Define an Alternative module giving implementations in terms of Alter…

…native.

fused-effects.cabal

@@ -56,6 +56,7 @@ library
                      , Control.Carrier.Trace.Returning
                      , Control.Carrier.Writer.Strict
                      , Control.Effect
+                     , Control.Effect.Alternative
                      , Control.Effect.Choose
                      , Control.Effect.Class
                      , Control.Effect.Cull

src/Control/Effect/Alternative.hs

@@ -0,0 +1,43 @@
+module Control.Effect.Alternative
+( -- * NonDet effects
+  module Control.Effect.Choose
+, module Control.Effect.Empty
+, oneOf
+, foldMapA
+  -- * Re-exports
+, Alternative(..)
+, guard
+) where
+
+import Control.Applicative (Alternative(..))
+import Control.Effect.Choose hiding ((<|>), many, some)
+import Control.Effect.Empty hiding (empty, guard)
+import Control.Monad (guard)
+import Data.Coerce
+import Data.Monoid (Alt(..))
+
+-- | Nondeterministically choose an element from a 'Foldable' collection.
+-- This can be used to emulate the style of nondeterminism associated with
+-- programming in the list monad:
+-- @
+--   pythagoreanTriples = do
+--     a <- oneOf [1..10]
+--     b <- oneOf [1..10]
+--     c <- oneOf [1..10]
+--     guard (a^2 + b^2 == c^2)
+--     pure (a, b, c)
+-- @
+oneOf :: (Foldable t, Alternative m) => t a -> m a
+oneOf = foldMapA pure
+
+-- | Map a 'Foldable' collection of values into a nondeterministic computation using the supplied action.
+foldMapA :: (Foldable t, Alternative m) => (a -> m b) -> t a -> m b
+foldMapA f = getAlt #. foldMap (Alt #. f)
+
+
+-- | Compose a function operationally equivalent to 'id' on the left.
+--
+--   cf https://github.com/fused-effects/diffused-effects/pull/1#discussion_r323560758
+(#.) :: Coercible b c => (b -> c) -> (a -> b) -> (a -> c)
+(#.) _ = coerce
+{-# INLINE (#.) #-}