algebra-checkers alternatives and similar packages
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"Any fool can make a rule, and any fool will mind it."
Henry David Thoreau
algebra-checkers is a little library for testing algebraic laws. For example,
imagine we're writing an ADT:
data Foo a instance Semigroup (Foo a) instance Monoid (Foo a) data Key get :: Key -> Foo a -> a get = undefined set :: Key -> a -> Foo a -> Foo a set = undefined
Let's say we expect the lens laws to hold for
set, as well for
to be a monoid homomorphism. We can express those facts to
and have it generate tests for us:
lawTests :: [Property] lawTests = $(testModel [e| do law "set/set" (set i x' (set i x s) == set i x' s) law "set/get" (set i (get i s) s == s) law "get/set" (get i (set i x s) == x) homo @Monoid (\s -> set i x s) |])
algebra-checkers will generate tests to show that these laws are
confluent. We can run these tests via
If we use the
theoremsOf function instead of
will dump out all the additional theorems it has proven about our algebra. This
serves as a good sanity check:
Theorems: • set i x' (set i x s) = set i x' s (definition of "set/set") • set i (get i s) s = s (definition of "set/get") • get i (set i x s) = x (definition of "get/set") • set i x mempty = mempty (definition of "set:Monoid:mempty") • set i x (s1 <> s2) = set i x s1 <> set i x s2 (definition of "set:Monoid:<>") • set i1 (get i1 (set i1 x1 s1)) s1 = set i1 x1 s1 (implied by "set/get" and "set/set") • set i1 (get i1 (s12 <> s22)) s12 <> set i1 (get i1 (s12 <> s22)) s22 = s12 <> s22 (implied by "set/get" and "set:Monoid:<>") • set i1 x'2 (set i1 x1 s11 <> set i1 x1 s21) = set i1 x'2 (s11 <> s21) (implied by "set/set" and "set:Monoid:<>") • get i1 (set i1 x1 s11 <> set i1 x1 s21) = x1 (implied by "get/set" and "set:Monoid:<>") Contradictions: • get i1 mempty = x1 the variable x1 is undetermined (implied by "get/set" and "set:Monoid:mempty")
Uh oh! Look at that! This contradiction is clearly a bogus theorem, which lets us know that "get/set" and "set mempty" are nonconfluent with one another!