luau/prototyping/Luau/Substitution.agda
Lily Brown 0bd21762ae
Prototype bools and relational operators (#387)
Prototypes booleans and relational operators.

As part of this I removed `FFI/Data/Bool.agda`, because it was getting in the way - we already use `Agda.Builtin.Bool` instead for other cases.
2022-02-24 11:17:46 -08:00

34 lines
1.6 KiB
Agda

module Luau.Substitution where
open import Luau.Syntax using (Expr; Stat; Block; nil; true; false; addr; var; function_is_end; _$_; block_is_end; local_←_; _∙_; done; return; _⟨_⟩ ; name; fun; arg; number; binexp)
open import Luau.Value using (Value; val)
open import Luau.Var using (Var; _≡ⱽ_)
open import Properties.Dec using (Dec; yes; no)
_[_/_]ᴱ : {a} Expr a Value Var Expr a
_[_/_]ᴮ : {a} Block a Value Var Block a
var_[_/_]ᴱwhenever_ : {a P} Var Value Var (Dec P) Expr a
_[_/_]ᴮunless_ : {a P} Block a Value Var (Dec P) Block a
nil [ v / x ]ᴱ = nil
true [ v / x ]ᴱ = true
false [ v / x ]ᴱ = false
var y [ v / x ]ᴱ = var y [ v / x ]ᴱwhenever (x ≡ⱽ y)
addr a [ v / x ]ᴱ = addr a
(number y) [ v / x ]ᴱ = number y
(M $ N) [ v / x ]ᴱ = (M [ v / x ]ᴱ) $ (N [ v / x ]ᴱ)
function F is C end [ v / x ]ᴱ = function F is C [ v / x ]ᴮunless (x ≡ⱽ name(arg F)) end
block b is C end [ v / x ]ᴱ = block b is C [ v / x ]ᴮ end
(binexp e₁ op e₂) [ v / x ]ᴱ = binexp (e₁ [ v / x ]ᴱ) op (e₂ [ v / x ]ᴱ)
(function F is C end B) [ v / x ]ᴮ = function F is (C [ v / x ]ᴮunless (x ≡ⱽ name(arg F))) end (B [ v / x ]ᴮunless (x ≡ⱽ fun F))
(local y M B) [ v / x ]ᴮ = local y (M [ v / x ]ᴱ) (B [ v / x ]ᴮunless (x ≡ⱽ name y))
(return M B) [ v / x ]ᴮ = return (M [ v / x ]ᴱ) (B [ v / x ]ᴮ)
done [ v / x ]ᴮ = done
var y [ v / x ]ᴱwhenever yes p = val v
var y [ v / x ]ᴱwhenever no p = var y
B [ v / x ]ᴮunless yes p = B
B [ v / x ]ᴮunless no p = B [ v / x ]ᴮ