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Require Coq.Unicode.Utf8.
(** The purpose of this file is to test printing of the destructive
patterns used in binders ([fun] and [forall]). *)
Parameters (A B : Type) (P:A->Prop).
Definition swap '((x,y) : A*B) := (y,x).
Print swap.
Check fun '((x,y) : A*B) => (y,x).
Check forall '(x,y), swap (x,y) = (y,x).
Definition proj_informative '(exist _ x _ : { x:A | P x }) : A := x.
Print proj_informative.
Inductive Foo := Bar : nat -> bool -> unit -> nat -> Foo.
Definition foo '(Bar n b tt p) :=
if b then n+p else n-p.
Print foo.
Definition baz '(Bar n1 b1 tt p1) '(Bar n2 b2 tt p2) := n1+p1.
Print baz.
Module WithParameters.
Definition swap {A B} '((x,y) : A*B) := (y,x).
Print swap.
Check fun (A B:Type) '((x,y) : A*B) => swap (x,y) = (y,x).
Check forall (A B:Type) '((x,y) : A*B), swap (x,y) = (y,x).
Check exists '((x,y):A*A), swap (x,y) = (y,x).
Check exists '((x,y):A*A) '(z,w), swap (x,y) = (z,w).
End WithParameters.
(** Some test involving unicode notations. *)
Module WithUnicode.
Import Coq.Unicode.Utf8.
Check λ '((x,y) : A*B), (y,x).
Check ∀ '(x,y), swap (x,y) = (y,x).
End WithUnicode.
(** * Suboptimal printing *)
Module Suboptimal.
(** This test shows an example which exposes the [let] introduced by
the pattern notation in binders. *)
Inductive Fin (n:nat) := Z : Fin n.
Definition F '(n,p) : Type := (Fin n * Fin p)%type.
Definition both_z '(n,p) : F (n,p) := (Z _,Z _).
Print both_z.
(** Test factorization of binders *)
Check fun '((x,y) : A*B) '(z,t) => swap (x,y) = (z,t).
Check forall '(x,y) '((z,t) : B*A), swap (x,y) = (z,t).
End Suboptimal.
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