PairSpec.hs

module Language.Lambda.Examples.PairSpec where

import Language.Lambda.HspecUtils

import Test.Hspec

spec :: Spec
spec = describe "Pair" $ do
  -- Pair is the definition of tuples with two items. Pairs,
  -- again are represented using Church Encodings:
  --
  -- pair = \x y f. f x y
  describe "first" $ do
    -- The function first returns the first item in a pair
    -- first(x, y) = x
    --
    -- first is defined by
    -- first = \p. p (\t f. t)
    it "first 0 1 = 0" $
      "(\\p. p (\\t f. t)) ((\\x y f. f x y) (\\f x. x) (\\f x. f x))"
        `shouldEvalTo` "\\f x. x"

    it "first x y = x" $
      "(\\p. p (\\t f. t)) ((\\x y f. f x y) x y)" `shouldEvalTo` "x"

  describe "second" $ do
    -- The function second returns the second item in a pair
    -- second(x, y) = y
    --
    -- second is defined by
    -- second = \p. p (\t f. f)
    it "second 0 1 = 1" $
      "(\\p. p (\\t f. f)) ((\\x y f. f x y) (\\f x. x) (\\f x. f x))"
        `shouldEvalTo` "\\f x. f x"

    it "second x y = y" $ do
      "(\\p. p (\\t f. f)) ((\\x y f. f x y) x y)" `shouldEvalTo` "y"
      "(\\p. p (\\x y z. x)) ((\\x y z f. f x y z) x y z)" `shouldEvalTo` "x"