add Filterable algebra

README.md

@@ -22,6 +22,7 @@ structures:
 * [Applicative](#applicative)
 * [Alt](#alt)
 * [Plus](#plus)
+* [Filterable](#filterable)
 * [Alternative](#alternative)
 * [Foldable](#foldable)
 * [Traversable](#traversable)
@@ -33,7 +34,7 @@ structures:
 * [Bifunctor](#bifunctor)
 * [Profunctor](#profunctor)
 
-<img src="figures/dependencies.png" width="888" height="257" />
+<img src="figures/dependencies.png" width="888" height="245" />
 
 ## General
 
@@ -497,6 +498,34 @@ Given a value `x`, one can access its type representative via the
 
 1. `zero` must return a value of the same Plus
 
+### Filterable
+
+A value that implements the Filterable specification must also implement
+the [Plus](#plus) specification.
+
+1. `f.filter(x => true)` is equivalent to `f` (identity)
+2. `f.filter(x => false)` is equivalent to `f.constructor.zero()` (annihilation)
+3. `f.filter(p).filter(p)` is equivalent to `f.filter(p)` (idempotence)
+
+#### `filter` method
+
+```hs
+filter :: Filterable f => f a ~> (a -> Boolean) -> f a
+```
+
+A value which has a Filterable must provide a `filter` method. The `filter`
+method takes one argument:
+
+    f.filter(p)
+
+1. `p` must be a function.
+
+    1. If `p` is not a function, the behaviour of `filter` is unspecified.
+    2. `p` must return either `true` or `false`. If it returns any other value,
+       the behaviour of `filter` is unspecified.
+
+2. `filter` must return a value of the same Filterable.
+
 ### Alternative
 
 A value that implements the Alternative specification must also implement
@@ -836,7 +865,7 @@ to implement certain methods then derive the remaining methods. Derivations:
     function(f) {
       function Id(value) {
         this.value = value;
-      };
+      }
       Id.of = function(x) {
         return new Id(x);
       };
@@ -850,6 +879,15 @@ to implement certain methods then derive the remaining methods. Derivations:
     }
     ```
 
+  - [`filter`][] may be derived from [`of`][], [`chain`][], and [`zero`][]:
+
+    ```js
+    function(pred) {
+      var F = this.constructor;
+      return this.chain(x => pred(x) ? F.of(x) : F.zero());
+    }
+    ```
+
 If a data type provides a method which *could* be derived, its behaviour must
 be equivalent to that of the derivation (or derivations).
 
@@ -873,12 +911,14 @@ be equivalent to that of the derivation (or derivations).
 [`equals`]: #equals-method
 [`extend`]: #extend-method
 [`extract`]: #extract-method
+[`filter`]: #filter-method
 [`lte`]: #lte-method
 [`map`]: #map-method
 [`of`]: #of-method
 [`promap`]: #promap-method
 [`reduce`]: #reduce-method
 [`sequence`]: #sequence-method
+[`zero`]: #zero-method
 
 ## Alternatives
 

figures/dependencies.dot

@@ -11,11 +11,12 @@ digraph {
   Chain;
   ChainRec;
   Comonad;
+  Contravariant;
   Extend;
+  Filterable;
   Foldable;
   Functor;
   Group;
-  Contravariant;
   Monad;
   Monoid;
   Ord;
@@ -44,6 +45,7 @@ digraph {
   Functor -> Traversable;
   Monoid -> Group;
   Plus -> Alternative;
+  Plus -> Filterable;
   Semigroup -> Monoid;
   Semigroupoid -> Category;
   Setoid -> Ord;

index.js

@@ -19,6 +19,7 @@
     of: 'fantasy-land/of',
     alt: 'fantasy-land/alt',
     zero: 'fantasy-land/zero',
+    filter: 'fantasy-land/filter',
     reduce: 'fantasy-land/reduce',
     traverse: 'fantasy-land/traverse',
     chain: 'fantasy-land/chain',

laws/filterable.js

@@ -0,0 +1,33 @@
+'use strict';
+
+const {filter, zero} = require('..');
+
+/**
+
+### Filterable
+
+1. `f.filter(x => true)` is equivalent to `f` (identity)
+2. `f.filter(x => false)` is equivalent to `f.constructor.zero()` (annihilation)
+3. `f.filter(p).filter(p)` is equivalent to `f.filter(p)` (idempotence)
+
+**/
+
+const identity = eq => filterable => {
+  const a = filterable[filter](x => true);
+  const b = filterable;
+  return eq(a, b);
+};
+
+const annihilation = eq => filterable => {
+  const a = filterable[filter](x => false);
+  const b = filterable.constructor[zero]();
+  return eq(a, b);
+};
+
+const idempotence = eq => pred => filterable => {
+  const a = filterable[filter](pred)[filter](pred);
+  const b = filterable[filter](pred);
+  return eq(a, b);
+};
+
+module.exports = {identity, annihilation, idempotence};