diff --git a/theories/functions.v b/theories/functions.v index 47349cc0b57cf89eb9facae2296e9c5d704eceb3..af040172bd7f1ceb12b2cc5d3e71b7a5240e3fe4 100644 --- a/theories/functions.v +++ b/theories/functions.v @@ -31,23 +31,19 @@ Section functions. End functions. (** "Cons-ing" of functions from nat to T *) -Section fcons. - Context {T : Type}. +Polymorphic Definition fn_cons {T : Type} (t : T) (f: nat → T) : nat → T := + λ n, match n with + | O => t + | S n => f n + end. - Definition fn_cons (t : T) (f: nat → T) : nat → T := - λ n, match n with - | O => t - | S n => f n - end. - - Definition fn_mcons (ts : list T) (f : nat → T) : nat → T := +Polymorphic Definition fn_mcons {T : Type} (ts : list T) (f : nat → T) : nat → T := fold_right fn_cons f ts. -End fcons. Infix ".::" := fn_cons (at level 60, right associativity) : C_scope. Infix ".++" := fn_mcons (at level 60, right associativity) : C_scope. -Lemma fn_mcons_app {T : Type} (ts1 ts2 : list T) f : +Polymorphic Lemma fn_mcons_app {T : Type} (ts1 ts2 : list T) f : (ts1 ++ ts2) .++ f = ts1 .++ (ts2 .++ f). Proof. unfold fn_mcons. rewrite fold_right_app. done.