complete day 1

ahmed/day1.agda

@@ -1,7 +1,6 @@
 {-# OPTIONS --prop #-}
 module Ahmed.Day1 where
 
-import Relation.Binary.PropositionalEquality as Eq
 open import Agda.Builtin.Sigma
 open import Data.Bool
 open import Data.Empty
@@ -10,11 +9,8 @@ open import Data.Maybe
 open import Data.Nat
 open import Data.Product
 open import Data.Sum
-open import Data.Unit
 open import Relation.Nullary
 
-open Eq using (_≡_; refl; trans; sym; cong; cong-app)
-
 id : {A : Set} → A → A
 id {A} x = x
 
@@ -66,7 +62,7 @@ data good-subst : ctx → sub → Set where
 
 data step : term → term → Set where
   step-if-1 : ∀ {e₁ e₂} → step (`if `true then e₁ else e₂) e₁
-  step-if-2 : ∀ {e₁ e₂} → step (`if `false then e₁ else e₂) e₁
+  step-if-2 : ∀ {e₁ e₂} → step (`if `false then e₁ else e₂) e₂
   step-`λ : ∀ {τ e v} → step ((`λ[ τ ] e) ∙ v) (subst e v)
 
 data steps : ℕ → term → term → Set where
@@ -107,37 +103,7 @@ _⊨_∶_ : (Γ : ctx) → (e : term) → (τ : type) → Set
 _⊨_∶_ Γ e τ = (γ : sub) → (good-subst Γ γ) → term-relation τ e
 
 fundamental : ∀ {Γ e τ} → Γ ⊢ e ∶ τ → Γ ⊨ e ∶ τ
-fundamental {Γ} {`true} {bool} type-sound γ good-sub = e-term λ e' steps irred →
+fundamental {Γ} {e} {τ} type-sound γ good-sub = e-term f
-  [ id , (λ exists → ⊥-elim (irred exists)) ] (snd type-sound e' steps)
-fundamental {Γ} {`false} {bool} type-sound γ good-sub = e-term λ e' steps irred →
-  [ id , (λ exists → ⊥-elim (irred exists)) ] (snd type-sound e' steps)
-fundamental {Γ} {`λ[ τ ] e} {τ₁ -→ τ₂} type-sound γ good-sub = e-term f
   where
-    f : {n : ℕ} (e' : term) → steps n (`λ[ τ ] e) e' → irreducible e' → value-rel (τ₁ -→ τ₂) e'
+    f : {n : ℕ} (e' : term) → steps n e e' → irreducible e' → value-rel τ e'
-    f e' steps irred = [ id , (λ exists → ⊥-elim (irred exists)) ] (snd type-sound e' steps)
+    f e' steps irred = [ id , (λ exists → ⊥-elim (irred exists)) ] (snd type-sound e' steps)
-
-fundamental {Γ} {`if e then e₁ else e₂} {τ} type-sound γ good-sub = e-term f
-  where
-    f : {n : ℕ} (e' : term) → steps n (`if e then e₁ else e₂) e' → irreducible e' → value-rel τ e'
-    f .(`if e then e₁ else e₂) zero irred =
-      let
-        ts : well-typed Γ (`if e then e₁ else e₂) τ
-        ts = fst type-sound 
-        ts2 = snd type-sound 
-      in ⊥-elim (irred {!   !})
-    f e' (suc n x steps₁) irred = {!   !}
-fundamental {Γ} {` x} {τ} type-sound γ good-sub = {!   !}
-fundamental {Γ} {e ∙ e₁} {τ} type-sound γ good-sub = {!   !}
-
--- fundamental {Γ} {`true} {τ -→ τ₁} type-sound γ good-sub = e-term f
---   where
---     el : ∀ {A} → well-typed Γ `true (τ -→ τ₁) → A
---     el ()
---     f : {n : ℕ} (e' : term) → steps n `true e' → irreducible e' → value-rel (τ -→ τ₁) e'
---     f e' steps irred = el (fst type-sound)
--- fundamental {Γ} {`false} {τ -→ τ₁} type-sound γ good-sub = e-term f
---   where
---     el : ∀ {A} → well-typed Γ `false (τ -→ τ₁) → A
---     el ()
---     f : {n : ℕ} (e' : term) → steps n `false e' → irreducible e' → value-rel (τ -→ τ₁) e'
---     f e' steps irred = el (fst type-sound)