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(**********************************************************************)
(* Test call to primitive printers in presence of coercion to *)
(* functions (cf bug #2044) *)
Inductive PAIR := P (n1:nat) (n2:nat).
Coercion P : nat >-> Funclass.
Check (2 3).
(* Check that notations with coercions to functions inserted still work *)
(* (were not working from revision 11886 to 12951) *)
Record Binop := { binop :> nat -> nat -> nat }.
Class Plusop := { plusop : Binop; zero : nat }.
Infix "[+]" := plusop (at level 40).
Instance Plus : Plusop := {| plusop := {| binop := plus |} ; zero := 0 |}.
Check 2[+]3.
(* Test bug #2091 (variable le was printed using <= !) *)
Check forall (A: Set) (le: A -> A -> Prop) (x y: A), le x y \/ le y x.
(* Test recursive notations in cases pattern *)
Remove Printing Let prod.
Check match (0,0,0) with (x,y,z) => x+y+z end.
Check let '(a,b,c) := ((2,3),4) in a.
(* Check printing of notations with mixed reserved binders (see bug #2571) *)
Implicit Type myx : bool.
Check exists myx y, myx = y.
(* Test notation for anonymous functions up to eta-expansion *)
Check fun P:nat->nat->Prop => fun x:nat => ex (P x).
(* Test notations with binders *)
Notation "∃ x .. y , P":= (ex (fun x => .. (ex (fun y => P)) ..))
(x binder, y binder, at level 200, right associativity,
format "'[ ' ∃ x .. y ']' , P").
Check (∃ n p, n+p=0).
Check ∃ (a:=0) (x:nat) y (b:=1) (c:=b) (d:=2) z (e:=3) (f:=4), x+y = z+d.
Notation "∀ x .. y , P":= (forall x, .. (forall y, P) ..)
(x binder, at level 200, right associativity).
Check (∀ n p, n+p=0).
Notation "'λ' x .. y , P":= (fun x => .. (fun y => P) ..)
(y binder, at level 200, right associativity).
Check (λ n p, n+p=0).
Generalizable Variable A.
Check `(λ n p : A, n=p).
Check `(∃ n p : A, n=p).
Check `(∀ n p : A, n=p).
Notation "'let'' f x .. y := t 'in' u":=
(let f := fun x => .. (fun y => t) .. in u)
(f ident, x closed binder, y closed binder, at level 200,
right associativity).
Check let' f x y (a:=0) z (b:bool) := x+y+z+1 in f 0 1 2.
(* In practice, only the printing rule is used here *)
(* Note: does not work for pattern *)
Module A.
Notation "f ( x )" := (f x) (at level 10, format "f ( x )").
Check fun f x => f x + S x.
Open Scope list_scope.
Notation list1 := (1::nil)%list.
Notation plus2 n := (S (S n)).
(* plus2 was not correctly printed in the two following tests in 8.3pl1 *)
Print plus2.
Check fun n => match n with list1 => 0 | _ => 2 end.
Unset Printing Allow Match Default Clause.
Check fun n => match n with list1 => 0 | _ => 2 end.
Unset Printing Factorizable Match Patterns.
Check fun n => match n with list1 => 0 | _ => 2 end.
Set Printing Allow Match Default Clause.
Set Printing Factorizable Match Patterns.
End A.
(* This one is not fully satisfactory because binders in the same type
are re-factorized and parentheses are needed even for atomic binder
Notation "'mylet' f [ x ; .. ; y ] := t 'in' u":=
(let f := fun x => .. (fun y => t) .. in u)
(f ident, x closed binder, y closed binder, at level 200,
right associativity).
Check mylet f [x;y;z;(a:bool)] := x+y+z+1 in f 0 1 2.
*)
(* Check notations for functional terms which do not necessarily
depend on their parameter *)
(* Old request mentioned again on coq-club 20/1/2012 *)
Notation "# x : T => t" := (fun x : T => t)
(at level 0, t at level 200, x ident).
Check # x : nat => x.
Check # _ : nat => 2.
(* Check bug 4677 *)
Check fun x (H:le x 0) => exist (le x) 0 H.
Parameters (A : Set) (x y : A) (Q : A -> A -> Prop) (conj : Q x y).
Check (exist (Q x) y conj).
(* Check bug #4854 *)
Notation "% i" := (fun i : nat => i) (at level 0, i ident).
Check %i.
Check %j.
(* Check bug raised on coq-club on Sep 12, 2016 *)
Notation "{ x , y , .. , v }" := (fun a => (or .. (or (a = x) (a = y)) .. (a = v))).
Check ({1, 2}).
(**********************************************************************)
(* Check notations of the form ".a", ".a≡", "a≡" *)
(* Only "a#", "a≡" and ".≡" were working properly for parsing. The *)
(* other ones were working only for printing. *)
Notation "a#" := nat.
Check nat.
Check a#.
Notation "a≡" := nat.
Check nat.
Check a≡.
Notation ".≡" := nat.
Check nat.
Check .≡.
Notation ".a#" := nat.
Check nat.
Check .a#.
Notation ".a≡" := nat.
Check nat.
Check .a≡.
Notation ".α" := nat.
Check nat.
Check .α.
(* A test for #6304 *)
Module M6304.
Notation "'for' m 'from' 0 'to' N 'updating' ( s1 ) {{ b }} ;; rest" :=
(let s1 :=
(fix rec(n: nat) := match n with
| 0 => s1
| S m => let s1 := rec m in b
end) N
in rest)
(at level 20).
Check fun (a b : nat) =>
let res := 0 in
for i from 0 to a updating (res) {{
for j from 0 to b updating (res) {{ S res }};;
res
}};; res.
End M6304.
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