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(**********************************************************************)
(* Notations for if and let (submitted by Roland Zumkeller) *)
Notation "a ? b ; c" := (if a then b else c) (at level 10).
Check (true ? 0 ; 1).
Check if true as x return (if x then nat else bool) then 0 else true.
Notation "'proj1' t" := (let (a,_) := t in a) (at level 1).
Check (fun e : nat * nat => proj1 e).
Notation "'decomp' a 'as' x , y 'in' b" := (let (x,y) := a in b) (at level 1).
Check (decomp (true,true) as t, u in (t,u)).
(**********************************************************************)
(* Behaviour wrt to binding variables (submitted by Roland Zumkeller) *)
Notation "! A" := (forall _:nat, A) (at level 60).
Check ! (0=0).
Check forall n, n=0.
Check forall n:nat, 0=0.
(**********************************************************************)
(* Conflict between notation and notation below coercions *)
(* Case of a printer conflict *)
Require Import BinInt.
Coercion Zpos : positive >-> Z.
Open Scope Z_scope.
(* Check that (Zpos 3) is better printed by the printer for Z than
by the printer for positive *)
Check (3 + Zpos 3).
(* Case of a num printer only below coercion (submitted by Georges Gonthier) *)
Open Scope nat_scope.
Inductive znat : Set := Zpos (n : nat) | Zneg (m : nat).
Coercion Zpos: nat >-> znat.
Delimit Scope znat_scope with znat.
Open Scope znat_scope.
Variable addz : znat -> znat -> znat.
Notation "z1 + z2" := (addz z1 z2) : znat_scope.
(* Check that "3+3", where 3 is in nat and the coercion to znat is implicit,
is printed the same way, and not "S 2 + S 2" as if numeral printing was
only tested with coercion still present *)
Check (3+3).
(**********************************************************************)
(* Check recursive notations *)
Require Import List.
Notation "[ x ; .. ; y ]" := (cons x .. (cons y nil) ..).
Check [1;2;4].
Reserved Notation "( x ; y , .. , z )" (at level 0).
Notation "( x ; y , .. , z )" := (pair .. (pair x y) .. z).
Check (1;2,4).
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