersection(['Variant']).append(medians.index)] + sorted_qi_dfs.append(sorted_df) + + # Now, sorted_qi_dfs contains the sorted DataFrames + qi_dfs = sorted_qi_dfs + + # Combine the DataFrames into a single DataFrame for plotting + qi_cdf = pd.concat(qi_dfs) + qi_mdf = qi_cdf.melt(id_vars="Variant", var_name="quantifier", value_name="instantiations") + + sns.set_theme(rc={'figure.figsize': args.qi_size}) + plt.figure() + + if len(qi_dfs[0]) == 1: + sns.barplot(x='instantiations', y='quantifier', hue='Variant', data=qi_mdf, orient="h") + else: + sns.boxplot(x='instantiations', y='quantifier', hue='Variant', data=qi_mdf, orient="h") + + if args.start_at_zero_qi: + plt.xlim(0, None) + + plt.xlabel('Number of Instantiations', labelpad=15) + plt.ylabel('Quantifier', labelpad=15) + plt.tight_layout() + + if args.name is None: + args.name = "multi" + + plt.savefig(f"{args.name}.qi.pdf", dpi=600) + plt.close() + + sns.set_theme(rc={'figure.figsize': args.execution_time_size}) + + # Combine DataFrames and rename the columns to the variant names + execution_time_cdf = pd.concat(execution_time_dfs, axis=1) + execution_time_cdf.columns = args.variants + + plt.figure() + + sns.boxplot(execution_time_cdf) + + if args.start_at_zero_execution_time: + plt.ylim(0, None) + plt.xlabel('Variant', labelpad=15) + plt.ylabel('Execution time (s)', labelpad=15) + + plt.tight_layout() + plt.savefig(f"{args.name}.execution_time.pdf", dpi=600) + plt.close() + + +def program_path(string): + """Checks that the string is a valid path to a CSV file.""" + path = file_path(string) + if path.suffix != ".csv": + raise argparse.ArgumentTypeError(f"Wrong suffix: {path} is not a valid path to a CSV file") + + return path + + +if __name__ == '__main__': + main() diff --git a/evaluation/scripts/profile-all.sh b/evaluation/scripts/profile-all.sh new file mode 100644 index 0000000..40f8ac1 --- /dev/null +++ b/evaluation/scripts/profile-all.sh @@ -0,0 +1,25 @@ +#!/bin/bash + +# In case you are using a laptop, make sure that power settings are set +# properly: +# - don't run from battery +# - make sure the correct profile is set, i.e. not the battery profile +# (e.g., in TLP) +# - make sure the laptop will not suspend +# - check packages that may interfere +# - use systemd-inhibit + +ITERATIONS=30 + +SILICON_PATH=~/practical-work/silicon/silicon.sh +Z3_PATH=~/practical-work/z3-4.8.7/bin/z3 +GOBRA_PATH=~/practical-work/gobra/target/scala-2.13/gobra.jar + +# profile with disabled set axioms +python profile.py ../experiments/synthetic_set/fully_assisted/fully_assisted.gobra --disableSetAxiomatization --z3RandomizeSeeds --iterations $ITERATIONS --silicon_path $SILICON_PATH --z3_path $Z3_PATH --gobra $GOBRA_PATH + +# profile all files "normally" +find ../experiments -type f -name "*.gobra" -exec python profile.py {} --z3RandomizeSeeds --iterations $ITERATIONS --silicon_path $SILICON_PATH --z3_path $Z3_PATH --gobra $GOBRA_PATH \; + +# generate plots for every csv +find ../experiments -type f -name "*.csv" -exec python plot.py --qi_size 9 9 {} \; diff --git a/evaluation/scripts/profile.py b/evaluation/scripts/profile.py new file mode 100644 index 0000000..bde8559 --- /dev/null +++ b/evaluation/scripts/profile.py @@ -0,0 +1,263 @@ +"""Module for profiling Viper and Gobra programs using Silicon and Z3's quantifier instantiation profiling.""" + +import argparse +import csv +import logging +import os +import time +import subprocess + +from util import file_path + + +def main(): + """Main function of the profiler.""" + # Set up logging. + logging.basicConfig(level=logging.DEBUG) + + args = parse_args() + + metadata = generate_metadata(args) + + # Set Z3 environment for Gobra and Silicon. + os.environ["Z3_EXE"] = str(args.z3_path) + + # Generate Gobra file if needed. + if args.program_path.suffix == '.gobra': + if args.gobra_path is None: + logging.error("Path to Gobra jar is required for Gobra files.") + raise ValueError("Path to Gobra jar is required for Gobra files.") + + # TODO Refactor this so we can pass it using shell=False + command = f"java -jar -Xss128m {args.gobra_path} --printVpr --noVerify -i {args.program_path}" + + logging.info("Generating Viper file.") + time_checked_command(command, shell=True) + logging.info("Viper file generated.") + + vpr_file_path = args.program_path.with_suffix(".gobra.vpr") + # Due to program_path(), this is a Viper file. + else: + vpr_file_path = args.program_path + + data = [] + for i in range(0, args.iterations): + # --useOldAxiomatization: At the time of writing, the new axiomatization has anonymous axioms, which is why + # we use the old one with names. + command = [args.silicon_path, "--useOldAxiomatization", "--numberOfParallelVerifiers", "1", "--z3Args", + f'smt.qi.profile=true smt.qi.profile_freq={args.granularity}', vpr_file_path] + if args.z3RandomizeSeeds: + command.append("--z3RandomizeSeeds") + if args.disableSetAxiomatization: + # Get current directory of this file. + script_dir = os.path.dirname(os.path.abspath(__file__)) + command.append("--setAxiomatizationFile") + command.append(os.path.join(script_dir, 'noaxioms_sets.vpr')) + + logging.info(f"Running Silicon with profiling. Iteration: {i + 1} of {args.iterations}.") + command, execution_time = time_checked_command(command) + logging.info(f"Silicon finished in {execution_time} seconds.") + + logging.info("Processing Silicon's profiling output") + data_point = process_output(command.stdout) + logging.info("Silicon's profiling output processed.") + data_point["execution_time"] = execution_time + + data.append(data_point) + + # Write CSV files. + csv_path = (metadata["program_path"].parent / format_metadata(metadata)).with_suffix(".csv") + write_to_csv(data, csv_path) + + +def process_output(output): + """Process the data from Silicon's output. + + When we profile Silicon, based on the granularity, a quantifier instantiation may trigger the printing of how often + that quantifier has been instantiated up until now. This function processes that output and returns a dictionary + which maps quantifier names to the latest number of instantiations. + """ + # Drop Silicon's preamble and epilogue. + output = output.splitlines() + output = output[1:-1] + + # Keeps track of current number of quantifier instantiations. + result = {} + + # Process the output. + # Example of rows we are processing: + # [quantifier_instances] $Multiset[Int]_prog.card_non_negative : 2500 : 10 : 11 + for line in output: + columns = [column.strip() for column in line.split(":")] + + # We don't want to include "[quantifier_instances] " in the name. + name = columns[0].removeprefix("[quantifier_instances]").strip() + instantiations = int(columns[1]) + + # We prefix the name with "qi-" to indicate that it is a quantifier instantiation to avoid potential name + # clashes with execution_time. + result[f"qi-{name}"] = instantiations + + return result + + +def time_checked_command(command, shell=False): + """Runs a command and returns its runtime and its results. + + This function is a wrapper around subprocess.run. It measures the runtime and checks whether the command was + successful. If it wasn't, it prints all the information and raises RuntimeError. + """ + logging.debug(f"Running {command}") + try: + start_time = time.time() + command = subprocess.run(command, capture_output=True, text=True, check=True, shell=shell) + end_time = time.time() + execution_time = end_time - start_time + logging.debug(f"Command finished in {execution_time} seconds.") + return command, execution_time + except subprocess.CalledProcessError as e: + logging.error(f"Command {e.cmd} failed with return code {e.returncode}.") + logging.error(f"stdout: {e.stdout}") + logging.error(f"stderr: {e.stderr}") + raise RuntimeError(f"Command {e.cmd} failed with return code {e.returncode}.") + + +def parse_args(): + """Parse command line arguments.""" + parser = argparse.ArgumentParser(formatter_class=argparse.ArgumentDefaultsHelpFormatter) + parser.add_argument("program_path", type=program_path, + help="Gobra or Viper program to be profiled") + parser.add_argument("--silicon_path", type=file_path, required=True, + help="path to silicon.sh") + parser.add_argument("--z3_path", type=file_path, required=True, + help="path to Z3 binary") + parser.add_argument("--gobra_path", type=file_path, required=False, + help="path to Gobra jar") + parser.add_argument("--iterations", type=positive, required=False, default=1, + help="number of times profiling is repeated") + parser.add_argument("--granularity", type=positive, required=False, default=1, + help="granularity of quantifier reporting") + parser.add_argument("--z3RandomizeSeeds", action="store_true", required=False, + help=("set various Z3 random seeds to random values. Note that " + "profiling may be non-deterministic even if this setting " + "is set to False.")) + parser.add_argument("--disableSetAxiomatization", action="store_true", required=False, + help="disable the axiomatization of set operations.") + return parser.parse_args() + + +def generate_metadata(args): + """Generate metadata for the CSV file.""" + logging.info("Generating metadata.") + metadata = {"program_path": args.program_path} + logging.info(f"Program path: {metadata['program_path']}") + + logging.info("Getting version of Silicon.") + command = [args.silicon_path] + logging.debug(f"Running {command}") + # This shouldn't be checked, as Silicon will return a non-zero exit code (no option for version). + command_stdout = subprocess.run(command, capture_output=True, text=True).stdout + # Convert + # Silicon 1.1-SNAPSHOT (7fea2aa7+) + # Command-line interface: Required option 'file' not found. + # Run with just --help for usage and options + # to + # 7fea2aa7 + metadata["silicon_version"] = command_stdout.splitlines()[0].split()[-1][1:-2] + logging.info(f"Silicon version: {metadata['silicon_version']}") + + logging.info("Getting version of Z3.") + command = [args.z3_path, "-version"] + command, _ = time_checked_command(command) + # Convert "Z3 version 4.8.7 - 64 bit" to "4_8_7". + metadata["z3_version"] = command.stdout.split()[2].replace('.', '_') + logging.info(f"Z3 version: {metadata['z3_version']}") + + # Get version of Gobra if applicable. + if args.gobra_path is not None: + logging.info("Getting version of Gobra.") + # TODO Refactor this so we can pass it using shell=False + command = f"java -jar {args.gobra_path} --version" + command, _ = time_checked_command(command, shell=True) + # Convert + # + # Gobra (c) Copyright ETH Zurich 2012 - 2022 + # version 1.1-SNAPSHOT (529d2a49@(detached)) + # + # to + # 529d2a49 + metadata["gobra_version"] = command.stdout.splitlines()[2].split()[-1].partition("@")[0][1:] + logging.info(f"Gobra version: {metadata['gobra_version']}") + else: + logging.info("Getting Gobra version not required. Continuing.") + + metadata["iterations"] = args.iterations + logging.info(f"Iterations: {metadata['iterations']}") + + metadata["granularity"] = args.granularity + logging.info(f"Granularity: {metadata['granularity']}") + metadata["z3RandomizeSeeds"] = args.z3RandomizeSeeds + logging.info(f"Z3 randomize seeds: {metadata['z3RandomizeSeeds']}") + metadata["disableSetAxiomatization"] = args.disableSetAxiomatization + logging.info(f"Disable set axiomatization: {metadata['disableSetAxiomatization']}") + + logging.info("Metadata generated.") + return metadata + + +def format_metadata(metadata): + """Format the metadata into a single string. + + This string is used as the filename of the CSV file. + """ + result = f'{metadata["program_path"].stem.replace(".", "_")}' + if metadata["z3RandomizeSeeds"]: + result += "-rand" + if metadata["disableSetAxiomatization"]: + result += "-no_set_axiom" + result += f'-iter_{metadata["iterations"]}' + result += f'-gran_{metadata["granularity"]}' + result += f'-sil_ver_{metadata["silicon_version"]}' + result += f'-z3_ver_{metadata["z3_version"]}' + if "gobra_version" in metadata: + result += f'-gobra_ver_{metadata["gobra_version"]}' + + return result + + +def write_to_csv(data, csv_path): + """Write the data to a CSV file.""" + logging.info(f"Writing {csv_path}.") + with open(csv_path, 'w', newline='') as csvfile: + writer = csv.DictWriter(csvfile, fieldnames=data[0].keys()) + writer.writeheader() + + for data_point in data: + writer.writerow(data_point) + + logging.info(f"Data written to {csv_path}.") + + +def program_path(string): + """Checks that the string is a valid path to either a Viper or Gobra program.""" + path = file_path(string) + if path.suffix not in [".gobra", ".vpr"]: + raise argparse.ArgumentTypeError(f"Wrong suffix: {path} is not a valid path to a program") + + # TODO Check whether this workaround is a bug in Gobra that we need to report + if not path.is_absolute(): + path = path.resolve() + + return path + + +def positive(string): + """Checks that the string is a positive integer.""" + value = int(string) + if value <= 0: + raise argparse.ArgumentTypeError(f"{value} is not larger or equal to 1") + return value + + +if __name__ == "__main__": + main() diff --git a/evaluation/scripts/util.py b/evaluation/scripts/util.py new file mode 100644 index 0000000..634b9b4 --- /dev/null +++ b/evaluation/scripts/util.py @@ -0,0 +1,11 @@ +import argparse +import os +from pathlib import Path + + +def file_path(string): + """Checks that the string is a valid path to a file.""" + if os.path.isfile(string): + return Path(string) + else: + raise argparse.ArgumentTypeError(f"{string} is not a valid path to a file") From 24c77d7c5be7c06df4e0fda49f8073ca1785d27b Mon Sep 17 00:00:00 2001 From: Daniel Nezamabadi <55559979+dnezam@users.noreply.github.com> Date: Sat, 13 Apr 2024 10:29:49 +0200 Subject: [PATCH 02/13] Remove configured values --- evaluation/scripts/profile-all.sh | 9 ++++++--- 1 file changed, 6 insertions(+), 3 deletions(-) diff --git a/evaluation/scripts/profile-all.sh b/evaluation/scripts/profile-all.sh index 40f8ac1..3700f7e 100644 --- a/evaluation/scripts/profile-all.sh +++ b/evaluation/scripts/profile-all.sh @@ -11,9 +11,12 @@ ITERATIONS=30 -SILICON_PATH=~/practical-work/silicon/silicon.sh -Z3_PATH=~/practical-work/z3-4.8.7/bin/z3 -GOBRA_PATH=~/practical-work/gobra/target/scala-2.13/gobra.jar +# Set the path to silicon.sh +SILICON_PATH= +# Set the path to the z3 binary +Z3_PATH= +# Set the path to the Gobra jar +GOBRA_PATH= # profile with disabled set axioms python profile.py ../experiments/synthetic_set/fully_assisted/fully_assisted.gobra --disableSetAxiomatization --z3RandomizeSeeds --iterations $ITERATIONS --silicon_path $SILICON_PATH --z3_path $Z3_PATH --gobra $GOBRA_PATH From 0445f77240cbe87b9265a107601c2dcc010c9cd5 Mon Sep 17 00:00:00 2001 From: Daniel Nezamabadi <55559979+dnezam@users.noreply.github.com> Date: Sat, 13 Apr 2024 10:50:46 +0200 Subject: [PATCH 03/13] Add license information --- .../dicts_not_opaque/dicts_not_opaque.gobra | 6 ++++++ .../standard_library/dicts_opaque/dicts_opaque.gobra | 6 ++++++ .../lemma_not_opaque/lemma_not_opaque.gobra | 6 ++++++ .../standard_library/lemma_opaque/lemma_opaque.gobra | 6 ++++++ .../sets_not_opaque/sets_not_opaque.gobra | 6 ++++++ .../standard_library/sets_opaque/sets_opaque.gobra | 6 ++++++ .../synthetic_set/fully_assisted/fully_assisted.gobra | 6 ++++++ .../synthetic_set/no_diffleneq/no_diffleneq.gobra | 6 ++++++ .../no_diffleneq_unionlenupper.gobra | 6 ++++++ .../synthetic_set/not_assisted/not_assisted.gobra | 6 ++++++ .../synthetic_set/weak_diffleneq/weak_diffleneq.gobra | 6 ++++++ evaluation/scripts/plot.py | 8 +++++++- evaluation/scripts/profile-all.sh | 4 ++++ evaluation/scripts/profile.py | 8 +++++++- evaluation/scripts/util.py | 6 ++++++ 15 files changed, 90 insertions(+), 2 deletions(-) diff --git a/evaluation/experiments/standard_library/dicts_not_opaque/dicts_not_opaque.gobra b/evaluation/experiments/standard_library/dicts_not_opaque/dicts_not_opaque.gobra index e0ae0b8..a96decb 100644 --- a/evaluation/experiments/standard_library/dicts_not_opaque/dicts_not_opaque.gobra +++ b/evaluation/experiments/standard_library/dicts_not_opaque/dicts_not_opaque.gobra @@ -1,3 +1,9 @@ +/* + This file is part of gobra-libs which is released under the MIT license. + See LICENSE or go to https://github.com/viperproject/gobra-libs/blob/main/LICENSE + for full license details. +*/ + // A copy of the dicts package from the standard library. // Lemmas are turned non-opaque. Uses the non-opaque version of the sets // package. diff --git a/evaluation/experiments/standard_library/dicts_opaque/dicts_opaque.gobra b/evaluation/experiments/standard_library/dicts_opaque/dicts_opaque.gobra index 27927cc..197cdee 100644 --- a/evaluation/experiments/standard_library/dicts_opaque/dicts_opaque.gobra +++ b/evaluation/experiments/standard_library/dicts_opaque/dicts_opaque.gobra @@ -1,3 +1,9 @@ +/* + This file is part of gobra-libs which is released under the MIT license. + See LICENSE or go to https://github.com/viperproject/gobra-libs/blob/main/LICENSE + for full license details. +*/ + // A copy of the dicts package from the standard library. // Uses the opaque version of the sets package. package dicts_opaque diff --git a/evaluation/experiments/standard_library/lemma_not_opaque/lemma_not_opaque.gobra b/evaluation/experiments/standard_library/lemma_not_opaque/lemma_not_opaque.gobra index 073e410..232a74f 100644 --- a/evaluation/experiments/standard_library/lemma_not_opaque/lemma_not_opaque.gobra +++ b/evaluation/experiments/standard_library/lemma_not_opaque/lemma_not_opaque.gobra @@ -1,3 +1,9 @@ +/* + This file is part of gobra-libs which is released under the MIT license. + See LICENSE or go to https://github.com/viperproject/gobra-libs/blob/main/LICENSE + for full license details. +*/ + // A copy of a non-trivial lemma from the standard library. package lemma_not_opaque diff --git a/evaluation/experiments/standard_library/lemma_opaque/lemma_opaque.gobra b/evaluation/experiments/standard_library/lemma_opaque/lemma_opaque.gobra index 99f4a32..fe7bbb6 100644 --- a/evaluation/experiments/standard_library/lemma_opaque/lemma_opaque.gobra +++ b/evaluation/experiments/standard_library/lemma_opaque/lemma_opaque.gobra @@ -1,3 +1,9 @@ +/* + This file is part of gobra-libs which is released under the MIT license. + See LICENSE or go to https://github.com/viperproject/gobra-libs/blob/main/LICENSE + for full license details. +*/ + // A copy of a non-trivial lemma from the standard library. // Lemmas are turned opaque. package lemma_opaque diff --git a/evaluation/experiments/standard_library/sets_not_opaque/sets_not_opaque.gobra b/evaluation/experiments/standard_library/sets_not_opaque/sets_not_opaque.gobra index 1abfa71..0673a83 100644 --- a/evaluation/experiments/standard_library/sets_not_opaque/sets_not_opaque.gobra +++ b/evaluation/experiments/standard_library/sets_not_opaque/sets_not_opaque.gobra @@ -1,3 +1,9 @@ +/* + This file is part of gobra-libs which is released under the MIT license. + See LICENSE or go to https://github.com/viperproject/gobra-libs/blob/main/LICENSE + for full license details. +*/ + // A copy of the sets package from the standard library. package sets_not_opaque diff --git a/evaluation/experiments/standard_library/sets_opaque/sets_opaque.gobra b/evaluation/experiments/standard_library/sets_opaque/sets_opaque.gobra index 1fae309..29c7690 100644 --- a/evaluation/experiments/standard_library/sets_opaque/sets_opaque.gobra +++ b/evaluation/experiments/standard_library/sets_opaque/sets_opaque.gobra @@ -1,3 +1,9 @@ +/* + This file is part of gobra-libs which is released under the MIT license. + See LICENSE or go to https://github.com/viperproject/gobra-libs/blob/main/LICENSE + for full license details. +*/ + // Copy of the sets package from the standard library where all lemmas are // turned opaque. package sets_opaque diff --git a/evaluation/experiments/synthetic_set/fully_assisted/fully_assisted.gobra b/evaluation/experiments/synthetic_set/fully_assisted/fully_assisted.gobra index 3709655..c00ae2b 100644 --- a/evaluation/experiments/synthetic_set/fully_assisted/fully_assisted.gobra +++ b/evaluation/experiments/synthetic_set/fully_assisted/fully_assisted.gobra @@ -1,3 +1,9 @@ +/* + This file is part of gobra-libs which is released under the MIT license. + See LICENSE or go to https://github.com/viperproject/gobra-libs/blob/main/LICENSE + for full license details. +*/ + // Contains a function to synthetically push the quantifier instantiations // to the hundreds. We prove the assertions "manually" using the standard // library. diff --git a/evaluation/experiments/synthetic_set/no_diffleneq/no_diffleneq.gobra b/evaluation/experiments/synthetic_set/no_diffleneq/no_diffleneq.gobra index d4c60ad..cb76fbf 100644 --- a/evaluation/experiments/synthetic_set/no_diffleneq/no_diffleneq.gobra +++ b/evaluation/experiments/synthetic_set/no_diffleneq/no_diffleneq.gobra @@ -1,3 +1,9 @@ +/* + This file is part of gobra-libs which is released under the MIT license. + See LICENSE or go to https://github.com/viperproject/gobra-libs/blob/main/LICENSE + for full license details. +*/ + // Contains a function to synthetically push the quantifier instantiations // to the hundreds. We prove the assertions "manually" using the standard // library. We do not use DifferenceLenEq. diff --git a/evaluation/experiments/synthetic_set/no_diffleneq_unionlenupper/no_diffleneq_unionlenupper.gobra b/evaluation/experiments/synthetic_set/no_diffleneq_unionlenupper/no_diffleneq_unionlenupper.gobra index a0588a8..31daaea 100644 --- a/evaluation/experiments/synthetic_set/no_diffleneq_unionlenupper/no_diffleneq_unionlenupper.gobra +++ b/evaluation/experiments/synthetic_set/no_diffleneq_unionlenupper/no_diffleneq_unionlenupper.gobra @@ -1,3 +1,9 @@ +/* + This file is part of gobra-libs which is released under the MIT license. + See LICENSE or go to https://github.com/viperproject/gobra-libs/blob/main/LICENSE + for full license details. +*/ + // Contains a function to synthetically push the quantifier instantiations // to the hundreds. We prove the assertions "manually" using the standard // library. We do not use DifferenceLenEq nor UnionLenUpper. diff --git a/evaluation/experiments/synthetic_set/not_assisted/not_assisted.gobra b/evaluation/experiments/synthetic_set/not_assisted/not_assisted.gobra index 44c624e..25f8543 100644 --- a/evaluation/experiments/synthetic_set/not_assisted/not_assisted.gobra +++ b/evaluation/experiments/synthetic_set/not_assisted/not_assisted.gobra @@ -1,3 +1,9 @@ +/* + This file is part of gobra-libs which is released under the MIT license. + See LICENSE or go to https://github.com/viperproject/gobra-libs/blob/main/LICENSE + for full license details. +*/ + // Contains a function to synthetically push the quantifier instantiations // to the hundreds. We do not assist the verifier. package not_assisted diff --git a/evaluation/experiments/synthetic_set/weak_diffleneq/weak_diffleneq.gobra b/evaluation/experiments/synthetic_set/weak_diffleneq/weak_diffleneq.gobra index aabef97..9b85023 100644 --- a/evaluation/experiments/synthetic_set/weak_diffleneq/weak_diffleneq.gobra +++ b/evaluation/experiments/synthetic_set/weak_diffleneq/weak_diffleneq.gobra @@ -1,3 +1,9 @@ +/* + This file is part of gobra-libs which is released under the MIT license. + See LICENSE or go to https://github.com/viperproject/gobra-libs/blob/main/LICENSE + for full license details. +*/ + // Contains a function to synthetically push the quantifier instantiations // to the hundreds. We prove the assertions "manually" using the standard // library. Additionally, we weaken DifferenceLenEq to only include diff --git a/evaluation/scripts/plot.py b/evaluation/scripts/plot.py index 832fe8e..b9f5dbf 100644 --- a/evaluation/scripts/plot.py +++ b/evaluation/scripts/plot.py @@ -1,4 +1,10 @@ -"""Module for plotting the results of profile.py.""" +""" +Module for plotting the results of profile.py. + +This file is part of gobra-libs which is released under the MIT license. +See LICENSE or go to https://github.com/viperproject/gobra-libs/blob/main/LICENSE +for full license details. +""" import argparse import pandas as pd diff --git a/evaluation/scripts/profile-all.sh b/evaluation/scripts/profile-all.sh index 3700f7e..50fe72d 100644 --- a/evaluation/scripts/profile-all.sh +++ b/evaluation/scripts/profile-all.sh @@ -1,5 +1,9 @@ #!/bin/bash +# This file is part of gobra-libs which is released under the MIT license. +# See LICENSE or go to https://github.com/viperproject/gobra-libs/blob/main/LICENSE +# for full license details. + # In case you are using a laptop, make sure that power settings are set # properly: # - don't run from battery diff --git a/evaluation/scripts/profile.py b/evaluation/scripts/profile.py index bde8559..e4d73e5 100644 --- a/evaluation/scripts/profile.py +++ b/evaluation/scripts/profile.py @@ -1,4 +1,10 @@ -"""Module for profiling Viper and Gobra programs using Silicon and Z3's quantifier instantiation profiling.""" +""" +Module for profiling Viper and Gobra programs using Silicon and Z3's quantifier instantiation profiling. + +This file is part of gobra-libs which is released under the MIT license. +See LICENSE or go to https://github.com/viperproject/gobra-libs/blob/main/LICENSE +for full license details. +""" import argparse import csv diff --git a/evaluation/scripts/util.py b/evaluation/scripts/util.py index 634b9b4..a560994 100644 --- a/evaluation/scripts/util.py +++ b/evaluation/scripts/util.py @@ -1,3 +1,9 @@ +""" +This file is part of gobra-libs which is released under the MIT license. +See LICENSE or go to https://github.com/viperproject/gobra-libs/blob/main/LICENSE +for full license details. +""" + import argparse import os from pathlib import Path From 10565b07ecbd5404e5ba690d085d05f5a91198a0 Mon Sep 17 00:00:00 2001 From: Daniel Nezamabadi <55559979+dnezam@users.noreply.github.com> Date: Sat, 13 Apr 2024 10:58:47 +0200 Subject: [PATCH 04/13] Add information about Z3 version --- evaluation/scripts/profile-all.sh | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/evaluation/scripts/profile-all.sh b/evaluation/scripts/profile-all.sh index 50fe72d..540161f 100644 --- a/evaluation/scripts/profile-all.sh +++ b/evaluation/scripts/profile-all.sh @@ -17,7 +17,8 @@ ITERATIONS=30 # Set the path to silicon.sh SILICON_PATH= -# Set the path to the z3 binary +# Set the path to the Z3 binary +# Tested Versions: 4.8.7 (newer versions may not work; produce errors and different output) Z3_PATH= # Set the path to the Gobra jar GOBRA_PATH= From 6561df85e8cc70123eaa5c0e874a3acfb9825a32 Mon Sep 17 00:00:00 2001 From: Daniel Nezamabadi <55559979+dnezam@users.noreply.github.com> Date: Sat, 13 Apr 2024 11:18:41 +0200 Subject: [PATCH 05/13] Rename folder --- ...amproofs_assisted_compare_all.execution_time.pdf | Bin .../programproofs_assisted_compare_all.qi.pdf | Bin ...ssisted_compare_no_first_half.execution_time.pdf | Bin ...gramproofs_assisted_compare_no_first_half.qi.pdf | Bin .../programproofs_first_half.execution_time.pdf | Bin .../programproofs_first_half.qi.pdf | Bin ...standard_library_dicts_opaque.execution_time.pdf | Bin .../standard_library_dicts_opaque.qi.pdf | Bin ...standard_library_lemma_opaque.execution_time.pdf | Bin .../standard_library_lemma_opaque.qi.pdf | Bin .../standard_library_sets_opaque.execution_time.pdf | Bin .../standard_library_sets_opaque.qi.pdf | Bin .../synthetic_assisted_compare.execution_time.pdf | Bin .../synthetic_assisted_compare.qi.pdf | Bin .../synthetic_compare_noaxioms.execution_time.pdf | 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b/evaluation/selected_plots/synthetic_assisted_compare.execution_time.pdf similarity index 100% rename from evaluation/plots/synthetic_assisted_compare.execution_time.pdf rename to evaluation/selected_plots/synthetic_assisted_compare.execution_time.pdf diff --git a/evaluation/plots/synthetic_assisted_compare.qi.pdf b/evaluation/selected_plots/synthetic_assisted_compare.qi.pdf similarity index 100% rename from evaluation/plots/synthetic_assisted_compare.qi.pdf rename to evaluation/selected_plots/synthetic_assisted_compare.qi.pdf diff --git a/evaluation/plots/synthetic_compare_noaxioms.execution_time.pdf b/evaluation/selected_plots/synthetic_compare_noaxioms.execution_time.pdf similarity index 100% rename from evaluation/plots/synthetic_compare_noaxioms.execution_time.pdf rename to evaluation/selected_plots/synthetic_compare_noaxioms.execution_time.pdf diff --git a/evaluation/plots/synthetic_not_assisted_single.qi.pdf b/evaluation/selected_plots/synthetic_not_assisted_single.qi.pdf similarity index 100% rename from evaluation/plots/synthetic_not_assisted_single.qi.pdf rename to evaluation/selected_plots/synthetic_not_assisted_single.qi.pdf diff --git a/evaluation/plots/used_commands.md b/evaluation/selected_plots/used_commands.md similarity index 100% rename from evaluation/plots/used_commands.md rename to evaluation/selected_plots/used_commands.md From b321539f095d8db04c0b399b6dc53e4af8923dd1 Mon Sep 17 00:00:00 2001 From: Daniel Nezamabadi <55559979+dnezam@users.noreply.github.com> Date: Sat, 13 Apr 2024 14:23:02 +0200 Subject: [PATCH 06/13] Add usage and dependencies as comment --- evaluation/scripts/profile-all.sh | 12 ++++++++++++ 1 file changed, 12 insertions(+) diff --git a/evaluation/scripts/profile-all.sh b/evaluation/scripts/profile-all.sh index 540161f..a385dea 100644 --- a/evaluation/scripts/profile-all.sh +++ b/evaluation/scripts/profile-all.sh @@ -4,6 +4,18 @@ # See LICENSE or go to https://github.com/viperproject/gobra-libs/blob/main/LICENSE # for full license details. +# DEPENDENCIES (plot.py): +# - pandas +# - numpy +# - seaborn +# - matplotlib +# In case you forgot to install the dependencies before running the script, you +# do not need to rerun this script (and in particular profiling); instead, simply use +# the command for plotting found below. + +# USAGE: +# Switch into the same directory as profile-all.sh, and run the script. +# # In case you are using a laptop, make sure that power settings are set # properly: # - don't run from battery From ba80f9d6c58d2413249fa44cb29be2211e14e3c3 Mon Sep 17 00:00:00 2001 From: Daniel Nezamabadi <55559979+dnezam@users.noreply.github.com> Date: Sat, 13 Apr 2024 14:33:01 +0200 Subject: [PATCH 07/13] Add missing noaxioms_sets.vpr --- evaluation/scripts/noaxioms_sets.vpr | 19 +++++++++++++++++++ 1 file changed, 19 insertions(+) create mode 100644 evaluation/scripts/noaxioms_sets.vpr diff --git a/evaluation/scripts/noaxioms_sets.vpr b/evaluation/scripts/noaxioms_sets.vpr new file mode 100644 index 0000000..f29cf71 --- /dev/null +++ b/evaluation/scripts/noaxioms_sets.vpr @@ -0,0 +1,19 @@ +// This Source Code Form is subject to the terms of the Mozilla Public +// License, v. 2.0. If a copy of the MPL was not distributed with this +// file, You can obtain one at http://mozilla.org/MPL/2.0/. +// +// Copyright (c) 2011-2023 ETH Zurich. + +domain $Set[E] { + function Set_in(e: E, s: $Set[E]): Bool + function Set_card(s: $Set[E]): Int + function Set_empty(): $Set[E] + function Set_singleton(e: E): $Set[E] + function Set_unionone(s: $Set[E], e: E): $Set[E] + function Set_union(s1: $Set[E], s2: $Set[E]): $Set[E] + function Set_disjoint(s1: $Set[E], s2: $Set[E]): Bool + function Set_difference(s1: $Set[E], s2: $Set[E]): $Set[E] + function Set_intersection(s1: $Set[E], s2: $Set[E]): $Set[E] + function Set_subset(s1: $Set[E], s2: $Set[E]): Bool + function Set_equal(s1: $Set[E], s2: $Set[E]): Bool +} From f0c1f1bd16cb5f186efbbd75bdcd2a153022576f Mon Sep 17 00:00:00 2001 From: Daniel Nezamabadi <55559979+dnezam@users.noreply.github.com> Date: Thu, 25 Apr 2024 11:20:21 +0200 Subject: [PATCH 08/13] Use env vars for profile-all.sh --- evaluation/scripts/profile-all.sh | 29 +++++++++++++++++++++-------- 1 file changed, 21 insertions(+), 8 deletions(-) diff --git a/evaluation/scripts/profile-all.sh b/evaluation/scripts/profile-all.sh index a385dea..a2bb0e9 100644 --- a/evaluation/scripts/profile-all.sh +++ b/evaluation/scripts/profile-all.sh @@ -14,7 +14,14 @@ # the command for plotting found below. # USAGE: -# Switch into the same directory as profile-all.sh, and run the script. +# First, make sure the following variables are set: +# - SILICON_PATH (should contain path to silicon.sh) +# - Z3_PATH (should contain path to the Z3 binary) +# - GOBRA_PATH (should contain path to Gobra jar) +# Note that we only tested Z3 4.8.7; newer versions may not work as +# they produce errors and different output. +# +# Finally, switch into the same directory as profile-all.sh, and run the script. # # In case you are using a laptop, make sure that power settings are set # properly: @@ -27,13 +34,19 @@ ITERATIONS=30 -# Set the path to silicon.sh -SILICON_PATH= -# Set the path to the Z3 binary -# Tested Versions: 4.8.7 (newer versions may not work; produce errors and different output) -Z3_PATH= -# Set the path to the Gobra jar -GOBRA_PATH= +# Check if the environment variables are unset or empty +if [ -z "$SILICON_PATH" ]; then + echo "Please set the environment variable SILICON_PATH to the path to silicon.sh." + exit 1 +fi +if [ -z "$Z3_PATH" ]; then + echo "Please set the environment variable Z3_PATH to the path to the Z3 binary." + exit 1 +fi +if [ -z "$GOBRA_PATH" ]; then + echo "Please set the environment variable GOBRA_PATH to the path to the Gobra jar." + exit 1 +fi # profile with disabled set axioms python profile.py ../experiments/synthetic_set/fully_assisted/fully_assisted.gobra --disableSetAxiomatization --z3RandomizeSeeds --iterations $ITERATIONS --silicon_path $SILICON_PATH --z3_path $Z3_PATH --gobra $GOBRA_PATH From da69ed5a8f4b8b4d74747d1da0cac34b0bfa7f81 Mon Sep 17 00:00:00 2001 From: Daniel Nezamabadi <55559979+dnezam@users.noreply.github.com> Date: Thu, 25 Apr 2024 11:28:00 +0200 Subject: [PATCH 09/13] Add titles to used_commands.md --- evaluation/selected_plots/used_commands.md | 8 +++++--- 1 file changed, 5 insertions(+), 3 deletions(-) diff --git a/evaluation/selected_plots/used_commands.md b/evaluation/selected_plots/used_commands.md index af7d6d7..169d636 100644 --- a/evaluation/selected_plots/used_commands.md +++ b/evaluation/selected_plots/used_commands.md @@ -1,20 +1,22 @@ +# Description This file lists the commands used to generate the combined plots used in the report. Note that single plots are stored in the same directory as the csv by default. Combined plots, or plots where `--name` was passed are stored in the current working directory. +# Commands The following commands were executed from the `combined_plots` directory. -# Using opaque +## Using opaque - standard_library_lemma_opaque: `python ../scripts/plot.py ../experiments/standard_library/lemma_not_opaque/lemma_not_opaque-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv ../experiments/standard_library/lemma_opaque/lemma_opaque-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv --top 2 --name standard_library_lemma_opaque --qi_size 8 4 --variants "Default" "opaque"` - standard_library_sets_opaque: `python ../scripts/plot.py ../experiments/standard_library/sets_not_opaque/sets_not_opaque-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv ../experiments/standard_library/sets_opaque/sets_opaque-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv --top 3 --qi_size 8 4 --name standard_library_sets_opaque --start_at_zero_qi --variants "Default" "opaque"` - standard_library_dicts_opaque: `python ../scripts/plot.py ../experiments/standard_library/dicts_not_opaque/dicts_not_opaque-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv ../experiments/standard_library/dicts_opaque/dicts_opaque-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv --name standard_library_dicts_opaque --top 3 --qi_size 8 4 --variants "Default" opaque` -# Manual Proofs +## Manual Proofs - synthetic_not_assisted_single: `python ../scripts/plot.py ../experiments/synthetic_set/not_assisted/not_assisted-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv --name synthetic_not_assisted_single --top 6` - synthetic_compare_noaxioms: `python ../scripts/plot.py ../experiments/synthetic_set/not_assisted/not_assisted-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv ../experiments/synthetic_set/fully_assisted/fully_assisted-rand-no_set_axiom-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv --name synthetic_compare_noaxioms --variants Automatic Manual` -# Assisting the Verifier +## Assisting the Verifier - synthetic_assisted_compare: `python ../scripts/plot.py --name synthetic_assisted_compare ../experiments/synthetic_set/fully_assisted/fully_assisted-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv ../experiments/synthetic_set/weak_diffleneq/weak_diffleneq-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv ../experiments/synthetic_set/no_diffleneq/no_diffleneq-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv ../experiments/synthetic_set/no_diffleneq_unionlenupper/no_diffleneq_unionlenupper-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv ../experiments/synthetic_set/not_assisted/not_assisted-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv --qi_size 8 4 --execution_time_size 7 4 --top 3 --variants "Fully Assisted" "Weak Eq" "No Eq" "No Eq/Upper" "Unassisted"` - programproofs_first_half: `python ../scripts/plot.py ../experiments/program_proofs_example_10_2/first_half/first_half-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv --name programproofs_first_half --top 5 --qi_size 8 4` - programproofs_assisted_compare_all: `python ../scripts/plot.py ../experiments/program_proofs_example_10_2/full/full-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv ../experiments/program_proofs_example_10_2/first_half/first_half-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv ../experiments/program_proofs_example_10_2/last_half/last_half-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv ../experiments/program_proofs_example_10_2/minimal/minimal-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv --name programproofs_assisted_compare_all --variants "Full" "First Half" "Last Half" "Minimal" --qi_size 12 20` From a9adec70106077bf65fd5cbc728c8db8ec39c1bd Mon Sep 17 00:00:00 2001 From: Daniel Nezamabadi <55559979+dnezam@users.noreply.github.com> Date: Thu, 25 Apr 2024 12:03:07 +0200 Subject: [PATCH 10/13] Add README.md for evaluation/ --- evaluation/README.md | 40 ++++++++++++++++++++++++++++++++++++++++ 1 file changed, 40 insertions(+) create mode 100644 evaluation/README.md diff --git a/evaluation/README.md b/evaluation/README.md new file mode 100644 index 0000000..e2d5f3d --- /dev/null +++ b/evaluation/README.md @@ -0,0 +1,40 @@ +# Overview +`evaluation/` contains Gobra files and scripts that can be used to +evaluate and plot, for example, the effect of using `opaque` in the +standard library or using the standard library on the execution time +and number of quantifier instantiations. + +## `scripts/` +Contains scripts to +- measure execution time and the number of quantifier instantiations +and store the results in a csv file (`profile.py`) +- plot the data from one or more csv files (`plot.py`) +- profile and plot every file in `experiments/` (`profile-all.sh`) + +## `selected_plots/` +Contains plots comparing the results from different experiments. + +## `experiments/` +### `program_proofs_example_10_2/` +We use the proof for `InsertCorrect` from [chapter 10.2 of Program Proofs encoded in Gobra] (https://github.com/viperproject/program-proofs-gobra/blob/main/chapter10/examples_10.2.gobra) +to investigate the effect of "assisting" the verifier on execution time +and quantifier instantiations by means of intermediate assertions. + +### `standard_library/` +We use parts of the standard library to investigate the effect of +making lemmas `opaque` on execution time and quantifier +instantiations. + +### `synthetic_set/` +We create a synthetic example using sets that exhibits a relatively +high number of quantifier instantiations to investigate the effect of +- disabling set axiomatization and using the standard library to +manually prove all proof obligations +- "assisting" the verifier by calling lemmas from the standard library +that may be useful to prove the proof obligations + +on execution time and quantifier instantiations. + +Note that `fully_assisted/` is used for both types of experiments; the +difference is that in one case we disable set axiomatization by +passing the corresponding flag, while in the other case we do not. \ No newline at end of file From 3a0515d331c41beaab355ef03677f4490bc67f54 Mon Sep 17 00:00:00 2001 From: Daniel Nezamabadi <55559979+dnezam@users.noreply.github.com> Date: Thu, 25 Apr 2024 12:05:38 +0200 Subject: [PATCH 11/13] Fix link in evaluation/README.md --- evaluation/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/evaluation/README.md b/evaluation/README.md index e2d5f3d..9d27819 100644 --- a/evaluation/README.md +++ b/evaluation/README.md @@ -16,7 +16,7 @@ Contains plots comparing the results from different experiments. ## `experiments/` ### `program_proofs_example_10_2/` -We use the proof for `InsertCorrect` from [chapter 10.2 of Program Proofs encoded in Gobra] (https://github.com/viperproject/program-proofs-gobra/blob/main/chapter10/examples_10.2.gobra) +We use the proof for `InsertCorrect` from [chapter 10.2 of Program Proofs encoded in Gobra](https://github.com/viperproject/program-proofs-gobra/blob/main/chapter10/examples_10.2.gobra) to investigate the effect of "assisting" the verifier on execution time and quantifier instantiations by means of intermediate assertions. From 95781f558b3648d2a140b706a300a461b3bd0bb6 Mon Sep 17 00:00:00 2001 From: dnezam <55559979+dnezam@users.noreply.github.com> Date: Fri, 26 Apr 2024 11:14:59 +0200 Subject: [PATCH 12/13] Use python3 + Extend README --- evaluation/README.md | 29 +++++++++++++++++++++++++++++ evaluation/scripts/profile-all.sh | 6 +++--- 2 files changed, 32 insertions(+), 3 deletions(-) diff --git a/evaluation/README.md b/evaluation/README.md index 9d27819..f899ace 100644 --- a/evaluation/README.md +++ b/evaluation/README.md @@ -11,6 +11,35 @@ and store the results in a csv file (`profile.py`) - plot the data from one or more csv files (`plot.py`) - profile and plot every file in `experiments/` (`profile-all.sh`) +### Dependencies and Usage +plot.py has the following dependencies: +- pandas +- numpy +- seaborn +- matplotlib +Install these packages using your favorite package manager +for Python packages (e.g., apt, pacman, nix, pip, conda, etc.). + +profile.py requires the path to the following files: +- silicon.sh +- Z3 (version 4.8.7) +- Gobra jar +We have only tested Z3 4.8.7; newer versions may not work as they produce +errors and different output. Additionally, in case you get errors of +the form +``` + metadata["silicon_version"] = command_stdout.splitlines()[0].split()[-1][1:-2] + ~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^ +IndexError: list index out of range +``` +there may be an issue with Silicon. In this case, consider pulling Silicon's +source again, followed by building its jar. + +Examples for the usage of plot.py can be found in +selected_plots/used_commands.md and profile-all.sh. +For the usage of profile.py, please take a look at its usage in +profile-all.sh. Finally, profile-all.sh contains comments describing its usage. + ## `selected_plots/` Contains plots comparing the results from different experiments. diff --git a/evaluation/scripts/profile-all.sh b/evaluation/scripts/profile-all.sh index a2bb0e9..497a238 100644 --- a/evaluation/scripts/profile-all.sh +++ b/evaluation/scripts/profile-all.sh @@ -49,10 +49,10 @@ if [ -z "$GOBRA_PATH" ]; then fi # profile with disabled set axioms -python profile.py ../experiments/synthetic_set/fully_assisted/fully_assisted.gobra --disableSetAxiomatization --z3RandomizeSeeds --iterations $ITERATIONS --silicon_path $SILICON_PATH --z3_path $Z3_PATH --gobra $GOBRA_PATH +python3 profile.py ../experiments/synthetic_set/fully_assisted/fully_assisted.gobra --disableSetAxiomatization --z3RandomizeSeeds --iterations $ITERATIONS --silicon_path $SILICON_PATH --z3_path $Z3_PATH --gobra $GOBRA_PATH # profile all files "normally" -find ../experiments -type f -name "*.gobra" -exec python profile.py {} --z3RandomizeSeeds --iterations $ITERATIONS --silicon_path $SILICON_PATH --z3_path $Z3_PATH --gobra $GOBRA_PATH \; +find ../experiments -type f -name "*.gobra" -exec python3 profile.py {} --z3RandomizeSeeds --iterations $ITERATIONS --silicon_path $SILICON_PATH --z3_path $Z3_PATH --gobra $GOBRA_PATH \; # generate plots for every csv -find ../experiments -type f -name "*.csv" -exec python plot.py --qi_size 9 9 {} \; +find ../experiments -type f -name "*.csv" -exec python3 plot.py --qi_size 9 9 {} \; From e6b5c5eedc024c6c70466bf345a6c67053647f3e Mon Sep 17 00:00:00 2001 From: dnezam <55559979+dnezam@users.noreply.github.com> Date: Fri, 26 Apr 2024 11:36:09 +0200 Subject: [PATCH 13/13] Make profile-all.sh executable --- evaluation/scripts/profile-all.sh | 0 1 file changed, 0 insertions(+), 0 deletions(-) mode change 100644 => 100755 evaluation/scripts/profile-all.sh diff --git a/evaluation/scripts/profile-all.sh b/evaluation/scripts/profile-all.sh old mode 100644 new mode 100755

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b/evaluation/experiments/program_proofs_example_10_2/last_half/last_half.gobra @@ -0,0 +1,110 @@ +// This package contains the last half of the proof for InsertCorrect from +// https://github.com/viperproject/program-proofs-gobra/blob/main/chapter10/examples_10.2.gobra +package last_half + +// Note that some parts that come after the induction hypothesis require +// definitions that originally came before the IH. +// Those dependencies are included at their original position. +ghost +requires pq.Valid() +ensures let pqPrime := pq.Insert(y) in + pqPrime.Valid() && + pqPrime.Elements() == pq.Elements() union mset[int]{y} +decreases len(pq) +pure func (pq PQueue) InsertCorrect(y int) Unit { + return match pq { + case Leaf{}: + Unit{} + case Node{?x, ?l, ?r}: + let pqPrime := pq.Insert(y) in + let max := y < x ? x : y in + let _ := r.InsertCorrect(max) in + let newRight := r.Insert(max) in + let _ := asserting(newRight.Valid()) in + let _ := asserting(newRight.IsBalanced()) in + let _ := asserting(l.IsBalanced()) in + let _ := asserting( + let Lprime := len(newRight.Elements()) in + let Rprime := len(l.Elements()) in + Lprime == Rprime || Lprime == Rprime + 1) in + let _ := asserting(pqPrime.IsBalanced()) in + asserting(pqPrime.IsBinaryHeap()) + } +} + +ghost +decreases len(pq) +pure func (pq PQueue) Valid() bool { + return pq.IsBinaryHeap() && pq.IsBalanced() +} + +ghost +decreases len(pq) +pure func (pq PQueue) Insert(y int) PQueue { + return match pq { + case Leaf{}: + Node{y, Leaf{}, Leaf{}} + case Node{?x, ?left, ?right}: + y < x ? Node{y, right.Insert(x), left} : Node{x, right.Insert(y), left} + } +} + +ghost +decreases len(pq) +pure func (pq PQueue) Elements() mset[int] { + return match pq { + case Leaf{}: + mset[int]{} + case Node{?x, ?left, ?right}: + mset[int]{x} union left.Elements() union right.Elements() + } +} + +ghost +decreases len(pq) +pure func (pq PQueue) IsBalanced() (res bool) { + return match pq { + case Leaf{}: + true + case Node{_, ?left, ?right}: + left.IsBalanced() && right.IsBalanced() && + (let L := len(left.Elements()) in + let R := len(right.Elements()) in + L == R || L == R + 1) + } +} + +ghost +decreases len(pq) +pure func (pq PQueue) IsBinaryHeap() bool { + return match pq { + case Leaf{}: + true + case Node{?x, ?left, ?right}: + left.IsBinaryHeap() && right.IsBinaryHeap() && + (left == Leaf{} || x <= left.x) && + (right == Leaf{} || x <= right.x) + } +} + + +type Unit struct{} + +ghost +requires b +decreases +pure func asserting(b bool) Unit { + return Unit{} +} + +type PQueue = BraunTree + +type BraunTree adt { + Leaf {} + + Node { + x int + left BraunTree + right BraunTree + } +} diff --git a/evaluation/experiments/program_proofs_example_10_2/minimal/minimal-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv b/evaluation/experiments/program_proofs_example_10_2/minimal/minimal-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv new file mode 100644 index 0000000..84727cf --- /dev/null +++ b/evaluation/experiments/program_proofs_example_10_2/minimal/minimal-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv @@ -0,0 +1,31 @@ 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a/evaluation/experiments/standard_library/dicts_not_opaque/dicts_not_opaque.gobra b/evaluation/experiments/standard_library/dicts_not_opaque/dicts_not_opaque.gobra new file mode 100644 index 0000000..e0ae0b8 --- /dev/null +++ b/evaluation/experiments/standard_library/dicts_not_opaque/dicts_not_opaque.gobra @@ -0,0 +1,451 @@ +// A copy of the dicts package from the standard library. +// Lemmas are turned non-opaque. Uses the non-opaque version of the sets +// package. +package dicts_not_opaque + +// ##(-I ./..) + +import "util" +import "sets_not_opaque" + +// A dictionary is empty if its domain is empty. +ghost +decreases +pure func IsEmpty(d dict[int]int) bool { + return sets_not_opaque.IsEmpty(domain(d)) +} + +// Returns the empty dictionary. +ghost +ensures IsEmpty(result) +decreases +pure func Empty() (result dict[int]int) { + return dict[int]int{} +} + +// Retrieves the value associated with the key, if present, as an option. +ghost +decreases +pure func Get(d dict[int]int, k int) option[int] { + return k in domain(d) ? some(d[k]) : none[int] +} + +// Keep all key-value pairs corresponding to the set of keys provided. +ghost +opaque +ensures forall x int :: {result[x]} (x in domain(d) && x in xs) ==> + (x in domain(result) && result[x] == d[x]) +ensures forall x int :: {x in domain(result)} x in domain(result) ==> + (x in domain(d) && x in xs) +ensures domain(result) == xs intersection domain(d) +decreases xs +pure func Restrict(d dict[int]int, xs set[int]) (result dict[int]int) { + return let ys := (xs intersection domain(d)) in + (sets_not_opaque.IsEmpty(ys) ? Empty() : + (let y := sets_not_opaque.Choose(ys) in + (let yr := sets_not_opaque.Remove(ys, y) in + (let _ := sets_not_opaque.IntersectLenUpper(xs, domain(d)) in + Restrict(d, yr)[y = d[y]])))) +} + +// Remove all key-value pairs corresponding to the set of keys provided. +ghost +decreases +pure func RemoveKeys(d dict[int]int, xs set[int]) (result dict[int]int) { + return Restrict(d, domain(d) setminus xs) +} + +// Remove a key-value pair. Returns d if k is not in the domain of d. +ghost +ensures len(result) <= len(d) +ensures k in domain(d) ==> len(result) == len(d) - 1 +ensures !(k in domain(d)) ==> len(result) == len(d) +decreases +pure func Remove(d dict[int]int, k int) (result dict[int]int) { + return let ys := (sets_not_opaque.Remove(domain(d), k)) in + let _ := util.Asserting(ys intersection domain(d) == ys) in + RemoveKeys(d, sets_not_opaque.SingletonSet(k)) +} + +// True iff k maps to the same value or is not in the domains of d1 and d2. +ghost +decreases +pure func IsEqualOnKey(d1, d2 dict[int]int, k int) bool { + return !(k in domain(d1) || k in domain(d2)) || + (k in domain(d1) && k in domain(d2) && d1[k] == d2[k]) +} + +// True iff if d1 is a subset of d2. +ghost +decreases +pure func IsSubset(d1, d2 dict[int]int) bool { + return domain(d1) subset domain(d2) && + forall k int :: {IsEqualOnKey(d1, d2, k)} {k in domain(d1)} (k in domain(d1)) ==> + IsEqualOnKey(d1, d2, k) +} + +// Union of two dictionaries. Does not require disjoint domains: on the intersection, +// values from the second dictionary are chosen. +ghost +opaque +ensures domain(result) == domain(d1) union domain(d2) +ensures forall k int :: {result[k]} (k in domain(d2)) ==> result[k] == d2[k] +ensures forall k int :: {result[k]} (!(k in domain(d2)) && k in domain(d1)) ==> + result[k] == d1[k] +decreases domain(d1) union domain(d2) +pure func Union(d1, d2 dict[int]int) (result dict[int]int) { + return let ks := domain(d1) union domain(d2) in + (sets_not_opaque.IsEmpty(ks) ? Empty() : + let k := sets_not_opaque.Choose(ks) in + let c1 := Remove(d1, k) in + let c2 := Remove(d2, k) in + let _ := sets_not_opaque.RemoveUnionLen(domain(d1), domain(d2), k) in + (k in domain(d2) ? Union(c1, c2)[k = d2[k]] : Union(c1, c2)[k = d1[k]])) +} + +// Dictionaries are disjoint iff their domains are disjoint. +ghost +decreases +pure func AreDisjoint(d1, d2 dict[int]int) bool { + return sets_not_opaque.AreDisjoint(domain(d1), domain(d2)) +} + +// The length of the union of two disjoint dictionaries is the sum of each of their lengths. +ghost +requires AreDisjoint(d1, d2) +ensures len(Union(d1, d2)) == len(d1) + len(d2) +decreases +pure func DisjointUnionLen(d1, d2 dict[int]int) util.Unit { + return util.Unit{} +} + +// True iff a dictionary is injective. +ghost +opaque +decreases +pure func IsInjective(d dict[int]int) bool { + return forall k1, k2 int :: {d[k1], d[k2]} (k1 != k2 && k1 in domain(d) && k2 in domain(d)) ==> + d[k1] != d[k2] +} + +// True iff a dictionary contains all valid keys. +ghost +opaque +decreases +pure func IsTotal(d dict[int]int) bool { + return forall k int :: {k in domain(d)} k in domain(d) +} + +// True iff a dictionary is monotonic. +ghost +opaque +decreases +pure func IsMonotonic(d dict[int]int) bool { + return forall k1, k2 int :: {d[k1], d[k2]} (k1 in domain(d) && k2 in domain(d) && k1 <= k2) ==> + d[k1] <= d[k2] +} + +// True iff a dictionary is monotonic. Only considers keys greater than or equal to start. +ghost +opaque +decreases +pure func IsMonotonicFrom(d dict[int]int, start int) bool { + return forall k1, k2 int :: {d[k1], d[k2]} (k1 in domain(d) && k2 in domain(d) && start <= k1 && k1 <= k2) ==> + d[k1] <= d[k2] +} + +// True iff a dictionary is monotonic. Only considers keys in the interval [start, end). +ghost +opaque +decreases +pure func IsMonotonicFromTo(d dict[int]int, start, end int) bool { + return forall k1, k2 int :: {d[k1], d[k2]} (k1 in domain(d) && + k2 in domain(d) && + start <= k1 && k1 <= k2 && k2 < end) ==> d[k1] <= d[k2] +} + +// True iff two dictionaries are equal in the interval [start, end). +ghost +opaque +decreases +pure func IsEqualInRange(d1, d2 dict[int]int, start, end int) bool { + return forall k int :: {d1[k], d2[k]} {k in domain(d1)} {k in domain(d2)}(start <= k && k < end) ==> + k in domain(d1) && k in domain(d2) && d1[k] == d2[k] +} + +// True iff d1 and d2 agree on all keys that their domains share. +ghost +decreases +pure func Agree(d1, d2 dict[int]int) bool { + return forall k int :: {d1[k], d2[k]} k in (domain(d1) intersection domain(d2)) ==> + d1[k] == d2[k] +} + +// The domain of a map after removing a key is equivalent to removing +// the key from the domain of the original map. +ghost +ensures domain(Remove(d, k)) == sets_not_opaque.Remove(domain(d), k) +decreases +pure func RemoveDomain(d dict[int]int, k int) util.Unit { + return util.Unit{} +} + +// The domain of the empty dictionary is the empty set. +ghost +requires IsEmpty(d) +ensures domain(d) == sets_not_opaque.Empty() +decreases +pure func EmptyDictEmptyDomain(d dict[int]int) util.Unit { + return util.Unit{} +} + +// The domain of a dictionary after inserting a key-value pair is equivalent to +// inserting the key into the original map's domain set. +ghost +ensures domain(d[k = v]) == sets_not_opaque.Add(domain(d), k) +decreases +pure func InsertDomain(d dict[int]int, k, v int) util.Unit { + return util.Unit{} +} + +// Inserting value at k in d results in a dictionary that maps k to v. +ghost +ensures d[k = v][k] == v +decreases +pure func UpdateSame(d dict[int]int, k, v int) util.Unit { + return util.Unit{} +} + +// Reassigning the corresponding value to a key does not change the dictionary. +ghost +requires k in domain(d) +requires v == d[k] +ensures d[k = v] == d +decreases +pure func UpdateEqual(d dict[int]int, k, v int) util.Unit { + return util.Unit{} +} + +// Inserting v at k2 does not change the value mapped to by any other keys in d. +ghost +requires k1 != k2 +ensures k2 in domain(d[k1 = v]) == k2 in domain(d) +ensures k2 in domain(d) ==> d[k1 = v][k2] == d[k2] +decreases +pure func UpdateDifferent(d dict[int]int, k1, k2, v int) util.Unit { + return util.Unit{} +} + +// Removing a key-value pair from a dictionary does not change the value mapped to +// by any other keys in the map. +ghost +requires k1 in domain(d) +requires k1 != k2 +ensures Remove(d, k2)[k1] == d[k1] +decreases +pure func RemoveDifferent(d dict[int]int, k1, k2 int) util.Unit { + return util.Unit{} +} + +// Two maps are equivalent if their domains are equivalent and every key in their +// domains map to the same value. +ghost +ensures (d1 == d2) == + (domain(d1) == domain(d2) && forall k int :: {d1[k], d2[k]} k in domain(d1) ==> d1[k] == d2[k]) +decreases +pure func ExtEqual(d1, d2 dict[int]int) util.Unit { + return util.Unit{} +} + +// The cardinality of a dictionary is non-negative. +ghost +ensures len(d) >= 0 +decreases +pure func NonNegativeLen(d dict[int]int) util.Unit { + return util.Unit{} +} + +// The cardinality of a dictionary is equal to the cardinality of its domain. +ghost +ensures len(d) == len(domain(d)) +decreases +pure func DomainLenEq(d dict[int]int) util.Unit { + return util.Unit{} +} + +// If two dictionaries are disjoint there is no key that is in both of their domains. +ghost +requires AreDisjoint(d1, d2) +ensures !(k in domain(d1) && k in domain(d2)) +decreases +pure func DisjointNoSharedKey(d1, d2 dict[int]int, k int) util.Unit { + return util.Unit{} +} + +// If two dictionaries are not disjoint, there exists a key that is in both of their domains. +ghost +requires !AreDisjoint(d1, d2) +ensures exists k int :: {k in domain(d1), k in domain(d2)} k in domain(d1) && k in domain(d2) +decreases +pure func NotDisjointSharedKey(d1, d2 dict[int]int) util.Unit { + return util.Unit{} +} + +// There is only one empty map. +ghost +requires IsEmpty(d) +ensures d == Empty() +decreases +pure func EmptyIsUnique(d dict[int]int) util.Unit { + return util.Unit{} +} + +// An empty dictionary contains no keys. +ghost +requires IsEmpty(d) +ensures !(k in domain(d)) +decreases +pure func NotInEmpty(d dict[int]int, k int) util.Unit { + return util.Unit{} +} + +// There exists a key in a non-empty dictionary. +ghost +requires !IsEmpty(d) +ensures exists k int :: {k in domain(d)} k in domain(d) +decreases +pure func NotEmptyKeyExists(d dict[int]int, k int) util.Unit { + return util.Unit{} +} + +// If a key is in d, d is not empty. +ghost +requires k in domain(d) +ensures !IsEmpty(d) +decreases +pure func KeyInDomainDictNotEmpty(d dict[int]int, k int) util.Unit { + return util.Unit{} +} + +// Inserting a new key increases the cardinality of the dictionary by 1. +// Updating the value of a key does not change the cardinality. +ghost +ensures k in domain(d) ==> len(d[k = v]) == len(d) +ensures !(k in domain(d)) ==> len(d[k = v]) == len(d) + 1 +decreases +pure func InsertUpdateLen(d dict[int]int, k, v int) util.Unit { + return util.Unit{} +} + +// If a value is in the range of a dictionary, there exists a corresponding key. +ghost +requires v in range(d) +ensures exists k int :: {k in domain(d)} k in domain(d) && d[k] == v +decreases +pure func ValueHasKey(d dict[int]int, v int) util.Unit { + return util.Unit{} +} + +// If a value is in the domain of a dictionary, the corresponding value is in its range. +ghost +requires k in domain(d) +ensures d[k] in range(d) +decreases +pure func KeyMapsToRange(d dict[int]int, k int) util.Unit { + return util.Unit{} +} + +// Returns a dictionary with the values at k1 and k2 swapped. +ghost +requires k1 in domain(d) && k2 in domain(d) +ensures domain(result) == domain(d) +ensures result[k1] == d[k2] && result[k2] == d[k1] +ensures forall k int :: {result[k]} (k in domain(d) && k != k1 && k != k2) ==> + result[k] == d[k] +decreases +pure func Swap(d dict[int]int, k1, k2 int) (result dict[int]int) { + return d[k1 = d[k2]][k2 = d[k1]] +} + +// Returns the set of keys from the given dictionary that map to the specified value. +ghost +opaque +ensures forall k int :: {k in result} (k in domain(d) && d[k] == v) == (k in result) +decreases len(d) +pure func Keys(d dict[int]int, v int) (result set[int]) { + return IsEmpty(d) ? sets_not_opaque.Empty() : + (let x := sets_not_opaque.Choose(domain(d)) in + (let subKeys := Keys(Remove(d, x), v) in + (d[x] == v ? sets_not_opaque.Add(subKeys, x) : subKeys))) + +} + +// Returns the number of occurences of the value in the dictionary. +ghost +decreases +pure func Occurrences(d dict[int]int, v int) int { + return len(Keys(d, v)) +} + +// Remove preserves the injectivity of a dictionary. +ghost +requires IsInjective(d) +ensures IsInjective(Remove(d, k)) +decreases +pure func RemovePreservesInjectivity(d dict[int]int, k int) util.Unit { + return let _ := reveal IsInjective(d) in + let _ := reveal IsInjective(Remove(d, k)) in + util.Unit{} +} + +// After removing a key, the corresponding value occurs one less time. +ghost +requires k in domain(d) +ensures Occurrences(Remove(d, k), d[k]) == Occurrences(d, d[k]) - 1 +decreases +pure func RemoveOccurrences(d dict[int]int, k int) util.Unit { + return let ks1 := reveal Keys(d, d[k]) in + let ks2 := reveal Keys(Remove(d, k), d[k]) in + util.Asserting(ks2 == sets_not_opaque.Remove(ks1, k)) +} + +// Adding a new key-value pair increases the occurrence of the value by one. +ghost +requires !(k in domain(d)) +ensures Occurrences(d[k = v], v) == Occurrences(d, v) + 1 +decreases +pure func AddOccurrences(d dict[int]int, k, v int) util.Unit { + return let ks1 := reveal Keys(d, v) in + let ks2 := reveal Keys(d[k = v], v) in + util.Asserting(ks2 == sets_not_opaque.Add(ks1, k)) +} + +// Updating a key to a new value results in an additional occurrences for the +// new value, and one less occurrence for the old value. +ghost +requires k in domain(d) +requires v != d[k] +ensures Occurrences(d[k = v], v) == Occurrences(d, v) + 1 +ensures Occurrences(d[k = v], d[k]) == Occurrences(d, d[k]) - 1 +decreases +pure func UpdateOccurrences(d dict[int]int, k, v int) util.Unit { + return let ks1v := reveal Keys(d, v) in + let ks2v := reveal Keys(d[k = v], v) in + let _ := util.Asserting(ks2v == sets_not_opaque.Add(ks1v, k)) in + let ks1dk := reveal Keys(d, d[k]) in + let ks2dk := reveal Keys(d[k = v], d[k]) in + util.Asserting(ks2dk == sets_not_opaque.Remove(ks1dk, k)) +} + +// v can occur at most once as a value in injective dictionaries. +ghost +requires IsInjective(d) +ensures Occurrences(d, v) <= 1 +decreases len(d) +pure func InjectiveOccurrences(d dict[int]int, v int) util.Unit { + return Occurrences(d, v) <= 1 ? util.Unit{} : + let x1 := sets_not_opaque.Choose(Keys(d, v)) in + let x2 := sets_not_opaque.Choose(sets_not_opaque.Remove(Keys(d, v), x1)) in + let _ := reveal IsInjective(d) in + util.Unit{} +} diff --git a/evaluation/experiments/standard_library/dicts_opaque/dicts_opaque-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv b/evaluation/experiments/standard_library/dicts_opaque/dicts_opaque-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv new file mode 100644 index 0000000..07a1f92 --- /dev/null +++ b/evaluation/experiments/standard_library/dicts_opaque/dicts_opaque-rand-iter_30-gran_1-sil_ver_0608ac9-z3_ver_4_8_7-gobra_ver_0608ac92.csv @@ -0,0 +1,31 @@ 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