mirror of
https://github.com/luau-lang/luau.git
synced 2024-12-14 06:00:39 +00:00
92 lines
2.8 KiB
Agda
92 lines
2.8 KiB
Agda
module Luau.OpSem where
|
||
|
||
open import Agda.Builtin.Equality using (_≡_)
|
||
open import FFI.Data.Maybe using (just)
|
||
open import Luau.Heap using (Heap; _≡_⊕_↦_; lookup; function_⟨_⟩_end)
|
||
open import Luau.Substitution using (_[_/_]ᴮ)
|
||
open import Luau.Syntax using (Expr; Stat; Block; nil; addr; var; function⟨_⟩_end; _$_; block_is_end; local_←_; _∙_; done; function_⟨_⟩_end; return)
|
||
open import Luau.Value using (addr; val)
|
||
|
||
data _⊢_⟶ᴮ_⊣_ : Heap → Block → Block → Heap → Set
|
||
data _⊢_⟶ᴱ_⊣_ : Heap → Expr → Expr → Heap → Set
|
||
|
||
data _⊢_⟶ᴱ_⊣_ where
|
||
|
||
nil : ∀ {H} →
|
||
|
||
-------------------
|
||
H ⊢ nil ⟶ᴱ nil ⊣ H
|
||
|
||
function : ∀ {H H′ a x B} →
|
||
|
||
H′ ≡ H ⊕ a ↦ (function "anon" ⟨ x ⟩ B end) →
|
||
-------------------------------------------
|
||
H ⊢ (function⟨ x ⟩ B end) ⟶ᴱ (addr a) ⊣ H′
|
||
|
||
app : ∀ {H H′ M M′ N} →
|
||
|
||
H ⊢ M ⟶ᴱ M′ ⊣ H′ →
|
||
-----------------------------
|
||
H ⊢ (M $ N) ⟶ᴱ (M′ $ N) ⊣ H′
|
||
|
||
beta : ∀ {H M a f x B} →
|
||
|
||
(lookup H a) ≡ just(function f ⟨ x ⟩ B end) →
|
||
-----------------------------------------------------
|
||
H ⊢ (addr a $ M) ⟶ᴱ (block f is local x ← M ∙ B end) ⊣ H
|
||
|
||
block : ∀ {H H′ B B′ b} →
|
||
|
||
H ⊢ B ⟶ᴮ B′ ⊣ H′ →
|
||
----------------------------------------------------
|
||
H ⊢ (block b is B end) ⟶ᴱ (block b is B′ end) ⊣ H′
|
||
|
||
return : ∀ {H V B b} →
|
||
|
||
--------------------------------------------------------
|
||
H ⊢ (block b is return (val V) ∙ B end) ⟶ᴱ (val V) ⊣ H
|
||
|
||
done : ∀ {H b} →
|
||
|
||
---------------------------------
|
||
H ⊢ (block b is done end) ⟶ᴱ nil ⊣ H
|
||
|
||
data _⊢_⟶ᴮ_⊣_ where
|
||
|
||
local : ∀ {H H′ x M M′ B} →
|
||
|
||
H ⊢ M ⟶ᴱ M′ ⊣ H′ →
|
||
-------------------------------------------------
|
||
H ⊢ (local x ← M ∙ B) ⟶ᴮ (local x ← M′ ∙ B) ⊣ H′
|
||
|
||
subst : ∀ {H x v B} →
|
||
|
||
-------------------------------------------------
|
||
H ⊢ (local x ← val v ∙ B) ⟶ᴮ (B [ v / x ]ᴮ) ⊣ H
|
||
|
||
function : ∀ {H H′ a f x B C} →
|
||
|
||
H′ ≡ H ⊕ a ↦ (function f ⟨ x ⟩ C end) →
|
||
--------------------------------------------------------------
|
||
H ⊢ (function f ⟨ x ⟩ C end ∙ B) ⟶ᴮ (B [ addr a / f ]ᴮ) ⊣ H′
|
||
|
||
return : ∀ {H H′ M M′ B} →
|
||
|
||
H ⊢ M ⟶ᴱ M′ ⊣ H′ →
|
||
--------------------------------------------
|
||
H ⊢ (return M ∙ B) ⟶ᴮ (return M′ ∙ B) ⊣ H′
|
||
|
||
data _⊢_⟶*_⊣_ : Heap → Block → Block → Heap → Set where
|
||
|
||
refl : ∀ {H B} →
|
||
|
||
----------------
|
||
H ⊢ B ⟶* B ⊣ H
|
||
|
||
step : ∀ {H H′ H″ B B′ B″} →
|
||
H ⊢ B ⟶ᴮ B′ ⊣ H′ →
|
||
H′ ⊢ B′ ⟶* B″ ⊣ H″ →
|
||
------------------
|
||
H ⊢ B ⟶* B″ ⊣ H″
|
||
|
||
|