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authorMiguel <m.i@gmx.at>2019-02-19 16:42:05 +0100
committerMiguel <m.i@gmx.at>2019-02-19 16:42:05 +0100
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+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