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completed soundness

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Philip Wadler 2017-07-11 17:57:24 +01:00
parent 32307b9e4b
commit 728e54cc83
1 changed files with 1 additions and 14 deletions
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15
src/StlcProp.lagda
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@ -620,7 +620,7 @@ Soundness′ : ∀ {M N A} → ∅ ⊢ M ∶ A → M ⟹* N → ¬ (Stuck N)
Soundness′ ⊢M (M ∎) (¬M⟹N , ¬ValueM) with progress ⊢M Soundness′ ⊢M (M ∎) (¬M⟹N , ¬ValueM) with progress ⊢M
... | steps M⟹N = ¬M⟹N M⟹N ... | steps M⟹N = ¬M⟹N M⟹N
... | done ValueM = ¬ValueM ValueM ... | done ValueM = ¬ValueM ValueM
Soundness′ {L} {N} {A} ⊢L (_⟹⟨_⟩_ .L {M} {.N} L⟹M M⟹*N) = {!Soundness′!} Soundness′ {L} {N} {A} ⊢L (_⟹⟨_⟩_ .L {M} {.N} L⟹M M⟹*N) = Soundness′ ⊢M M⟹*N
where where
⊢M : ∅ ⊢ M ∶ A ⊢M : ∅ ⊢ M ∶ A
⊢M = preservation ⊢L L⟹M ⊢M = preservation ⊢L L⟹M
@ -628,19 +628,6 @@ Soundness′ {L} {N} {A} ⊢L (_⟹⟨_⟩_ .L {M} {.N} L⟹M M⟹*N) = {!Soundn
</div> </div>
Definition stuck (t:tm) : Prop :=
(normal_form step) t /\ ~ Value t.
Corollary soundness : forall t t' T,
empty \vdash t : T →
t ==>* t' →
~(stuck t').
Proof.
intros t t' T Hhas_type Hmulti. unfold stuck.
intros `Hnf Hnot_val`. unfold normal_form in Hnf.
induction Hmulti.
## Uniqueness of Types ## Uniqueness of Types
#### Exercise: 3 stars (types_unique) #### Exercise: 3 stars (types_unique)