adamc@78: (* Copyright (c) 2008, Adam Chlipala
adamc@78:  * 
adamc@78:  * This work is licensed under a
adamc@78:  * Creative Commons Attribution-Noncommercial-No Derivative Works 3.0
adamc@78:  * Unported License.
adamc@78:  * The license text is available at:
adamc@78:  *   http://creativecommons.org/licenses/by-nc-nd/3.0/
adamc@78:  *)
adamc@78: 
adamc@78: (* Types and notations presented in Chapter 6 *)
adamc@78: 
adamc@78: Set Implicit Arguments.
adamc@78: 
adamc@78: 
adamc@78: Notation "!" := (False_rec _ _) : specif_scope.
adamc@78: Notation "[ e ]" := (exist _ e _) : specif_scope.
adamc@78: Notation "x <== e1 ; e2" := (let (x, _) := e1 in e2)
adamc@78: (right associativity, at level 60) : specif_scope.
adamc@78: 
adamc@78: Open Local Scope specif_scope.
adamc@78: Delimit Scope specif_scope with specif.
adamc@78: 
adamc@78: Notation "'Yes'" := (left _ _) : specif_scope.
adamc@78: Notation "'No'" := (right _ _) : specif_scope.
adamc@78: Notation "'Reduce' x" := (if x then Yes else No) (at level 50) : specif_scope.
adamc@78: 
adamc@78: Notation "x || y" := (if x then Yes else Reduce y) (at level 50) : specif_scope.
adamc@78: 
adamc@78: Inductive maybe (A : Type) (P : A -> Prop) : Set :=
adamc@78: | Unknown : maybe P
adamc@78: | Found : forall x : A, P x -> maybe P.
adamc@78: 
adamc@78: Notation "{{ x | P }}" := (maybe (fun x => P)) : specif_scope.
adamc@78: Notation "??" := (Unknown _) : specif_scope.
adamc@78: Notation "[[ x ]]" := (Found _ x _) : specif_scope.
adamc@78: 
adamc@78: Notation "x <- e1 ; e2" := (match e1 with
adamc@78:                              | Unknown => ??
adamc@78:                              | Found x _ => e2
adamc@78:                            end)
adamc@78: (right associativity, at level 60) : specif_scope.
adamc@78: 
adamc@79: Notation "!!" := (inright _ _) : specif_scope.
adamc@79: Notation "[[[ x ]]]" := (inleft _ [x]) : specif_scope.
adamc@79: 
adamc@78: Notation "x <-- e1 ; e2" := (match e1 with
adamc@78:                                | inright _ => !!
adamc@78:                                | inleft (exist x _) => e2
adamc@78:                              end)
adamc@78: (right associativity, at level 60) : specif_scope.
adamc@78: 
adamc@78: Notation "e1 ;; e2" := (if e1 then e2 else ??)
adamc@78:   (right associativity, at level 60) : specif_scope.
adamc@78: 
adamc@78: Notation "e1 ;;; e2" := (if e1 then e2 else !!)
adamc@78:   (right associativity, at level 60) : specif_scope.