Library prosa.util.notation

From mathcomp Require Import ssreflect ssrbool eqtype ssrnat seq fintype bigop.

We define a function converting a constant c to a function that ignores its argument and returns c.

Definition constant {X Y : Type} (c : Y) : (X → Y) := fun _ ⇒ c.

We define a notation for the big concatenation operator.

Reserved Notation "\cat_ ( m <= i < n ) F"
  (at level 41, F at level 41, i, m, n at level 50,
   format "'[' \cat_ ( m <= i < n ) '/ ' F ']'").

Notation "\cat_ ( m <= i < n ) F" :=
  (\big [cat /[::]]_(m ≤ i < n) F%N) : nat_scope.

Reserved Notation "\cat_ ( m <= i < n | P ) F"
  (at level 41, F at level 41, P at level 41, i, m, n at level 50,
   format "'[' \cat_ ( m <= i < n | P ) '/ ' F ']'").

Notation "\cat_ ( m <= i < n | P ) F" :=
  (\big [cat /[::]]_(m ≤ i < n | P) F%N) : nat_scope.

Reserved Notation "\cat_ ( i < n ) F"
  (at level 41, F at level 41, i, n at level 50,
   format "'[' \cat_ ( i < n ) '/ ' F ']'").

Notation "\cat_ ( i < n ) F" :=
  (\big [cat /[::]]_(i < n) F%N) : nat_scope.

Reserved Notation "\cat_ ( i < n | P ) F"
  (at level 41, F at level 41, i, n at level 50,
   format "'[' \cat_ ( i < n | P ) '/ ' F ']'").

Notation "\cat_ ( i < n | P ) F" :=
  (\big [cat /[::]]_(i < n | P) F%N) : nat_scope.

Reserved Notation "\cat_ ( x <- xs | P ) F"
  (at level 41, F at level 41, x, xs at level 50,
   format "'[' \cat_ ( x <- xs | P ) '/ ' F ']'").

Notation "\cat_ ( x <- xs | P ) F" :=
  (\big [cat /[::]]_(x <- xs | P) F) : big_scope.

Reserved Notation "\cat_ ( x <- xs ) F"
  (at level 41, F at level 41, x, xs at level 50,
   format "'[' \cat_ ( x <- xs ) '/ ' F ']'").

Notation "\cat_ ( x <- xs ) F" :=
   (\big [cat /[::]]_(x <- xs) F) : big_scope.