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Tags: Data Structures     Model

# algebra-checkers alternatives and similar packages

Based on the "Model" category.
Alternatively, view algebra-checkers alternatives based on common mentions on social networks and blogs.

• ### clafer

Clafer is a lightweight modeling language
• ### claferIG

Support for reasoning on Clafer models by instantiation and counter example generation.

Do you think we are missing an alternative of algebra-checkers or a related project?

## Dedication

"Any fool can make a rule, and any fool will mind it."

Henry David Thoreau

## Overview

`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 `get` and `set`, as well for `set` to be a monoid homomorphism. We can express those facts to `algebra-checkers` 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)

|])
``````

Furthermore, `algebra-checkers` will generate tests to show that these laws are confluent. We can run these tests via `quickCheck lawTests`.

If we use the `theoremsOf` function instead of `testModel`, `algebra-checkers` 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:<>")