add list concat sample

tests/black/Concat.newt

@@ -0,0 +1,38 @@
+module Concat
+
+data Nat : U where
+    Z : Nat
+    S : Nat -> Nat
+
+infixl 7 _+_
+_+_ : Nat -> Nat -> Nat
+Z + m = m
+S n + m = S (n + m)
+
+infixr 3 _::_
+data List : U -> U where
+    Nil : {A : U} -> List A
+    _::_ : {A : U} -> A -> List A -> List A
+
+length : {A : U} -> List A -> Nat
+length Nil = Z
+length (x :: xs) = S (length xs)
+
+infixl 2 _++_
+
+_++_ : {A : U} -> List A -> List A -> List A
+Nil ++ ys = ys
+x :: xs ++ ys = x :: (xs ++ ys)
+
+infixl 1 _≡_
+data _≡_ : {A : U} -> A -> A -> U where
+    Refl : {A : U} {a : A} -> a ≡ a
+
+replace : {A : U} {a b : A} -> (P : A -> U) -> a ≡ b -> P a -> P b
+replace p Refl x = x
+
+cong : {A B : U} {a b : A} -> (f : A -> B) -> a ≡ b -> f a ≡ f b
+
+thm : {A : U} (xs ys : List A) -> length (xs ++ ys) ≡ length xs + length ys
+thm Nil ys = Refl
+thm (x :: xs) ys = cong S (thm xs ys)