From 69688762bf24c323884315a91f60a90ec06f62c9 Mon Sep 17 00:00:00 2001
From: Michael Zhang <mail@mzhang.io>
Date: Thu, 9 Dec 2021 04:32:32 -0600
Subject: [PATCH] Better understanding of the types now

---
 src/Project/Cesk.agda        | 20 ++++++++++++++++----
 src/Project/Definitions.agda | 23 ++++++++++++++++++++---
 src/Project/notes.txt        |  6 ++++++
 3 files changed, 42 insertions(+), 7 deletions(-)

diff --git a/src/Project/Cesk.agda b/src/Project/Cesk.agda
index 550914c..804ccc6 100644
--- a/src/Project/Cesk.agda
+++ b/src/Project/Cesk.agda
@@ -28,11 +28,23 @@ step (mkState Tc Γ (case C isZ isS) E K) with astep C E
 ... | suc n = part $ mkState Tc Γ (isS · value n) E K
 step (mkState Tc Γ (x₁ · x₂) E K) with astep x₁ E
 ... | clo body env = apply-proc-clo body env (astep x₂ E) K
-... | cont halt = done $ {!  !}
-... | cont (kont k) = {! apply-kont (kont k) ? !}
+... | cont halt = {!   !}
+... | cont (kont x) = {!   !}
+-- ... | cont k = apply-kont {! k  !} (astep x₂ E)
 -- ... | clo body env = apply-proc-clo body env (astep x₂ E) K
-step (mkState Tc Γ (call/cc x) E K) with astep x E
-... | proc = {!   !}
+step (mkState Tc Γ (call/cc {A} aexp) E K) with astep aexp E
+... | clo {Γc} body env =
+  part $ mkState Tc (Γc , A ⇒ ⊥) body (env [ A ⇒ ⊥ ∶ cont K ]) K
+... | cont k = apply-kont K {!   !}
+-- part $ mkState ((A ⇒ ⊥) ⇒ Tc) Γ aexp E K′
+--  let Γ′ = Γ , A ⇒ ⊥ in
+--  let E′ = E [ A ⇒ ⊥ ∶ cont {!   !} ] in
+--  part $ mkState (((A ⇒ ⊥) ⇒ Tc)) Γ′ aexp E′ {!   !}
+step (mkState Tc Γ (abort V⊥) E K) with astep V⊥ E
+... | ()
+step (mkState Tc Γ (`let {A} C₁ C₂) E K) =
+  let K′ = letk Γ C₂ E K in
+  part $ mkState A Γ C₁ E (kont K′)
 --... | clo {Γc} {A} {B} body env =
 --  let T = Κ[ Tc ⇒ ⊥ ] in
 --  let v = cont K in
diff --git a/src/Project/Definitions.agda b/src/Project/Definitions.agda
index bd7bf68..83bf70d 100644
--- a/src/Project/Definitions.agda
+++ b/src/Project/Definitions.agda
@@ -12,8 +12,8 @@ infixr 7 _⇒_
 
 data Type : Set where
   ⊥ : Type
-  _⇒_ : Type → Type → Type
   `ℕ : Type
+  _⇒_ : Type → Type → Type
 
 data Context : Set where
   ∅ : Context
@@ -49,6 +49,8 @@ data Aexp Γ where
   ƛ : ∀ {B} {A : Type} → Exp (Γ , A) B → Aexp Γ (A ⇒ B)
 
 data Exp Γ where
+  abort : ∀ {A} → Aexp Γ ⊥ → Exp Γ A
+
   -- Atomic expressions
   atomic : ∀ {A} → Aexp Γ A → Exp Γ A
 
@@ -59,7 +61,21 @@ data Exp Γ where
   _·_ : ∀ {A B} → Aexp Γ (A ⇒ B) → Aexp Γ A → Exp Γ B
 
   -- Call/cc
-  call/cc : ∀ {A B Tω} → Aexp Γ ((A ⇒ ⊥) ⇒ B) → Exp Γ Tω
+  call/cc : ∀ {A Tω} → Aexp (Γ) ((A ⇒ ⊥) ⇒ Tω) → Exp Γ Tω
+
+  -- Let
+  `let : ∀ {A B : Type} → Exp Γ A → Exp (Γ , A) B → Exp Γ B
+
+
+-- exp = let (call/cc ƛ . let (abort `0) (`0 · 2)) ((\ . suc `0) · `0)
+-- exp = let (s = call/cc ƛk . let (k' = abort k) (k' · 2)) (suc s)
+-- exp = 3
+exp : Exp ∅ `ℕ
+exp =
+  `let (call/cc (
+    -- `let (` zero · suc (suc zero)) (abort (` zero))
+    ƛ (` zero · suc (suc zero))
+  )) (`let (abort (` zero)) ((ƛ (atomic (suc (` suc zero)))) · ` zero))
 
 data Kont (Tω : Type) : Type → Set
 record Letk (Tv Tω : Type) : Set
@@ -73,7 +89,8 @@ data Value where
   clo : ∀ {Γ} {A B : Type} → Exp (Γ , A) B → Env Γ → Value (A ⇒ B)
 
   -- Call/CC
-  cont : ∀ {Tω A} → Kont Tω A → Value (A ⇒ ⊥)
+  -- cont : ∀ {Tω A} → Kont Tω A → Value (A ⇒ ⊥)
+  cont : ∀ {Tω A B} → Kont Tω A → Value (B ⇒ ⊥)
 
 record Letk Tω Tv where
   inductive
diff --git a/src/Project/notes.txt b/src/Project/notes.txt
index b2eccbd..38e4b1e 100644
--- a/src/Project/notes.txt
+++ b/src/Project/notes.txt
@@ -36,6 +36,12 @@ len (call/cc k . if k "hello" is even then true else false)
 
 ---
 
+(call/cc \k . k 3)
+
+done 3
+
+---
+
 3 + (call/cc \k . abort (k 2))
 
 abort : _|_ -> A