Fixed binding issues with existential syntax.
This commit is contained in:
Wen Kokke
parent
a92e1a08c4
commit
7345c36d80
5 changed files with 21 additions and 21 deletions
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@ -982,15 +982,15 @@ Remember to indent all code by two spaces.
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```
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ext∋ : ∀ {Γ B x y}
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→ x ≢ y
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→ ¬ (∃[ A ]( Γ ∋ x ⦂ A ))
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→ ¬ ∃[ A ]( Γ ∋ x ⦂ A )
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------------------------------
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→ ¬ (∃[ A ]( Γ , y ⦂ B ∋ x ⦂ A ))
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→ ¬ ∃[ A ]( Γ , y ⦂ B ∋ x ⦂ A )
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ext∋ x≢y _ ⟨ A , Z ⟩ = x≢y refl
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ext∋ _ ¬∃ ⟨ A , S _ ⊢x ⟩ = ¬∃ ⟨ A , ⊢x ⟩
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lookup : ∀ (Γ : Context) (x : Id)
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------------------------
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→ Dec (∃[ A ](Γ ∋ x ⦂ A))
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→ Dec (∃[ A ]( Γ ∋ x ⦂ A ))
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lookup ∅ x = no (λ ())
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lookup (Γ , y ⦂ B) x with x ≟ y
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... | yes refl = yes ⟨ B , Z ⟩
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@ -1006,7 +1006,7 @@ Remember to indent all code by two spaces.
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→ Γ ⊢ L ↑ A ⇒ B
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→ ¬ Γ ⊢ M ↓ A
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----------------------------
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→ ¬ (∃[ B′ ]( Γ ⊢ L · M ↑ B′ ))
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→ ¬ ∃[ B′ ]( Γ ⊢ L · M ↑ B′ )
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¬arg ⊢L ¬⊢M ⟨ B′ , ⊢L′ · ⊢M′ ⟩ rewrite dom≡ (uniq-↑ ⊢L ⊢L′) = ¬⊢M ⊢M′
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¬switch : ∀ {Γ M A B}
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@ -589,9 +589,9 @@ module Problem3 where
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```
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ext∋ : ∀ {Γ B x y}
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→ x ≢ y
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→ ¬ ( ∃[ A ] Γ ∋ x ⦂ A )
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→ ¬ ∃[ A ]( Γ ∋ x ⦂ A )
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-----------------------------
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→ ¬ ( ∃[ A ] Γ , y ⦂ B ∋ x ⦂ A )
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→ ¬ ∃[ A ]( Γ , y ⦂ B ∋ x ⦂ A )
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ext∋ x≢y _ ⟨ A , Z ⟩ = x≢y refl
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ext∋ _ ¬∃ ⟨ A , S _ ⊢x ⟩ = ¬∃ ⟨ A , ⊢x ⟩
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@ -614,7 +614,7 @@ module Problem3 where
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→ Γ ⊢ L ↑ A ⇒ B
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→ ¬ Γ ⊢ M ↓ A
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----------------------------
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→ ¬ ( ∃[ B′ ] Γ ⊢ L · M ↑ B′ )
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→ ¬ ∃[ B′ ]( Γ ⊢ L · M ↑ B′ )
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¬arg ⊢L ¬⊢M ⟨ B′ , ⊢L′ · ⊢M′ ⟩ rewrite dom≡ (uniq-↑ ⊢L ⊢L′) = ¬⊢M ⊢M′
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¬switch : ∀ {Γ M A B}
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@ -631,7 +631,7 @@ module Problem3 where
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```
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synthesize : ∀ (Γ : Context) (M : Term⁺)
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-----------------------
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→ Dec (∃[ A ](Γ ⊢ M ↑ A))
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→ Dec (∃[ A ]( Γ ⊢ M ↑ A ))
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inherit : ∀ (Γ : Context) (M : Term⁻) (A : Type)
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---------------
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@ -257,7 +257,7 @@ main = do
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>>= loadAndApplyTemplate "templates/page.html" siteContext
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>>= loadAndApplyTemplate "templates/default.html" siteContext
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>>= prettifyUrls
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match "src/plfa/backmatter/acknowledgements.md" $ version "raw" $ do
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route $ constRoute "acknowledgements.md"
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compile $ getResourceBody
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@ -7,7 +7,7 @@ Dependencies (relative to the root):
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- `README.md`
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- the font `DejaVu mononoki Symbola Droid` installed globally. (Could change to local?)
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First, run `stack build && stack exec site rebuild` from the parent directory to generate acknowledgements.md under `_site`, which is needed by the pdf (Only need to do this once).
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First, run `stack build && stack exec site rebuild` from the parent directory to generate acknowledgements.md under `_site`, which is needed by the pdf (Only need to do this once).
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Then, running `make pdf` from the parent directory should be sufficient to compile the book. The book will be generated in this folder as `plfa.pdf`.
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@ -17,4 +17,4 @@ Alternatively, makefile in this directory provide these options:
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all # Build plfa.pdf (can also run from the parent as "make pdf")
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plfa-sample.pdf # Build a shrinked version of the book for testing
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all_tex # generate all tex version of lagda files under tex/
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```
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```
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@ -208,11 +208,11 @@ _decidable_:
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synthesize : ∀ (Γ : Context) (M : Term⁺)
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-----------------------
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→ Dec (∃[ A ](Γ ⊢ M ↑ A))
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→ Dec (∃[ A ]( Γ ⊢ M ↑ A ))
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inherit : ∀ (Γ : Context) (M : Term⁻) (A : Type)
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---------------
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→ Dec (Γ ⊢ M ↓ A)
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---------------
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→ Dec (Γ ⊢ M ↓ A)
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Given context `Γ` and synthesised term `M`, we must decide whether
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there exists a type `A` such that `Γ ⊢ M ↑ A` holds, or its negation.
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@ -580,9 +580,9 @@ such that `Γ ∋ x ⦂ A` holds, then there is also no type `A` such that
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```
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ext∋ : ∀ {Γ B x y}
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→ x ≢ y
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→ ¬ ( ∃[ A ] Γ ∋ x ⦂ A )
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→ ¬ ∃[ A ]( Γ ∋ x ⦂ A )
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-----------------------------
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→ ¬ ( ∃[ A ] Γ , y ⦂ B ∋ x ⦂ A )
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→ ¬ ∃[ A ]( Γ , y ⦂ B ∋ x ⦂ A )
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ext∋ x≢y _ ⟨ A , Z ⟩ = x≢y refl
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ext∋ _ ¬∃ ⟨ A , S _ ∋x ⟩ = ¬∃ ⟨ A , ∋x ⟩
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```
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@ -597,8 +597,8 @@ there exists a type `A` such that `Γ ∋ x ⦂ A` holds, or its
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negation:
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```
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lookup : ∀ (Γ : Context) (x : Id)
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-----------------------
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→ Dec (∃[ A ](Γ ∋ x ⦂ A))
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-------------------------
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→ Dec (∃[ A ]( Γ ∋ x ⦂ A ))
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lookup ∅ x = no (λ ())
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lookup (Γ , y ⦂ B) x with x ≟ y
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... | yes refl = yes ⟨ B , Z ⟩
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@ -639,7 +639,7 @@ there is no term `B′` such that `Γ ⊢ L · M ↑ B′` holds:
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→ Γ ⊢ L ↑ A ⇒ B
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→ ¬ Γ ⊢ M ↓ A
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----------------------------
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→ ¬ ( ∃[ B′ ] Γ ⊢ L · M ↑ B′ )
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→ ¬ ∃[ B′ ]( Γ ⊢ L · M ↑ B′ )
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¬arg ⊢L ¬⊢M ⟨ B′ , ⊢L′ · ⊢M′ ⟩ rewrite dom≡ (uniq-↑ ⊢L ⊢L′) = ¬⊢M ⊢M′
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```
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Let `⊢L` be evidence that `Γ ⊢ L ↑ A ⇒ B` holds and `¬⊢M` be evidence
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@ -686,8 +686,8 @@ and a type `A` and either returns evidence that `Γ ⊢ M ↓ A`,
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or its negation:
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```
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synthesize : ∀ (Γ : Context) (M : Term⁺)
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-----------------------
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→ Dec (∃[ A ](Γ ⊢ M ↑ A))
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---------------------------
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→ Dec (∃[ A ]( Γ ⊢ M ↑ A ))
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inherit : ∀ (Γ : Context) (M : Term⁻) (A : Type)
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---------------
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