Commit 0b443c97 authored by Robbert Krebbers's avatar Robbert Krebbers
Browse files

Merge branch 'master' of gitlab.mpi-sws.org:FP/iris-coq

parents 52ac9252 e61a2997
......@@ -29,3 +29,43 @@ Section functions.
Proof. unfold alter, fn_alter. by destruct (decide (a = b)). Qed.
End functions.
(** "Cons-ing" of functions from nat to T *)
(* Coq's standard lists are not universe polymorphic. Hence we have to re-define them. Ouch.
TODO: If we decide to end up going with this, we should move this elsewhere. *)
Polymorphic Inductive plist {A : Type} : Type :=
| pnil : plist
| pcons: A plist plist.
Arguments plist : clear implicits.
Polymorphic Fixpoint papp {A : Type} (l1 l2 : plist A) : plist A :=
match l1 with
| pnil => l2
| pcons a l => pcons a (papp l l2)
end.
(* TODO: Notation is totally up for debate. *)
Infix "`::`" := pcons (at level 60, right associativity) : C_scope.
Infix "`++`" := papp (at level 60, right associativity) : C_scope.
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.
Polymorphic Fixpoint fn_mcons {T : Type} (ts : plist T) (f : nat T) : nat T :=
match ts with
| pnil => f
| pcons t ts => fn_cons t (fn_mcons ts f)
end.
(* TODO: Notation is totally up for debate. *)
Infix ".::" := fn_cons (at level 60, right associativity) : C_scope.
Infix ".++" := fn_mcons (at level 60, right associativity) : C_scope.
Polymorphic Lemma fn_mcons_app {T : Type} (ts1 ts2 : plist T) f :
(ts1 `++` ts2) .++ f = ts1 .++ (ts2 .++ f).
Proof.
induction ts1; simpl; eauto. congruence.
Qed.
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