Triangles-testreport.md

Test report for Triangles

Total time spent by two persons on this Lab exercise: 8 hours

Source

The source can be found in the files Triangles.hs and TrianglesTest.hs. Please load TrianglesTest with :load TrianglesTest. This will also load the Triangles source.

Requirements

Write a program (in Haskell) that takes a triple of integer values as arguments and gives as output one of the following statements:

• Not a triangle if the three numbers cannot occur as the lengths of the sides of triangle,
• Equilateral if the three numbers are the lengths of the sides of an equilateral triangle,
• Rectangular if the three numbers are the lengths of the sides of a rectangular triangle,
• Isosceles if the three numbers are the lengths of the sides of an isosceles (but not equilateral) triangle,
• Other if the three numbers are the lengths of the sides of a triangle that is not equilateral, not rectangular, and not isosceles.

Postconditions

• The result should be a member of the set {NoTriangle, Equilateral, Isosceles, Rectangular, Other}.
• The result should return the correct triangle based on the given input in relation with the above requirements.
• When we have a Equilateral and change one side, we either end up with a Isosceles or a NoTriangle.
• When we have an a, b and c that comply to Pythagoras, then the triangle is Rectangular.
• When we have a Rectangular triangle and change one side, we end up with a shape that is not a Rectangular.

Tests

We applied different approaches to test the implementation. In the following paragraphs when we mention a, b and c, we assume that a <= b <= c.

Base Cases

We tested some of the base cases which exploit the base properties of each shape. In addition we checked the NoTriangle property that holds when the triangle sides have the form a + b <= c. It is impossible to draw these triangles. This directly implies that triangles with at least one side of 0 or less will be of the class NoTriangle, since a <= b <= c.

The base cases can be executed with the following command:

testBaseCases

Statistics over a certain domain

We have generated all possible triples over a domain of natural numbers with 3 <= n <= 5 and we determined the number of instances with logic for each class of triangle that should occur in this set. We came to the conclusion that the set should contain (n is the size of the domain):

• 3 Equilateral triangles (n);
• 18 Isosceles triangles (3 * n (n - 1 ). This will only hold for a domain where it is not possible to have triangles of the class NoTriangle);
• and 6 Rectangular triangles (3, 4, 5 is the only Pythagoras triangle, which will result in 6 permutations).

The statistics tests can be executed with the following command:

testOccurrences

Property based tests

We tested properties that we did not use in the definition of the function triangle.

• When we change one of the sides of a triangle that would produce an Equilateral the result can never result in an Equilateral, but has to be an Isosceles or a NoTriangle. This is tested with testChangeEquilateral.
• When we change one of the sides of a triangle that would produce a Rectangular the result can never result in a Rectangular. This is tested with testChangeRectangular.
• When we order of the input, the resulting shape should be the same. This is tested with testPermutations.