Not sure if this is working.

Yggdrasil/World.agda

@@ -1,17 +1,18 @@
 module Yggdrasil.World where
 
 open import Data.Bool using (Bool; T)
-open import Data.List using (List; _∷_; []; map)
+open import Data.List using (List; _∷_; []; map; _++_; length; lookup)
 open import Data.List.Any using (here; there)
 open import Data.List.Membership.Propositional using (_∈_)
+open import Data.Fin using (Fin)
 open import Data.Maybe using (Maybe; just; nothing) renaming (map to mmap)
 open import Data.Nat using (ℕ; suc)
-open import Data.Product as Π using (_×_; ∃; ∃-syntax; proj₁; proj₂) renaming (_,_ to ⟨_,_⟩)
+open import Data.Product as Π using (_×_; ∃; ∃-syntax; proj₁; proj₂; map₂) renaming (_,_ to ⟨_,_⟩)
 open import Data.String using (String)
 import Data.String.Unsafe as S
 open import Function using (id)
 open import Level using (Level; _⊔_; Lift) renaming (suc to lsuc; zero to lzero)
-open import Relation.Binary.PropositionalEquality using (_≡_; refl)
+open import Relation.Binary.PropositionalEquality using (_≡_; _≢_; refl)
 open import Relation.Nullary using (Dec; yes; no)
 
 -- Auto-lifted variant of ⊤.
@@ -21,128 +22,147 @@ data ⊤ {ℓ : Level} : Set ℓ where
 Table : ∀ {ℓ} → Set ℓ → Set ℓ
 Table A = List (String × A)
 
-lookup : ∀ {ℓ A} → Table {ℓ} A → String → Maybe A
-lookup [] _ = nothing
-lookup (⟨ s₁ , x ⟩ ∷ xs) s₂ with s₁ S.≟ s₂
-... | yes _ = just x
-... | no _  = lookup xs s₂
+_∪_ : ∀ {ℓ A} → Table {ℓ} A → Table {ℓ} A → Table {ℓ} A
+_∪_ = _++_
 
 module Weak where
+
   record WeakState {ℓ : Level} : Set (lsuc ℓ)
 
-  record WeakTransition {ℓ : Level} : Set (lsuc ℓ) where
+  record WeakTransition {ℓ : Level} (n : ℕ) : Set (lsuc ℓ) where
     inductive
     field
       A : Set ℓ
       B : A → Set ℓ
-      Σ : A → WeakState {ℓ}
+      Σ : A → Fin n
 
   record WeakState {ℓ} where
     inductive
     field
-      δ↑ : Table (WeakTransition {ℓ})
-      δ↓ : Table (WeakTransition {ℓ})
+      states : List (Set ℓ)
+      current : Fin (length states)
+      δ↑ : Fin (length states) → Table (WeakTransition {ℓ} (length states))
+      δ↓ : Fin (length states) → Table (WeakTransition {ℓ} (length states))
 
 open Weak using (WeakState; WeakTransition)
+open WeakState
 
 record State {ℓ : Level} (Σʷ : WeakState {ℓ}) : Set (lsuc ℓ)
-data Action {ℓ : Level} : {Σʷ₁ Σʷ₂ : WeakState {ℓ}} → (Σ₁ : Π.Σ (Set ℓ) id) →
+
+data Action {ℓ : Level} : {Σʷ₁ Σʷ₂ : WeakState {ℓ}} →
+    (Σ₁ : Fin (length (states Σʷ₁))) →
     (Σ₂ : State Σʷ₂) → Set ℓ → Set (lsuc ℓ)
 
-Transition↑ : {ℓ : Level} {Σʷ : WeakState {ℓ}} → (Σ₁ : Π.Σ (Set ℓ) id) →
-  WeakTransition {ℓ} → Set (lsuc ℓ)
-Transition↑ {Σʷ = Σʷ} Σ₁ T = (x : A T) → Π.Σ (State (Σ T x))
+Transition↑ : {ℓ : Level} {Σʷ : WeakState {ℓ}} →
+  (Σ₁ : Fin (length (states Σʷ))) → WeakTransition {ℓ} (length (states Σʷ)) →
+  Set (lsuc ℓ)
+Transition↑ {Σʷ = Σʷ} Σ₁ T = (x : A T) → Π.Σ
+    (State (record Σʷ { current = Σ T x }))
     (λ Σ₂ → Action {Σʷ₁ = Σʷ} Σ₁ Σ₂ (B T x))
   where open WeakTransition using (A; B; Σ)
 
-Transition↓ : {ℓ : Level} → WeakTransition {ℓ} → Set (lsuc ℓ)
-Transition↓ T = (x : A T) → State (Σ T x)
+Transition↓ : {ℓ : Level} {Σʷ : WeakState {ℓ}} →
+  WeakTransition {ℓ} (length (states Σʷ)) → Set ℓ
+Transition↓ {Σʷ = Σʷ} T = (x : A T) → Π.Σ (Fin (length (states Σʷ)))
+    (λ n → lookup (states Σʷ) n)
   where open WeakTransition using (A; Σ)
 
-data Transitions↑ {ℓ : Level} (Σ : Π.Σ (Set ℓ) id) :
-    Table (WeakTransition {ℓ}) → Set (lsuc ℓ) where
-  [] : Transitions↑ Σ []
-  _∷_ : ∀ {Σʷ T Ts name} → Transition↑ {Σʷ = Σʷ} Σ T → Transitions↑ Σ Ts →
-    Transitions↑ Σ (⟨ name , T ⟩ ∷ Ts)
-
-data Transitions↓ {ℓ : Level} :
-    Table (WeakTransition {ℓ}) → Set (lsuc ℓ) where
-  [] : Transitions↓ []
-  _∷_ : ∀ {T Ts name} → Transition↓ T → Transitions↓ Ts →
-    Transitions↓ (⟨ name , T ⟩ ∷ Ts)
-
+--data Transitions↑ {ℓ : Level} (Σ : Π.Σ (Set ℓ) id) :
+--    Table (WeakTransition {ℓ}) → Set (lsuc ℓ) where
+--  [] : Transitions↑ Σ []
+--  _∷_ : ∀ {Σʷ T Ts name} → Transition↑ {Σʷ = Σʷ} Σ T → Transitions↑ Σ Ts →
+--    Transitions↑ Σ (⟨ name , T ⟩ ∷ Ts)
+--
+--data Transitions↓ {ℓ : Level} :
+--    Table (WeakTransition {ℓ}) → Set (lsuc ℓ) where
+--  [] : Transitions↓ []
+--  _∷_ : ∀ {T Ts name} → Transition↓ T → Transitions↓ Ts →
+--    Transitions↓ (⟨ name , T ⟩ ∷ Ts)
+--
 record State {ℓ} Σʷ where
-  inductive
+  open WeakState
   field
-    Σ : Set ℓ
-    σ : Σ
-    δ↑ : Transitions↑ ⟨ Σ , σ ⟩ (WeakState.δ↑ Σʷ)
-    δ↓ : Transitions↓ (WeakState.δ↓ Σʷ)
-
-⌊_⌋ : ∀ {ℓ Σʷ} → (Σ : State {ℓ} Σʷ) → Π.Σ (Set ℓ) id
-⌊ Σ ⌋ = ⟨ State.Σ Σ , State.σ Σ ⟩
-
-lookup↓ : ∀ {ℓ xs δ} → δ ∈ xs → (Ts : Transitions↓ {ℓ} xs) → Transition↓ (proj₂ δ)
-lookup↓ (here refl) (x ∷ _) = x
-lookup↓ (there ∈xs) (_ ∷ xs) = lookup↓ ∈xs xs
-
-∈↓ʷ⇒∈↓ : ∀ {ℓ Σʷ δ} {Σ : State Σʷ} → δ ∈ (WeakState.δ↓ Σʷ) →
-  Transition↓ {ℓ} (proj₂ δ)
-∈↓ʷ⇒∈↓ {Σ = Σ} δ∈ = lookup↓ δ∈ (State.δ↓ Σ)
+    n : Fin (length (states Σʷ))
+    σ : lookup (states Σʷ) n
+--    δ↑ : Transitions↑ ⟨ Σ , σ ⟩ (WeakState.δ↑ Σʷ)
+--    δ↓ : Transitions↓ (WeakState.δ↓ Σʷ)
 --
---open Weak
+--⌊_⌋ : ∀ {ℓ Σʷ} → (Σ : State {ℓ} Σʷ) → Π.Σ (Set ℓ) id
+--⌊ Σ ⌋ = ⟨ State.Σ Σ , State.σ Σ ⟩
+--
+--lookup↓ : ∀ {ℓ xs δ} → δ ∈ xs → (Ts : Transitions↓ {ℓ} xs) → Transition↓ (proj₂ δ)
+--lookup↓ (here refl) (x ∷ _) = x