luau-lang/luau
1
0
Fork 0
mirror of https://github.com/luau-lang/luau.git synced 2024-12-13 21:40:43 +00:00
Code Issues Projects Releases Packages Wiki Activity Actions 3
luau/prototyping/Properties/FunctionTypes.agda
Alan Jeffrey 74c84815a0
Prototyping type normalizaton (#466) 
* Added type normalization
2022-04-28 15:00:55 -05:00

150 lines
9.4 KiB
Agda
Raw Blame History

This file contains ambiguous Unicode characters

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

{-# OPTIONS --rewriting #-}
module Properties.FunctionTypes where
open import FFI.Data.Either using (Either; Left; Right; mapLR; swapLR; cond)
open import Luau.FunctionTypes using (srcⁿ; src; tgt)
open import Luau.Subtyping using (_<:_; _≮:_; Tree; Language; ¬Language; witness; unknown; never; scalar; function; scalar-function; scalar-function-ok; scalar-function-err; scalar-scalar; function-scalar; function-ok; function-err; left; right; _,_)
open import Luau.Type using (Type; Scalar; nil; number; string; boolean; never; unknown; _⇒_; _∪_; _∩_; skalar)
open import Properties.Contradiction using (CONTRADICTION; ¬; ⊥)
open import Properties.Functions using (_∘_)
open import Properties.Subtyping using (<:-refl; ≮:-refl; <:-trans-≮:; skalar-scalar; <:-impl-⊇; skalar-function-ok; language-comp)
open import Properties.TypeNormalization using (FunType; Normal; never; unknown; _∩_; _∪_; _⇒_; normal; <:-normalize; normalize-<:)
-- Properties of src
function-err-srcⁿ : ∀ {T t} → (FunType T) → (¬Language (srcⁿ T) t) → Language T (function-err t)
function-err-srcⁿ (S ⇒ T) p = function-err p
function-err-srcⁿ (S ∩ T) (p₁ , p₂) = (function-err-srcⁿ S p₁ , function-err-srcⁿ T p₂)
¬function-err-srcᶠ : ∀ {T t} → (FunType T) → (Language (srcⁿ T) t) → ¬Language T (function-err t)
¬function-err-srcᶠ (S ⇒ T) p = function-err p
¬function-err-srcᶠ (S ∩ T) (left p) = left (¬function-err-srcᶠ S p)
¬function-err-srcᶠ (S ∩ T) (right p) = right (¬function-err-srcᶠ T p)
¬function-err-srcⁿ : ∀ {T t} → (Normal T) → (Language (srcⁿ T) t) → ¬Language T (function-err t)
¬function-err-srcⁿ never p = never
¬function-err-srcⁿ unknown (scalar ())
¬function-err-srcⁿ (S ⇒ T) p = function-err p
¬function-err-srcⁿ (S ∩ T) (left p) = left (¬function-err-srcᶠ S p)
¬function-err-srcⁿ (S ∩ T) (right p) = right (¬function-err-srcᶠ T p)
¬function-err-srcⁿ (S ∪ T) (scalar ())
¬function-err-src : ∀ {T t} → (Language (src T) t) → ¬Language T (function-err t)
¬function-err-src {T = S ⇒ T} p = function-err p
¬function-err-src {T = nil} p = scalar-function-err nil
¬function-err-src {T = never} p = never
¬function-err-src {T = unknown} (scalar ())
¬function-err-src {T = boolean} p = scalar-function-err boolean
¬function-err-src {T = number} p = scalar-function-err number
¬function-err-src {T = string} p = scalar-function-err string
¬function-err-src {T = S ∪ T} p = <:-impl-⊇ (<:-normalize (S ∪ T)) _ (¬function-err-srcⁿ (normal (S ∪ T)) p)
¬function-err-src {T = S ∩ T} p = <:-impl-⊇ (<:-normalize (S ∩ T)) _ (¬function-err-srcⁿ (normal (S ∩ T)) p)
src-¬function-errᶠ : ∀ {T t} → (FunType T) → Language T (function-err t) → (¬Language (srcⁿ T) t)
src-¬function-errᶠ (S ⇒ T) (function-err p) = p
src-¬function-errᶠ (S ∩ T) (p₁ , p₂) = (src-¬function-errᶠ S p₁ , src-¬function-errᶠ T p₂)
src-¬function-errⁿ : ∀ {T t} → (Normal T) → Language T (function-err t) → (¬Language (srcⁿ T) t)
src-¬function-errⁿ unknown p = never
src-¬function-errⁿ (S ⇒ T) (function-err p) = p
src-¬function-errⁿ (S ∩ T) (p₁ , p₂) = (src-¬function-errᶠ S p₁ , src-¬function-errᶠ T p₂)
src-¬function-errⁿ (S ∪ T) p = never
src-¬function-err : ∀ {T t} → Language T (function-err t) → (¬Language (src T) t)
src-¬function-err {T = S ⇒ T} (function-err p) = p
src-¬function-err {T = unknown} p = never
src-¬function-err {T = S ∪ T} p = src-¬function-errⁿ (normal (S ∪ T)) (<:-normalize (S ∪ T) _ p)
src-¬function-err {T = S ∩ T} p = src-¬function-errⁿ (normal (S ∩ T)) (<:-normalize (S ∩ T) _ p)
fun-¬scalar : ∀ {S T} (s : Scalar S) → FunType T → ¬Language T (scalar s)
fun-¬scalar s (S ⇒ T) = function-scalar s
fun-¬scalar s (S ∩ T) = left (fun-¬scalar s S)
¬fun-scalar : ∀ {S T t} (s : Scalar S) → FunType T → Language T t → ¬Language S t
¬fun-scalar s (S ⇒ T) function = scalar-function s
¬fun-scalar s (S ⇒ T) (function-ok p) = scalar-function-ok s
¬fun-scalar s (S ⇒ T) (function-err p) = scalar-function-err s
¬fun-scalar s (S ∩ T) (p₁ , p₂) = ¬fun-scalar s T p₂
fun-function : ∀ {T} → FunType T → Language T function
fun-function (S ⇒ T) = function
fun-function (S ∩ T) = (fun-function S , fun-function T)
srcⁿ-¬scalar : ∀ {S T t} (s : Scalar S) → Normal T → Language T (scalar s) → (¬Language (srcⁿ T) t)
srcⁿ-¬scalar s never (scalar ())
srcⁿ-¬scalar s unknown p = never
srcⁿ-¬scalar s (S ⇒ T) (scalar ())
srcⁿ-¬scalar s (S ∩ T) (p₁ , p₂) = CONTRADICTION (language-comp (scalar s) (fun-¬scalar s S) p₁)
srcⁿ-¬scalar s (S ∪ T) p = never
src-¬scalar : ∀ {S T t} (s : Scalar S) → Language T (scalar s) → (¬Language (src T) t)
src-¬scalar {T = nil} s p = never
src-¬scalar {T = T ⇒ U} s (scalar ())
src-¬scalar {T = never} s (scalar ())
src-¬scalar {T = unknown} s p = never
src-¬scalar {T = boolean} s p = never
src-¬scalar {T = number} s p = never
src-¬scalar {T = string} s p = never
src-¬scalar {T = T ∪ U} s p = srcⁿ-¬scalar s (normal (T ∪ U)) (<:-normalize (T ∪ U) (scalar s) p)
src-¬scalar {T = T ∩ U} s p = srcⁿ-¬scalar s (normal (T ∩ U)) (<:-normalize (T ∩ U) (scalar s) p)
srcⁿ-unknown-≮: : ∀ {T U} → (Normal U) → (T ≮: srcⁿ U) → (U ≮: (T ⇒ unknown))
srcⁿ-unknown-≮: never (witness t p q) = CONTRADICTION (language-comp t q unknown)
srcⁿ-unknown-≮: unknown (witness t p q) = witness (function-err t) unknown (function-err p)
srcⁿ-unknown-≮: (U ⇒ V) (witness t p q) = witness (function-err t) (function-err q) (function-err p)
srcⁿ-unknown-≮: (U ∩ V) (witness t p q) = witness (function-err t) (function-err-srcⁿ (U ∩ V) q) (function-err p)
srcⁿ-unknown-≮: (U ∪ V) (witness t p q) = witness (scalar V) (right (scalar V)) (function-scalar V)
src-unknown-≮: : ∀ {T U} → (T ≮: src U) → (U ≮: (T ⇒ unknown))
src-unknown-≮: {U = nil} (witness t p q) = witness (scalar nil) (scalar nil) (function-scalar nil)
src-unknown-≮: {U = T ⇒ U} (witness t p q) = witness (function-err t) (function-err q) (function-err p)
src-unknown-≮: {U = never} (witness t p q) = CONTRADICTION (language-comp t q unknown)
src-unknown-≮: {U = unknown} (witness t p q) = witness (function-err t) unknown (function-err p)
src-unknown-≮: {U = boolean} (witness t p q) = witness (scalar boolean) (scalar boolean) (function-scalar boolean)
src-unknown-≮: {U = number} (witness t p q) = witness (scalar number) (scalar number) (function-scalar number)
src-unknown-≮: {U = string} (witness t p q) = witness (scalar string) (scalar string) (function-scalar string)
src-unknown-≮: {U = T ∪ U} p = <:-trans-≮: (normalize-<: (T ∪ U)) (srcⁿ-unknown-≮: (normal (T ∪ U)) p)
src-unknown-≮: {U = T ∩ U} p = <:-trans-≮: (normalize-<: (T ∩ U)) (srcⁿ-unknown-≮: (normal (T ∩ U)) p)
unknown-src-≮: : ∀ {S T U} → (U ≮: S) → (T ≮: (U ⇒ unknown)) → (U ≮: src T)
unknown-src-≮: (witness t x x₁) (witness (scalar s) p (function-scalar s)) = witness t x (src-¬scalar s p)
unknown-src-≮: r (witness (function-ok (scalar s)) p (function-ok (scalar-scalar s () q)))
unknown-src-≮: r (witness (function-ok (function-ok _)) p (function-ok (scalar-function-ok ())))
unknown-src-≮: r (witness (function-err t) p (function-err q)) = witness t q (src-¬function-err p)
-- Properties of tgt
tgt-function-ok : ∀ {T t} → (Language (tgt T) t) → Language T (function-ok t)
tgt-function-ok {T = nil} (scalar ())
tgt-function-ok {T = T₁ ⇒ T₂} p = function-ok p
tgt-function-ok {T = never} (scalar ())
tgt-function-ok {T = unknown} p = unknown
tgt-function-ok {T = boolean} (scalar ())
tgt-function-ok {T = number} (scalar ())
tgt-function-ok {T = string} (scalar ())
tgt-function-ok {T = T₁ ∪ T₂} (left p) = left (tgt-function-ok p)
tgt-function-ok {T = T₁ ∪ T₂} (right p) = right (tgt-function-ok p)
tgt-function-ok {T = T₁ ∩ T₂} (p₁ , p₂) = (tgt-function-ok p₁ , tgt-function-ok p₂)
function-ok-tgt : ∀ {T t} → Language T (function-ok t) → (Language (tgt T) t)
function-ok-tgt (function-ok p) = p
function-ok-tgt (left p) = left (function-ok-tgt p)
function-ok-tgt (right p) = right (function-ok-tgt p)
function-ok-tgt (p₁ , p₂) = (function-ok-tgt p₁ , function-ok-tgt p₂)
function-ok-tgt unknown = unknown
tgt-never-≮: : ∀ {T U} → (tgt T ≮: U) → (T ≮: (skalar ∪ (never ⇒ U)))
tgt-never-≮: (witness t p q) = witness (function-ok t) (tgt-function-ok p) (skalar-function-ok , function-ok q)
never-tgt-≮: : ∀ {T U} → (T ≮: (skalar ∪ (never ⇒ U))) → (tgt T ≮: U)
never-tgt-≮: (witness (scalar s) p (q₁ , q₂)) = CONTRADICTION (≮:-refl (witness (scalar s) (skalar-scalar s) q₁))
never-tgt-≮: (witness function p (q₁ , scalar-function ()))
never-tgt-≮: (witness (function-ok t) p (q₁ , function-ok q₂)) = witness t (function-ok-tgt p) q₂
never-tgt-≮: (witness (function-err (scalar s)) p (q₁ , function-err (scalar ())))
src-tgtᶠ-<: : ∀ {T U V} → (FunType T) → (U <: src T) → (tgt T <: V) → (T <: (U ⇒ V))
src-tgtᶠ-<: T p q (scalar s) r = CONTRADICTION (language-comp (scalar s) (fun-¬scalar s T) r)
src-tgtᶠ-<: T p q function r = function
src-tgtᶠ-<: T p q (function-ok s) r = function-ok (q s (function-ok-tgt r))
src-tgtᶠ-<: T p q (function-err s) r = function-err (<:-impl-⊇ p s (src-¬function-err r))
Reference in a new issue View git blame Copy permalink