ability to run code and check output in tests

tests/TestCase4.newt

@@ -0,0 +1,75 @@
+module TestCase4
+
+data Nat : U where
+  Z : Nat
+  S : Nat -> Nat
+
+data Vect : Nat -> U -> U where
+  Nil : {a : U} -> Vect Z a
+  _::_ : {a : U} -> {k : Nat} -> a -> Vect k a -> Vect (S k) a
+
+infixr 5 _::_
+
+head : {a : U} {k : Nat} -> Vect (S k) a -> a
+head (x :: xs) = x
+
+-- These came from a Conor McBride lecture where they use SHE
+
+vapp : {s t : U} {k : Nat} -> Vect k (s -> t) -> Vect k s -> Vect k t
+vapp (f :: fs) (t :: ts) = f t :: vapp fs ts
+vapp Nil Nil = Nil
+
+vec : { a : U } -> (n : Nat) -> a -> Vect n a
+vec Z x = Nil
+vec (S k) x = x :: vec k x
+
+-- And then typeclass, which I don't have yet. I'll add a few underlying functions
+
+fmap : {a b : U} {n : Nat} -> (a -> b) -> Vect n a -> Vect n b
+fmap f Nil = Nil
+fmap f (x :: xs) = (f x :: fmap f xs)
+
+pure : {a : U} {n : Nat} -> a -> Vect n a
+pure {a} {n} = vec n
+
+_<*>_ : {s t : U} {k : Nat} -> Vect k (s -> t) -> Vect k s -> Vect k t
+_<*>_ = vapp
+
+-- and idiom brackets (maybe someday)
+
+-- I'll add foldl
+
+foldl : {acc el : U} {n : Nat} -> (acc -> el -> acc) -> acc -> Vect n el -> acc
+foldl f acc Nil = acc
+foldl f acc (x :: xs) = foldl f (f acc x) xs
+
+zipWith : {a b c : U} {m : Nat} -> (a -> b -> c) -> Vect m a -> Vect m b -> Vect m c
+zipWith f Nil Nil = Nil
+zipWith f (x :: xs) (y :: ys) = f x y :: zipWith f xs ys
+
+transpose : {a : U} {m n : Nat} -> Vect m (Vect n a) -> Vect n (Vect m a)
+transpose {a} {Z} {n} Nil = vec n Nil
+transpose {a} {S z} {n} (_::_ {a'} {j} x xs) = zipWith (_::_) x (transpose xs)
+
+
+
+myArr : Vect (S (S (S Z))) (Vect (S (S Z)) Int)
+myArr = (1 :: 2 :: Nil) :: (3 :: 4 :: Nil) :: (5 :: 6 :: Nil) :: Nil
+
+
+/-
+
+-- this possibly needs dynamic pattern unification
+-- It's complaining about a meta in a pattern
+data Ix : U where
+
+infixr 2 _:-:_
+data Path : (Sig : Ix -> Ix -> U) (i j : Ix) -> U where
+  Stop : {Sig : Ix -> Ix -> U} {i : Ix} -> Path Sig i i
+  _:-:_ : {Sig : Ix -> Ix -> U} {i j k : Ix} -> Sig i j -> Path Sig j k -> Path Sig i k
+
+
+pmap : {s t : Ix -> Ix -> U} -> (f : {i j : Ix} -> s i j -> t i j) -> {i j : Ix} -> Path s i j -> Path t i j
+pmap f Stop = Stop
+pmap f (s :-: ss) = f s :-: pmap f ss
+-/