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1 (* Copyright (c) 2008, Adam Chlipala
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2 *
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3 * This work is licensed under a
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4 * Creative Commons Attribution-Noncommercial-No Derivative Works 3.0
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5 * Unported License.
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6 * The license text is available at:
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7 * http://creativecommons.org/licenses/by-nc-nd/3.0/
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8 *)
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9
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10 (* Types and notations presented in Chapter 6 *)
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11
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12 Set Implicit Arguments.
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13
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14
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15 Notation "!" := (False_rec _ _) : specif_scope.
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16 Notation "[ e ]" := (exist _ e _) : specif_scope.
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17 Notation "x <== e1 ; e2" := (let (x, _) := e1 in e2)
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18 (right associativity, at level 60) : specif_scope.
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19
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20 Open Local Scope specif_scope.
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21 Delimit Scope specif_scope with specif.
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22
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23 Notation "'Yes'" := (left _ _) : specif_scope.
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24 Notation "'No'" := (right _ _) : specif_scope.
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25 Notation "'Reduce' x" := (if x then Yes else No) (at level 50) : specif_scope.
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26
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27 Notation "x || y" := (if x then Yes else Reduce y) (at level 50) : specif_scope.
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28
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29 Inductive maybe (A : Type) (P : A -> Prop) : Set :=
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30 | Unknown : maybe P
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31 | Found : forall x : A, P x -> maybe P.
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32
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33 Notation "{{ x | P }}" := (maybe (fun x => P)) : specif_scope.
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34 Notation "??" := (Unknown _) : specif_scope.
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35 Notation "[[ x ]]" := (Found _ x _) : specif_scope.
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36
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37 Notation "x <- e1 ; e2" := (match e1 with
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38 | Unknown => ??
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39 | Found x _ => e2
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40 end)
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41 (right associativity, at level 60) : specif_scope.
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42
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43 Notation "!!" := (inright _ _) : specif_scope.
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44 Notation "[[[ x ]]]" := (inleft _ [x]) : specif_scope.
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45
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46 Notation "x <-- e1 ; e2" := (match e1 with
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47 | inright _ => !!
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48 | inleft (exist x _) => e2
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49 end)
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50 (right associativity, at level 60) : specif_scope.
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51
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52 Notation "e1 ;; e2" := (if e1 then e2 else ??)
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53 (right associativity, at level 60) : specif_scope.
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54
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55 Notation "e1 ;;; e2" := (if e1 then e2 else !!)
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56 (right associativity, at level 60) : specif_scope.
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