Fix pat->Condition[...] apply rules

CHANGES.rst

@@ -72,6 +72,7 @@ Bugs
 
 # ``0`` with a given precision (like in ```0`3```) is now parsed as ``0``, an integer number.
 #. ``RandomSample`` with one list argument now returns a random ordering of the list items. Previously it would return just one item.
+#. Rules of the form ``pat->Condition[expr, cond]`` are handled as in WL. The same also works for nested `Condition` expressions. In particular, the comparison between two Rules with the same pattern but an iterated ``Condition`` expressionare considered equal if the conditions are the same. 
 #. Origin placement corrected on ``ListPlot`` and ``LinePlot``.
 #. Fix long-standing bugs in Image handling
 

mathics/builtin/assignments/assignment.py

@@ -211,11 +211,21 @@ class SetDelayed(Set):
     'Condition' ('/;') can be used with 'SetDelayed' to make an
     assignment that only holds if a condition is satisfied:
     >> f[x_] := p[x] /; x>0
+    >> f[x_] := p[-x]/; x<-2
     >> f[3]
      = p[3]
     >> f[-3]
-     = f[-3]
-    It also works if the condition is set in the LHS:
+     = p[3]
+    >> f[-1]
+     = f[-1]
+    Notice that the LHS is the same in both definitions, but the second
+    does not overwrite the first one.
+
+    To overwrite one of these definitions, we have to assign using the same condition:
+    >> f[x_] := Sin[x] /; x>0
+    >> f[3]
+     = Sin[3] 
+    In a similar way, the condition can be set in the LHS:
     >> F[x_, y_] /; x < y /; x>0  := x / y;
     >> F[x_, y_] := y / x;
     >> F[2, 3]

mathics/builtin/patterns.py

@@ -163,7 +163,8 @@ def create_rules(rules_expr, expr, name, evaluation, extra_args=[]):
     else:
         result = []
         for rule in rules:
-            if rule.get_head_name() not in ("System`Rule", "System`RuleDelayed"):
+            head_name = rule.get_head_name()
+            if head_name not in ("System`Rule", "System`RuleDelayed"):
                 evaluation.message(name, "reps", rule)
                 return None, True
             elif len(rule.elements) != 2:
@@ -177,7 +178,13 @@ def create_rules(rules_expr, expr, name, evaluation, extra_args=[]):
                 )
                 return None, True
             else:
-                result.append(Rule(rule.elements[0], rule.elements[1]))
+                result.append(
+                    Rule(
+                        rule.elements[0],
+                        rule.elements[1],
+                        delayed=(head_name == "System`RuleDelayed"),
+                    )
+                )
         return result, False
 
 
@@ -1706,7 +1713,7 @@ def __init__(self, rulelist, evaluation):
         self._elements = None
         self._head = SymbolDispatch
 
-    def get_sort_key(self) -> tuple:
+    def get_sort_key(self, pattern_sort=False) -> tuple:
         return self.src.get_sort_key()
 
     def get_atom_name(self):

mathics/core/definitions.py

@@ -10,11 +10,13 @@
 
 from mathics_scanner.tokeniser import full_names_pattern
 
-from mathics.core.atoms import String
+from mathics.core.atoms import Integer, String
 from mathics.core.attributes import A_NO_ATTRIBUTES
 from mathics.core.convert.expression import to_mathics_list
 from mathics.core.element import fully_qualified_symbol_name
 from mathics.core.expression import Expression
+from mathics.core.pattern import Pattern
+from mathics.core.rules import Rule
 from mathics.core.symbols import Atom, Symbol, strip_context
 from mathics.core.systemsymbols import SymbolGet
 
@@ -642,9 +644,6 @@ def get_ownvalue(self, name):
         return None
 
     def set_ownvalue(self, name, value) -> None:
-        from .expression import Symbol
-        from .rules import Rule
-
         name = self.lookup_name(name)
         self.add_rule(name, Rule(Symbol(name), value))
         self.clear_cache(name)
@@ -680,8 +679,6 @@ def get_config_value(self, name, default=None):
             return default
 
     def set_config_value(self, name, new_value) -> None:
-        from mathics.core.expression import Integer
-
         self.set_ownvalue(name, Integer(new_value))
 
     def set_line_no(self, line_no) -> None:
@@ -701,6 +698,25 @@ def get_history_length(self):
 
 
 def get_tag_position(pattern, name) -> Optional[str]:
+    # Strip first the pattern from HoldPattern, Pattern
+    # and Condition wrappings
+    while True:
+        # TODO: Not Atom/Expression,
+        # pattern -> pattern.to_expression()
+        if isinstance(pattern, Pattern):
+            pattern = pattern.expr
+            continue
+        if pattern.has_form("System`HoldPattern", 1):
+            pattern = pattern.elements[0]
+            continue
+        if pattern.has_form("System`Pattern", 2):
+            pattern = pattern.elements[1]
+            continue
+        if pattern.has_form("System`Condition", 2):
+            pattern = pattern.elements[0]
+            continue
+        break
+
     if pattern.get_name() == name:
         return "own"
     elif isinstance(pattern, Atom):
@@ -709,10 +725,8 @@ def get_tag_position(pattern, name) -> Optional[str]:
         head_name = pattern.get_head_name()
         if head_name == name:
             return "down"
-        elif head_name == "System`N" and len(pattern.elements) == 2:
+        elif pattern.has_form("System`N", 2):
             return "n"
-        elif head_name == "System`Condition" and len(pattern.elements) > 0:
-            return get_tag_position(pattern.elements[0], name)
         elif pattern.get_lookup_name() == name:
             return "sub"
         else:
@@ -722,11 +736,18 @@ def get_tag_position(pattern, name) -> Optional[str]:
         return None
 
 
-def insert_rule(values, rule) -> None:
+def insert_rule(values: list, rule: Rule) -> None:
+    rhs_conds = getattr(rule, "rhs_conditions", [])
     for index, existing in enumerate(values):
         if existing.pattern.sameQ(rule.pattern):
-            del values[index]
-            break
+            # Check for coincidences in the replace conditions,
+            # it they are there.
+            # This ensures that the rules are equivalent even taking
+            # into accound the RHS conditions.
+            existing_rhs_conds = getattr(existing, "rhs_conditions", [])
+            if existing_rhs_conds == rhs_conds:
+                del values[index]
+                break
     # use insort_left to guarantee that if equal rules exist, newer rules will
     # get higher precedence by being inserted before them. see DownValues[].
     bisect.insort_left(values, rule)

mathics/core/rules.py

@@ -7,7 +7,7 @@
 from mathics.core.element import KeyComparable
 from mathics.core.expression import Expression
 from mathics.core.pattern import Pattern, StopGenerator
-from mathics.core.symbols import strip_context
+from mathics.core.symbols import SymbolTrue, strip_context
 
 
 def _python_function_arguments(f):
@@ -18,6 +18,10 @@ def function_arguments(f):
     return _python_function_arguments(f)
 
 
+class StopMatchConditionFailed(StopGenerator):
+    pass
+
+
 class StopGenerator_BaseRule(StopGenerator):
     pass
 
@@ -58,7 +62,11 @@ def yield_match(vars, rest):
                 if name.startswith("_option_"):
                     options[name[len("_option_") :]] = value
                     del vars[name]
-            new_expression = self.do_replace(expression, vars, options, evaluation)
+            try:
+                new_expression = self.do_replace(expression, vars, options, evaluation)
+            except StopMatchConditionFailed:
+                return
+
             if new_expression is None:
                 new_expression = expression
             if rest[0] or rest[1]:
@@ -106,7 +114,7 @@ def yield_match(vars, rest):
     def do_replace(self):
         raise NotImplementedError
 
-    def get_sort_key(self) -> tuple:
+    def get_sort_key(self, pattern_sort=False) -> tuple:
         # FIXME: check if this makes sense:
         return tuple((self.system, self.pattern.get_sort_key(True)))
 
@@ -130,12 +138,131 @@ class Rule(BaseRule):
     ``G[1.^2, a^2]``
     """
 
-    def __init__(self, pattern, replace, system=False) -> None:
+    def __ge__(self, other):
+        if isinstance(other, Rule):
+            sys, key, rhs_cond = self.get_sort_key()
+            sys_other, key_other, rhs_cond_other = other.get_sort_key()
+            if sys != sys_other:
+                return sys > sys_other
+            if key != key_other:
+                return key > key_other
+
+            # larger and more complex conditions come first
+            len_cond, len_cond_other = len(rhs_cond), len(rhs_cond_other)
+            if len_cond != len_cond_other:
+                return len_cond_other > len_cond
+            if len_cond == 0:
+                return False
+            for me_cond, other_cond in zip(rhs_cond, rhs_cond_other):
+                me_sk = me_cond.get_sort_key(True)
+                o_sk = other_cond.get_sort_key(True)
+                if me_sk > o_sk:
+                    return False
+            return True
+        # Follow the usual rule
+        return self.get_sort_key(True) >= other.get_sort_key(True)
+
+    def __gt__(self, other):
+        if isinstance(other, Rule):
+            sys, key, rhs_cond = self.get_sort_key()
+            sys_other, key_other, rhs_cond_other = other.get_sort_key()
+            if sys != sys_other:
+                return sys > sys_other
+            if key != key_other:
+                return key > key_other
+
+            # larger and more complex conditions come first
+            len_cond, len_cond_other = len(rhs_cond), len(rhs_cond_other)
+            if len_cond != len_cond_other:
+                return len_cond_other > len_cond
+            if len_cond == 0:
+                return False
+
+            for me_cond, other_cond in zip(rhs_cond, rhs_cond_other):
+                me_sk = me_cond.get_sort_key(True)
+                o_sk = other_cond.get_sort_key(True)
+                if me_sk > o_sk:
+                    return False
+            return me_sk > o_sk
+        # Follow the usual rule
+        return self.get_sort_key(True) > other.get_sort_key(True)
+
+    def __le__(self, other):
+        if isinstance(other, Rule):
+            sys, key, rhs_cond = self.get_sort_key()
+            sys_other, key_other, rhs_cond_other = other.get_sort_key()
+            if sys != sys_other:
+                return sys < sys_other
+            if key != key_other:
+                return key < key_other
+
+            # larger and more complex conditions come first
+            len_cond, len_cond_other = len(rhs_cond), len(rhs_cond_other)
+            if len_cond != len_cond_other:
+                return len_cond_other < len_cond
+            if len_cond == 0:
+                return False
+            for me_cond, other_cond in zip(rhs_cond, rhs_cond_other):
+                me_sk = me_cond.get_sort_key(True)
+                o_sk = other_cond.get_sort_key(True)
+                if me_sk < o_sk:
+                    return False
+            return True
+        # Follow the usual rule
+        return self.get_sort_key(True) <= other.get_sort_key(True)
+
+    def __lt__(self, other):
+        if isinstance(other, Rule):
+            sys, key, rhs_cond = self.get_sort_key()
+            sys_other, key_other, rhs_cond_other = other.get_sort_key()
+            if sys != sys_other:
+                return sys < sys_other
+            if key != key_other:
+                return key < key_other
+
+            # larger and more complex conditions come first
+            len_cond, len_cond_other = len(rhs_cond), len(rhs_cond_other)
+            if len_cond != len_cond_other:
+                return len_cond_other < len_cond
+            if len_cond == 0:
+                return False
+
+            for me_cond, other_cond in zip(rhs_cond, rhs_cond_other):
+                me_sk = me_cond.get_sort_key(True)
+                o_sk = other_cond.get_sort_key(True)
+                if me_sk < o_sk:
+                    return False
+            return me_sk > o_sk
+        # Follow the usual rule
+        return self.get_sort_key(True) < other.get_sort_key(True)
+
+    def __init__(self, pattern, replace, delayed=True, system=False) -> None:
         super(Rule, self).__init__(pattern, system=system)
         self.replace = replace
+        self.delayed = delayed
+        # If delayed is True, and replace is a nested
+        # Condition expression, stores the conditions and the
+        # remaining stripped expression.
+        # This is going to be used to compare and sort rules,
+        # and also to decide if the rule matches an expression.
+        conds = []
+        if delayed:
+            while replace.has_form("System`Condition", 2):
+                replace, cond = replace.elements
+                conds.append(cond)
+
+        self.rhs_conditions = sorted(conds)
+        self.strip_replace = replace
 
     def do_replace(self, expression, vars, options, evaluation):
-        new = self.replace.replace_vars(vars)
+        replace = self.replace if self.rhs_conditions == [] else self.strip_replace
+        for cond in self.rhs_conditions:
+            cond = cond.replace_vars(vars)
+            cond = cond.evaluate(evaluation)
+            if cond is not SymbolTrue:
+                raise StopMatchConditionFailed
+
+        new = replace.replace_vars(vars)
         new.options = options
 
         # if options is a non-empty dict, we need to ensure reevaluation of the whole expression, since 'new' will
@@ -158,6 +285,12 @@ def do_replace(self, expression, vars, options, evaluation):
     def __repr__(self) -> str:
         return "<Rule: %s -> %s>" % (self.pattern, self.replace)
 
+    def get_sort_key(self, pattern_sort=False) -> tuple:
+        # FIXME: check if this makes sense:
+        return tuple(
+            (self.system, self.pattern.get_sort_key(True), self.rhs_conditions)
+        )
+
 
 class BuiltinRule(BaseRule):
     """

mathics/core/systemsymbols.py

@@ -183,6 +183,7 @@
 SymbolSeries = Symbol("System`Series")
 SymbolSeriesData = Symbol("System`SeriesData")
 SymbolSet = Symbol("System`Set")
+SymbolSetDelayed = Symbol("System`SetDelayed")
 SymbolSign = Symbol("System`Sign")
 SymbolSimplify = Symbol("System`Simplify")
 SymbolSin = Symbol("System`Sin")
@@ -201,6 +202,8 @@
 SymbolSubsuperscriptBox = Symbol("System`SubsuperscriptBox")
 SymbolSuperscriptBox = Symbol("System`SuperscriptBox")
 SymbolTable = Symbol("System`Table")
+SymbolTagSet = Symbol("System`TagSet")
+SymbolTagSetDelayed = Symbol("System`TagSetDelayed")
 SymbolTan = Symbol("System`Tan")
 SymbolTanh = Symbol("System`Tanh")
 SymbolTeXForm = Symbol("System`TeXForm")
@@ -212,5 +215,7 @@
 SymbolUndefined = Symbol("System`Undefined")
 SymbolUnequal = Symbol("System`Unequal")
 SymbolUnevaluated = Symbol("System`Unevaluated")
+SymbolUpSet = Symbol("System`UpSet")
+SymbolUpSetDelayed = Symbol("System`UpSetDelayed")
 SymbolUpValues = Symbol("System`UpValues")
 SymbolXor = Symbol("System`Xor")