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diff --git a/080_blog/00120_Lambda-Calculus-(Haskell)/index.md b/080_blog/00120_Lambda-Calculus-(Haskell)/index.md new file mode 100644 index 0000000..25c6b83 --- /dev/null +++ b/080_blog/00120_Lambda-Calculus-(Haskell)/index.md @@ -0,0 +1,38 @@ +Lambda Calculus +=============== + + May 2, 2018 + +Playing with Type Quantifiers and Haskell's Rank 2 Type Polymorphsim, +implementing Boolean logic from scratch. We use the conventional +definitions for `True` an `False` also known as Church booleans, after Alonzo Church, who +intruced them along Lambda Calculus in the 1930s [1]. + +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ {.haskell .numberLines} +{-# LANGUAGE Rank2Types #-} + +fTrue :: forall a. a->a->a +fTrue x y = x + +fFalse :: forall a. a->a->a +fFalse x y = y + +fAnd :: (forall a. a->a->a)->(forall a. a->a->a)->(forall a. a->a->a) +fAnd p q = p q p + +fOr :: (forall a. a->a->a)->(forall a. a->a->a)->(forall a. a->a->a) +fOr p q = p p q + +fNot :: (forall a. a->a->a)->(forall a. a->a->a) +fNot p = p fFalse fTrue + +ifThenElse :: (forall a. a->a->a)->(forall a. a->a->a) + ->(forall a. a->a->a)->(forall a. a->a->a) +ifThenElse p a b = p a b + +-- Example -- + +main = print $ (ifThenElse fFalse fFalse $ fAnd fTrue $ fNot fFalse) "T" "F" +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + + [1] https://en.wikipedia.org/wiki/Lambda_calculus |