add nats: natural numbers for lazy unfoldable

Author: matthewleon

bower.json

@@ -18,7 +18,8 @@
   ],
   "dependencies": {
     "purescript-partial": "^1.2.0",
-    "purescript-tuples": "^4.0.0"
+    "purescript-tuples": "^4.0.0",
+    "purescript-control": "^3.3.1"
   },
   "devDependencies": {
     "purescript-assert": "^3.0.0",

src/Data/Unfoldable.purs

@@ -10,15 +10,16 @@ module Data.Unfoldable
   , replicateA
   , none
   , singleton
+  , nats
   , fromMaybe
   ) where
 
 import Prelude
 
+import Control.Lazy (class Lazy)
 import Data.Maybe (Maybe(..), isNothing, fromJust)
 import Data.Traversable (class Traversable, sequence)
 import Data.Tuple (Tuple(..), fst, snd)
-
 import Partial.Unsafe (unsafePartial)
 
 -- | This class identifies data structures which can be _unfolded_,
@@ -88,6 +89,15 @@ none = unfoldr (const Nothing) unit
 singleton :: forall f a. Unfoldable f => a -> f a
 singleton = replicate 1
 
+-- | Produce a Lazy Unfoldable structure representing the natural numbers.
+--
+-- The result of this function is infinite.
+nats :: forall f a. Unfoldable f => Semiring a => Lazy (f a) => f a
+nats = unfoldr increment zero
+  where
+    increment :: a -> Maybe (Tuple a a)
+    increment a = Just (Tuple a $ add one a)
+
 -- | Convert a Maybe to any Unfoldable like lists and arrays.
 fromMaybe :: forall f a. Unfoldable f => Maybe a -> f a
 fromMaybe = unfoldr (\b -> flip Tuple Nothing <$> b)