adds contravariant functor to spec (#150)

* adds contravariant functor to spec

* adds to list of structures

* Adds type signature; removes contravariant dependency in profunctor

* Fix linting errors

* Update figures

* Update height of img in README

* Remove 'functor' from 'Contravariant' section name

* Update algebra name in dependencies graph

* Should be the last few fixes necessary for merge

* Update contramap laws

README.md

@@ -13,6 +13,7 @@ structures:
 * [Semigroup](#semigroup)
 * [Monoid](#monoid)
 * [Functor](#functor)
+* [Contravariant](#contravariant)
 * [Apply](#apply)
 * [Applicative](#applicative)
 * [Alt](#alt)
@@ -28,7 +29,7 @@ structures:
 * [Bifunctor](#bifunctor)
 * [Profunctor](#profunctor)
 
-<img src="figures/dependencies.png" width="888" height="347" />
+<img src="figures/dependencies.png" width="888" height="289" />
 
 ## General
 
@@ -186,6 +187,32 @@ method takes one argument:
 
 2. `map` must return a value of the same Functor
 
+### Contravariant
+
+1. `u.contramap(a => a)` is equivalent to `u` (identity)
+2. `u.contramap(x => f(g(x)))` is equivalent to `u.contramap(f).contramap(g)`
+(composition)
+
+#### `contramap` method
+
+```hs
+contramap :: Contravariant f => f a ~> (b -> a) -> f b
+```
+
+A value which has a Contravariant must provide a `contramap` method. The
+`contramap` method takes one argument:
+
+    u.contramap(f)
+
+1. `f` must be a function,
+
+    1. If `f` is not a function, the behaviour of `contramap` is
+       unspecified.
+    2. `f` can return any value.
+    3. No parts of `f`'s return value should be checked.
+
+2. `contramap` must return a value of the same Contravariant
+
 ### Apply
 
 A value that implements the Apply specification must also

figures/dependencies.dot

@@ -13,6 +13,7 @@ digraph {
   Extend;
   Foldable;
   Functor;
+  Contravariant;
   Monad;
   Monoid;
   Plus;

index.js

@@ -10,6 +10,7 @@
     concat: 'fantasy-land/concat',
     empty: 'fantasy-land/empty',
     map: 'fantasy-land/map',
+    contramap: 'fantasy-land/contramap',
     ap: 'fantasy-land/ap',
     of: 'fantasy-land/of',
     alt: 'fantasy-land/alt',

laws/contravariant.js

@@ -0,0 +1,27 @@
+'use strict';
+
+const {identity, compose} = require('fantasy-combinators');
+const {contramap} = require('..');
+
+/*
+
+### Contravariant Functor
+
+1. `u.contramap(a => a)` is equivalent to `u` (identity)
+2. `u.contramap(x => f(g(x)))` is equivalent to `u.contramap(f).contramap(g)` (composition)
+
+*/
+
+const identityʹ = t => eq => x => {
+  const a = t(x)[contramap](identity);
+  const b = t(x);
+  return eq(a, b);
+};
+
+const composition = t => eq => x => {
+  const a = t(x)[contramap](compose(identity)(identity));
+  const b = t(x)[contramap](identity)[contramap](identity);
+  return eq(a, b);
+};
+
+module.exports = {identity: identityʹ, composition};