Fixed binding issues with existential syntax.

courses/tspl/2019/Assignment4.lagda.md

@@ -982,15 +982,15 @@ Remember to indent all code by two spaces.
 ```
   ext∋ : ∀ {Γ B x y}
     → x ≢ y
-    → ¬ (∃[ A ]( Γ ∋ x ⦂ A ))
+    → ¬ ∃[ A ]( Γ ∋ x ⦂ A )
       ------------------------------
-    → ¬ (∃[ A ]( Γ , y ⦂ B ∋ x ⦂ A ))
+    → ¬ ∃[ A ]( Γ , y ⦂ B ∋ x ⦂ A )
   ext∋ x≢y _  ⟨ A , Z ⟩       =  x≢y refl
   ext∋ _   ¬∃ ⟨ A , S _ ⊢x ⟩  =  ¬∃ ⟨ A , ⊢x ⟩
 
   lookup : ∀ (Γ : Context) (x : Id)
            ------------------------
-         → Dec (∃[ A ](Γ ∋ x ⦂ A))
+         → Dec (∃[ A ]( Γ ∋ x ⦂ A ))
   lookup ∅ x                        =  no  (λ ())
   lookup (Γ , y ⦂ B) x with x ≟ y
   ... | yes refl                    =  yes ⟨ B , Z ⟩
@@ -1006,7 +1006,7 @@ Remember to indent all code by two spaces.
     → Γ ⊢ L ↑ A ⇒ B
     → ¬ Γ ⊢ M ↓ A
       ----------------------------
-    → ¬ (∃[ B′ ]( Γ ⊢ L · M ↑ B′ ))
+    → ¬ ∃[ B′ ]( Γ ⊢ L · M ↑ B′ )
   ¬arg ⊢L ¬⊢M ⟨ B′ , ⊢L′ · ⊢M′ ⟩ rewrite dom≡ (uniq-↑ ⊢L ⊢L′) = ¬⊢M ⊢M′
 
   ¬switch : ∀ {Γ M A B}

courses/tspl/2019/Exam.lagda.md

@@ -589,9 +589,9 @@ module Problem3 where
 ```
   ext∋ : ∀ {Γ B x y}
     → x ≢ y
-    → ¬ ( ∃[ A ] Γ ∋ x ⦂ A )
+    → ¬ ∃[ A ]( Γ ∋ x ⦂ A )
       -----------------------------
-    → ¬ ( ∃[ A ] Γ , y ⦂ B ∋ x ⦂ A )
+    → ¬ ∃[ A ]( Γ , y ⦂ B ∋ x ⦂ A )
   ext∋ x≢y _  ⟨ A , Z ⟩       =  x≢y refl
   ext∋ _   ¬∃ ⟨ A , S _ ⊢x ⟩  =  ¬∃ ⟨ A , ⊢x ⟩
 
@@ -614,7 +614,7 @@ module Problem3 where
     → Γ ⊢ L ↑ A ⇒ B
     → ¬ Γ ⊢ M ↓ A
       ----------------------------
-    → ¬ ( ∃[ B′ ] Γ ⊢ L · M ↑ B′ )
+    → ¬ ∃[ B′ ]( Γ ⊢ L · M ↑ B′ )
   ¬arg ⊢L ¬⊢M ⟨ B′ , ⊢L′ · ⊢M′ ⟩ rewrite dom≡ (uniq-↑ ⊢L ⊢L′) = ¬⊢M ⊢M′
 
   ¬switch : ∀ {Γ M A B}
@@ -631,7 +631,7 @@ module Problem3 where
 ```
   synthesize : ∀ (Γ : Context) (M : Term⁺)
       -----------------------
-    → Dec (∃[ A ](Γ ⊢ M ↑ A))
+    → Dec (∃[ A ]( Γ ⊢ M ↑ A ))
 
   inherit : ∀ (Γ : Context) (M : Term⁻) (A : Type)
       ---------------

hs/Main.hs

@@ -257,7 +257,7 @@ main = do
         >>= loadAndApplyTemplate "templates/page.html"    siteContext
         >>= loadAndApplyTemplate "templates/default.html" siteContext
         >>= prettifyUrls
-    
+
     match "src/plfa/backmatter/acknowledgements.md" $ version "raw" $ do
       route $ constRoute "acknowledgements.md"
       compile $ getResourceBody

pdf/README.md

@@ -7,7 +7,7 @@ Dependencies (relative to the root):
 - `README.md`
 - the font `DejaVu mononoki Symbola Droid` installed globally. (Could change to local?)
 
-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). 
+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).
 
 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`.
 
@@ -17,4 +17,4 @@ Alternatively, makefile in this directory provide these options:
 all                      # Build plfa.pdf (can also run from the parent as "make pdf")
 plfa-sample.pdf          # Build a shrinked version of the book for testing
 all_tex                  # generate all tex version of lagda files under tex/
-```
+```

src/plfa/part2/Inference.lagda.md

@@ -208,11 +208,11 @@ _decidable_:
 
     synthesize : ∀ (Γ : Context) (M : Term⁺)
         -----------------------
-      → Dec (∃[ A ](Γ ⊢ M ↑ A))
+      → Dec (∃[ A ]( Γ ⊢ M ↑ A ))
 
     inherit : ∀ (Γ : Context) (M : Term⁻) (A : Type)
-        ---------------
+              ---------------
-      → Dec (Γ ⊢ M ↓ A)
+            → Dec (Γ ⊢ M ↓ A)
 
 Given context `Γ` and synthesised term `M`, we must decide whether
 there exists a type `A` such that `Γ ⊢ M ↑ A` holds, or its negation.
@@ -580,9 +580,9 @@ such that `Γ ∋ x ⦂ A` holds, then there is also no type `A` such that
 ```
 ext∋ : ∀ {Γ B x y}
   → x ≢ y
-  → ¬ ( ∃[ A ] Γ ∋ x ⦂ A )
+  → ¬ ∃[ A ]( Γ ∋ x ⦂ A )
     -----------------------------
-  → ¬ ( ∃[ A ] Γ , y ⦂ B ∋ x ⦂ A )
+  → ¬ ∃[ A ]( Γ , y ⦂ B ∋ x ⦂ A )
 ext∋ x≢y _  ⟨ A , Z ⟩       =  x≢y refl
 ext∋ _   ¬∃ ⟨ A , S _ ∋x ⟩  =  ¬∃ ⟨ A , ∋x ⟩
 ```
@@ -597,8 +597,8 @@ there exists a type `A` such that `Γ ∋ x ⦂ A` holds, or its
 negation:
 ```
 lookup : ∀ (Γ : Context) (x : Id)
-    -----------------------
+         -------------------------
-  → Dec (∃[ A ](Γ ∋ x ⦂ A))
+       → Dec (∃[ A ]( Γ ∋ x ⦂ A ))
 lookup ∅ x                        =  no  (λ ())
 lookup (Γ , y ⦂ B) x with x ≟ y
 ... | yes refl                    =  yes ⟨ B , Z ⟩
@@ -639,7 +639,7 @@ there is no term `B′` such that `Γ ⊢ L · M ↑ B′` holds:
   → Γ ⊢ L ↑ A ⇒ B
   → ¬ Γ ⊢ M ↓ A
     ----------------------------
-  → ¬ ( ∃[ B′ ] Γ ⊢ L · M ↑ B′ )
+  → ¬ ∃[ B′ ]( Γ ⊢ L · M ↑ B′ )
 ¬arg ⊢L ¬⊢M ⟨ B′ , ⊢L′ · ⊢M′ ⟩ rewrite dom≡ (uniq-↑ ⊢L ⊢L′) = ¬⊢M ⊢M′
 ```
 Let `⊢L` be evidence that `Γ ⊢ L ↑ A ⇒ B` holds and `¬⊢M` be evidence
@@ -686,8 +686,8 @@ and a type `A` and either returns evidence that `Γ ⊢ M ↓ A`,
 or its negation:
 ```
 synthesize : ∀ (Γ : Context) (M : Term⁺)
-    -----------------------
+             ---------------------------
-  → Dec (∃[ A ](Γ ⊢ M ↑ A))
+           → Dec (∃[ A ]( Γ ⊢ M ↑ A ))
 
 inherit : ∀ (Γ : Context) (M : Term⁻) (A : Type)
     ---------------