diff --git a/prelude/functions.v b/prelude/functions.v index 2e4c93caaab6e18a2fc09df2dc4658ab03c5aa05..bc12965f09d24873bf54f2416f132e87843c4946 100644 --- a/prelude/functions.v +++ b/prelude/functions.v @@ -29,3 +29,26 @@ Section functions. Proof. unfold alter, fn_alter. by destruct (decide (a = b)). Qed. End functions. + +(** "Cons-ing" of functions from nat to T *) +Section fcons. + Context {T : Type}. + + 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 := + 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 : + (ts1 ++ ts2) .++ f = ts1 .++ (ts2 .++ f). +Proof. + unfold fn_mcons. rewrite fold_right_app. done. +Qed.