Populate README.md for simple-semigroupoids package.

simple-semigroupoids/README.md

@@ -1 +1,67 @@
-# simple-semigroupoids
+# simple-semigroupoids
+
+This package implements simple versions of type classes for groupoid-like types.
+In addition, this package provides helpers for testing type class laws for
+group-like and groupoid-like types.
+
+## Groupoid-like types: semigroupoids and groupoids
+
+A `Semigroupoid` is like a `Semigroup`, but the binary sum operator `(<>)` is
+now a partial operation `(<>?)`. A `Groupoid` is a `Semigroupoid` with a unary
+invert operation `pinv`. A `Groupoid` is similar to what a `Group` is to a
+`Semigroup`.
+
+```haskell
+class Semigroupoid a where (<>?) :: a -> a -> Maybe a
+class Semigroupoid a => Groupoid a where pinv :: a -> a
+```
+
+Instances of the `Semigroupoid` class should adhere to the *associativity law*.
+Instances of the `Groupoid` class should adhere to the *inverse law* and the
+*identity law*. An algebraic definition of semigroupoids/groupoids can be found
+[here](https://en.wikipedia.org/wiki/Groupoid#Algebraic). The documentation in
+the `Data.Semigroupoid.Simple` module restates these properties/laws in terms of
+Haskell terms and types.
+
+Semigroupoids are a more general definition of semigroups, and groupoids are a
+more general definition of groups. This means that by definition, a semigroup is
+also a semigroupoid, and a group is also a groupoid. The `Auto a` newtype in
+`Data.Semigroupoids.Auto` automatically derives a `Semigroupoid` or `Groupoid`
+instance for `Auto a` in case `a` is a `Semigroup` or `Group` respectively.
+
+```haskell
+newtype Auto a = Auto a
+  deriving newtype (Semigroup, Monoid, Group)
+
+instance Semigroup (Auto a) => Semigroupoid (Auto a) where
+  x <>? y = Just $ x <> y
+
+instance Group (Auto a) => Groupoid (Auto a) where
+  pinv = invert
+```
+
+## Helpers for testing type-class laws
+
+The `Data.Semigroupoid.Simple.Laws` module provides helpers for creating `tasty`
+`TestTree`s that test type class laws for group-like and groupoid-like types.
+For example, `testSemigroupLaws` will test the associativity law for the
+`Semigroup` type class, given some proxy of the type that is under test.
+
+```haskell
+testSemigroupLaws ::
+     ( Semigroup a, Arbitrary a
+     , Eq a, Show a
+     )
+  => Proxy a
+  -> TestTree
+```
+
+Using `testGroupWithProxy` makes testing type class laws as easy as providing a
+proxy of the type under test, and a list of type class law test functions.
+
+```haskell
+testGroupWithProxy :: Typeable a => Proxy a -> [Proxy a -> TestTree] -> TestTree
+
+tests :: TestTree
+tests = testgroupWithProxy (Proxy @(Sum Int)) [testSemigroupLaws, testGroupLaws]
+```

simple-semigroupoids/simple-semigroupoids.cabal

@@ -12,7 +12,7 @@ author:              Joris Dral
 maintainer:          operations@iohk.io
 category:            Control, Testing
 build-type:          Simple
-tested-with:           GHC == { 8.10.7, 9.2.5 }
+tested-with:         GHC == { 8.10.7, 9.2.5 }
 
 library
   default-language:    Haskell2010

simple-semigroupoids/src/Data/Semigroupoid/Simple.hs

@@ -23,7 +23,7 @@ infix 6 <>?
 --
 -- The following laws are from
 -- <https://en.wikipedia.org/wiki/Groupoid#Algebraic>, with @*@ representing
--- 'poperatorM'.
+-- 'pappendM'.
 --
 -- /Associativity/ If @Just x ∗ Just y@ and @Just y ∗ Just z@ are defined, then
 -- @(Just x ∗ Just y) ∗ Just z@ and @Just x ∗ (Just y ∗ Just z)@ are defined and
@@ -53,7 +53,7 @@ pappendUnsafe l r = case l <>? r of
 --
 -- The following laws are from
 -- <https://en.wikipedia.org/wiki/Groupoid#Algebraic>, with @*@ representing
--- 'poperatorM'.
+-- 'pappendM'.
 --
 -- /Inverse/ @Just ('pinv' x) ∗ Just x@ and @Just x ∗ Just ('pinv' x)@ are
 -- always defined.