initial

Dep.agda

@@ -0,0 +1,30 @@
+module dep where
+
+data Nat : Set where
+  zero : Nat
+  suc  : Nat → Nat
+
+data L (A : Set) : Set where
+  []   : L A
+  _::_ : A → L A → L A
+
+data Vect (A : Set) : Nat → Set where
+  vnil  : Vect A zero
+  vcons : {n : Nat} → A → Vect A n → Vect A (suc n)
+
+infix 2 _+_
+infix 3 _*_
+
+_+_ : Nat → Nat → Nat
+n + zero = n
+n + suc m = suc (n + m)
+
+_*_ : Nat -> Nat -> Nat
+n * zero = zero
+n * suc m = n * m + n
+
+inner : {n : Nat} → Vect Nat n → Vect Nat n → Nat
+inner vnil vnil = zero
+inner (vcons x xs) (vcons y ys) = x * y + inner xs ys
+
+