module IFam.Vector where open import IType.Nat -- List is a polymorphic type. In Haskell we have the type [a] of lists where the elements belong -- to an arbitrary type a. In Agda we declare the polymorphic data type of lists as follows: data Vect (A : Set) : Nat → Set where [] : Vect A zero _::_ : {n : Nat} → A → Vect A n → Vect A (succ n) -- This notation means that we define a list constructor -- -- List : Set → Set -- -- and two polymorphic constructors with implicit arguments: -- -- [] : {A : Set} → List A -- _::_ : {A : Set} → A → List A → List A -- head is a partial functions in Haskell, -- it is not defined on the empty list head : {A : Set} → {n : Nat} → Vect A (succ n) → A head (a :: as) = a tail : {A : Set} → {n : Nat} → Vect A (succ n) → Vect A n tail (a :: as) = as -- We can define polymorphic map map : {A B : Set} → {n : Nat} → (A → B) → Vect A n → Vect B n map f [] = [] map f (a :: as) = f a :: map f as -- and polymorphic zip as in Haskell (we need to import and open the type of pairs first) open import IType.Product zip : {A B : Set} → {n : Nat} → Vect A n → Vect B n → Vect (A × B) n zip [] [] = [] zip (x :: xs) (y :: ys) = < x , y > :: zip xs ys -- The intention is to "zip" lists of the same length, the last clause will -- only be used when lists are of different lengths