initial commit

Functions.idr

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+double : Num ty => ty -> ty
+double x = x + x
+
+add : Int -> Int -> Int
+add x y = x + y
+
+identity : ty -> ty
+identity x = x
+
+-- the
+der : (ty : Type) -> ty -> ty
+der ty x = x
+
+
+||| Higher-Order-Functions
+
+twice : (a -> a) -> a -> a
+twice f x = f (f x)
+
+Shape : Type
+
+rotate : Shape -> Shape
+
+quadruple : Num a => a -> a
+quadruple = twice double
+
+turn_around : Shape -> Shape
+turn_around = twice rotate
+
+apply_n : (a -> a) -> Nat -> a -> a
+
+longer : String -> String -> Nat
+longer word1 word2 =
+    let len1 = length word1
+        len2 = length word2 in
+        max len1 len2
+
+
+pythagoras : Double -> Double -> Double
+pythagoras x y = sqrt (square x + square y)
+  where
+    square : Double -> Double
+    square x = x * x