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Revising for Wednesday's lecture

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Adam Chlipala 2021-04-04 14:51:02 -04:00
parent d177e9fb6f
commit 45124f3686
1 changed files with 8 additions and 6 deletions
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14
SubsetTypes.v
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@ -216,10 +216,8 @@ Definition pred_strong4 : forall (n : nat), n > 0 -> {m : nat | n = S m}.
* to [False_rec], and the second subgoal comes from the second underscore * to [False_rec], and the second subgoal comes from the second underscore
* passed to [exist]. In the first case, we see that, though we bound the * passed to [exist]. In the first case, we see that, though we bound the
* proof variable with an underscore, it is still available in our proof * proof variable with an underscore, it is still available in our proof
* context. It is hard to refer to underscore-named variables in manual * context. Both subgoals are easy to discharge, so let us back up and ask to
* proofs, but automation makes short work of them. Both subgoals are easy to * prove all subgoals automatically. *)
* discharge that way, so let us back up and ask to prove all subgoals
* automatically. *)
Undo. Undo.
refine (fun n => refine (fun n =>
@ -272,6 +270,10 @@ Compute pred_strong5 two_gt0.
Print sumbool. Print sumbool.
(* We have been using this type family behind the scenes for various equality
* checks, for instance: *)
Check "x" ==v "y".
(* Here, the constructors of [sumbool] have types written in terms of a (* Here, the constructors of [sumbool] have types written in terms of a
* registered notation for [sumbool], such that the result type of each * registered notation for [sumbool], such that the result type of each
* constructor desugars to [sumbool A B]. We can define some notations of our * constructor desugars to [sumbool A B]. We can define some notations of our
@ -534,7 +536,7 @@ Notation "e1 ;; e2" := (if e1 then e2 else ??)
* [hasType] proof obligation, and [eauto] makes short work of them when we add * [hasType] proof obligation, and [eauto] makes short work of them when we add
* [hasType]'s constructors as hints. *) * [hasType]'s constructors as hints. *)
Hint Constructors hasType. Local Hint Constructors hasType.
Definition typeCheck : forall e : exp, {{t | hasType e t}}. Definition typeCheck : forall e : exp, {{t | hasType e t}}.
refine (fix F (e : exp) : {{t | hasType e t}} := refine (fix F (e : exp) : {{t | hasType e t}} :=
@ -587,7 +589,7 @@ Qed.
(* Now we can define the type-checker. Its type expresses that it only fails on (* Now we can define the type-checker. Its type expresses that it only fails on
* untypable expressions. *) * untypable expressions. *)
Hint Resolve hasType_det. Local Hint Resolve hasType_det.
(* The lemma [hasType_det] will also be useful for proving proof obligations (* The lemma [hasType_det] will also be useful for proving proof obligations
* with contradictory contexts. *) * with contradictory contexts. *)