mirror of
https://github.com/luau-lang/luau.git
synced 2024-12-13 13:30:40 +00:00
62 lines
2.3 KiB
Agda
62 lines
2.3 KiB
Agda
{-# OPTIONS --rewriting #-}
|
||
|
||
open import Luau.Type using (Type; Scalar; nil; number; string; boolean; none; any; _⇒_; _∪_; _∩_)
|
||
open import Properties.Equality using (_≢_)
|
||
|
||
module Luau.Subtyping where
|
||
|
||
-- An implementation of semantic subtyping
|
||
|
||
-- We think of types as languages of trees
|
||
|
||
data Tree : Set where
|
||
|
||
scalar : ∀ {T} → Scalar T → Tree
|
||
function : Tree
|
||
function-ok : Tree → Tree
|
||
function-err : Tree → Tree
|
||
|
||
data Language : Type → Tree → Set
|
||
data ¬Language : Type → Tree → Set
|
||
|
||
data Language where
|
||
|
||
scalar : ∀ {T} → (s : Scalar T) → Language T (scalar s)
|
||
function : ∀ {T U} → Language (T ⇒ U) function
|
||
function-ok : ∀ {T U u} → (Language U u) → Language (T ⇒ U) (function-ok u)
|
||
function-err : ∀ {T U t} → (¬Language T t) → Language (T ⇒ U) (function-err t)
|
||
scalar-function-err : ∀ {S t} → (Scalar S) → Language S (function-err t)
|
||
left : ∀ {T U t} → Language T t → Language (T ∪ U) t
|
||
right : ∀ {T U u} → Language U u → Language (T ∪ U) u
|
||
_,_ : ∀ {T U t} → Language T t → Language U t → Language (T ∩ U) t
|
||
any : ∀ {t} → Language any t
|
||
|
||
data ¬Language where
|
||
|
||
scalar-scalar : ∀ {S T} → (s : Scalar S) → (Scalar T) → (S ≢ T) → ¬Language T (scalar s)
|
||
scalar-function : ∀ {S} → (Scalar S) → ¬Language S function
|
||
scalar-function-ok : ∀ {S u} → (Scalar S) → ¬Language S (function-ok u)
|
||
function-scalar : ∀ {S T U} (s : Scalar S) → ¬Language (T ⇒ U) (scalar s)
|
||
function-ok : ∀ {T U u} → (¬Language U u) → ¬Language (T ⇒ U) (function-ok u)
|
||
function-err : ∀ {T U t} → (Language T t) → ¬Language (T ⇒ U) (function-err t)
|
||
_,_ : ∀ {T U t} → ¬Language T t → ¬Language U t → ¬Language (T ∪ U) t
|
||
left : ∀ {T U t} → ¬Language T t → ¬Language (T ∩ U) t
|
||
right : ∀ {T U u} → ¬Language U u → ¬Language (T ∩ U) u
|
||
none : ∀ {t} → ¬Language none t
|
||
|
||
-- Subtyping as language inclusion
|
||
|
||
_<:_ : Type → Type → Set
|
||
(T <: U) = ∀ t → (Language T t) → (Language U t)
|
||
|
||
-- For warnings, we are interested in failures of subtyping,
|
||
-- which is whrn there is a tree in T's language that isn't in U's.
|
||
|
||
data _≮:_ (T U : Type) : Set where
|
||
|
||
witness : ∀ t →
|
||
|
||
Language T t →
|
||
¬Language U t →
|
||
-----------------
|
||
T ≮: U
|