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agda style

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Jeremy Siek 2019-08-20 15:37:15 -04:00
parent b88cd2478b
commit 69da80df93
1 changed files with 72 additions and 73 deletions
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src/plfa/part3/Compositional.lagda.md
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@ -35,7 +35,8 @@ open import plfa.part2.Untyped
using (Context; _,_; ★; _∋_; _⊢_; `_; ƛ_; _·_) using (Context; _,_; ★; _∋_; _⊢_; `_; ƛ_; _·_)
open import plfa.part3.Denotational open import plfa.part3.Denotational
using (Value; _↦_; _`,_; _⊔_; ⊥; _⊑_; _⊢_↓_; using (Value; _↦_; _`,_; _⊔_; ⊥; _⊑_; _⊢_↓_;
⊑-bot; ⊑-fun; ⊑-conj-L; ⊑-conj-R1; ⊑-conj-R2; ⊑-dist; ⊑-refl; ⊑-trans; ⊔↦⊔-dist; ⊑-bot; ⊑-fun; ⊑-conj-L; ⊑-conj-R1; ⊑-conj-R2;
⊑-dist; ⊑-refl; ⊑-trans; ⊔↦⊔-dist;
var; ↦-intro; ↦-elim; ⊔-intro; ⊥-intro; sub; var; ↦-intro; ↦-elim; ⊔-intro; ⊥-intro; sub;
up-env; ℰ; _≃_; ≃-sym; Denotation; Env) up-env; ℰ; _≃_; ≃-sym; Denotation; Env)
open plfa.part3.Denotational.≃-Reasoning open plfa.part3.Denotational.≃-Reasoning
@ -308,8 +309,7 @@ To round-out the semantic equations, we establish the following one
for variables. for variables.
``` ```
var-equiv : ∀{Γ}{x : Γ ∋ ★} var-equiv : ∀{Γ}{x : Γ ∋ ★} → ℰ (` x) ≃ (λ γ v → v ⊑ γ x)
→ ℰ (` x) ≃ (λ γ v → v ⊑ γ x)
var-equiv γ v = ⟨ var-inv , (λ lt → sub var lt) ⟩ var-equiv γ v = ⟨ var-inv , (λ lt → sub var lt) ⟩
``` ```
@ -507,8 +507,7 @@ straightforward induction, using the three equations
with the congruence lemmas for `ℱ` and `●`. with the congruence lemmas for `ℱ` and `●`.
``` ```
ℰ≃⟦⟧ : ∀ {Γ} {M : Γ ⊢ ★} ℰ≃⟦⟧ : ∀ {Γ} {M : Γ ⊢ ★} → ℰ M ≃ ⟦ M ⟧
→ ℰ M ≃ ⟦ M ⟧
ℰ≃⟦⟧ {Γ} {` x} = var-equiv ℰ≃⟦⟧ {Γ} {` x} = var-equiv
ℰ≃⟦⟧ {Γ} {ƛ N} = ℰ≃⟦⟧ {Γ} {ƛ N} =
let ih = ℰ≃⟦⟧ {M = N} in let ih = ℰ≃⟦⟧ {M = N} in