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ajeffrey@roblox.com 2022-02-24 11:08:12 -06:00
parent ae0745e800
commit 9c7311c19d
1 changed files with 21 additions and 22 deletions
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43
prototyping/Properties/Step.agda
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@ -1,5 +1,4 @@
{-# OPTIONS --rewriting #-}
{-# OPTIONS --allow-unsolved-metas #-}
module Properties.Step where
@ -9,7 +8,7 @@ open import FFI.Data.Maybe using (just; nothing)
open import Luau.Heap using (Heap; _[_]; alloc; ok; function_is_end)
open import Luau.Syntax using (Block; Expr; nil; var; addr; function_is_end; block_is_end; _$_; local_←_; return; done; _∙_; name; fun; arg; number; binexp; +)
open import Luau.OpSem using (_⊢_⟶ᴱ_⊣_; _⊢_⟶ᴮ_⊣_; app₁ ; app₂ ; beta; function; block; return; done; local; subst; binOpEval; evalBinOp; binOp₁; binOp₂)
open import Luau.RuntimeError using (RuntimeErrorᴱ; RuntimeErrorᴮ; UnboundVariable; SEGV; app₁; app₂; block; local; return; bin₁; bin₂)
open import Luau.RuntimeError using (RuntimeErrorᴱ; RuntimeErrorᴮ; FunctionMismatch; BinopMismatch₁; BinopMismatch₂; UnboundVariable; SEGV; app₁; app₂; block; local; return; bin₁; bin₂)
open import Luau.RuntimeType using (function; number)
open import Luau.Substitution using (_[_/_]ᴮ)
open import Luau.Value using (nil; addr; val; number)
@ -40,37 +39,37 @@ stepᴱ H (M $ N) with stepᴱ H M
stepᴱ H (M $ N) | step H′ M′ D = step H′ (M′ $ N) (app₁ D)
stepᴱ H (_ $ N) | value v refl with stepᴱ H N
stepᴱ H (_ $ N) | value v refl | step H′ N′ s = step H′ (val v $ N′) (app₂ v s)
stepᴱ H (_ $ _) | value nil refl | value W refl = {!!} -- error (app₁ (TypeMismatch function nil λ()))
stepᴱ H (_ $ _) | value (number n) refl | value W refl = {!!} -- error (app₁ (TypeMismatch function (number n) λ()))
stepᴱ H (_ $ _) | value (addr a) refl | value W refl with remember (H [ a ])
stepᴱ H (_ $ _) | value (addr a) refl | value W refl | (nothing , p) = error (app₁ (SEGV a p))
stepᴱ H (_ $ _) | value (addr a) refl | value W refl | (just(function F is B end) , p) = {!!} -- step H (block fun F is B [ W / name (arg F) ]ᴮ end) (beta refl p)
stepᴱ H (_ $ _) | value (addr a) refl | value w refl with remember (H [ a ])
stepᴱ H (_ $ _) | value (addr a) refl | value w refl | (nothing , p) = error (app₁ (SEGV a p))
stepᴱ H (_ $ _) | value (addr a) refl | value w refl | (just(function F is B end) , p) = step H (block (fun F) is B [ w / name (arg F) ]ᴮ end) (beta function F is B end w refl p)
stepᴱ H (_ $ _) | value nil refl | value w refl = error (FunctionMismatch nil w refl refl (λ ()))
stepᴱ H (_ $ _) | value (number x) refl | value w refl = error (FunctionMismatch (number x) w refl refl (λ ()))
stepᴱ H (M $ N) | value V p | error E = error (app₂ E)
stepᴱ H (M $ N) | error E = error (app₁ E)
stepᴱ H (block b is B end) with stepᴮ H B
stepᴱ H (block b is B end) | step H′ B′ D = step H′ (block b is B′ end) (block D)
stepᴱ H (block b is (return _ ∙ B′) end) | return V refl = {!!} -- step H (val V) (return refl)
stepᴱ H (block b is (return _ ∙ B′) end) | return v refl = step H (val v) (return v)
stepᴱ H (block b is done end) | done refl = step H nil done
stepᴱ H (block b is B end) | error E = error (block b E)
stepᴱ H (function F is C end) with alloc H (function F is C end)
stepᴱ H function F is C end | ok a H′ p = {!!} -- step H′ (addr a) (function p)
stepᴱ H (binexp x op y) with stepᴱ H x
stepᴱ H (binexp x op y) | value x′ refl with stepᴱ H y
stepᴱ H (binexp x op y) | value (number x′) refl | value (number y′) refl = step H (number (evalBinOp x′ op y′)) binOpEval
stepᴱ H (binexp x op y) | value (number x′) refl | step H′ y′ s = step H′ (binexp (number x′) op y′) (binOp₂ s)
stepᴱ H (binexp x op y) | value (number x′) refl | error E = error (bin₂ E)
stepᴱ H (binexp x op y) | value nil refl | _ = {!!} -- error (bin₁ (TypeMismatch number nil λ()))
stepᴱ H (binexp x op y) | _ | value nil refl = {!!} -- error (bin₂ (TypeMismatch number nil λ()))
stepᴱ H (binexp x op y) | value (addr a) refl | _ = {!!} -- error (bin₁ (TypeMismatch number (addr a) λ()))
stepᴱ H (binexp x op y) | _ | value (addr a) refl = {!!} -- error (bin₂ (TypeMismatch number (addr a) λ()))
stepᴱ H (binexp x op y) | step H′ x′ s = step H′ (binexp x′ op y) (binOp₁ s)
stepᴱ H (binexp x op y) | error E = error (bin₁ E)
stepᴱ H function F is C end | ok a H′ p = step H′ (addr a) (function a p)
stepᴱ H (binexp M op N) with stepᴱ H M
stepᴱ H (binexp M op N) | value v refl with stepᴱ H N
stepᴱ H (binexp M op N) | value v refl | step H′ N′ s = step H′ (binexp (val v) op N′) (binOp₂ s)
stepᴱ H (binexp M op N) | value v refl | error E = error (bin₂ E)
stepᴱ H (binexp M op N) | value (number m) refl | value (number n) refl = step H (number (evalBinOp m op n)) binOpEval
stepᴱ H (binexp M op N) | value nil refl | value w refl = error (BinopMismatch₁ op nil w refl refl λ ())
stepᴱ H (binexp M op N) | value (addr a) refl | value w refl = error (BinopMismatch₁ op (addr a) w refl refl λ ())
stepᴱ H (binexp M op N) | value v refl | value nil refl = error (BinopMismatch₂ op v nil refl refl (λ ()))
stepᴱ H (binexp M op N) | value v refl | value (addr a) refl = error (BinopMismatch₂ op v (addr a) refl refl (λ ()))
stepᴱ H (binexp M op N) | step H′ M′ s = step H′ (binexp M′ op N) (binOp₁ s)
stepᴱ H (binexp M op N) | error E = error (bin₁ E)
stepᴮ H (function F is C end ∙ B) with alloc H (function F is C end)
stepᴮ H (function F is C end ∙ B) | ok a H′ p = {!!} -- step H′ (B [ addr a / name(fun F) ]ᴮ) (function p)
stepᴮ H (function F is C end ∙ B) | ok a H′ p = step H′ (B [ addr a / name (fun F) ]ᴮ) (function a p)
stepᴮ H (local x ← M ∙ B) with stepᴱ H M
stepᴮ H (local x ← M ∙ B) | step H′ M′ D = step H′ (local x ← M′ ∙ B) (local D)
stepᴮ H (local x ← _ ∙ B) | value V refl = {!!} -- step H (B [ V / name x ]ᴮ) subst
stepᴮ H (local x ← _ ∙ B) | value v refl = step H (B [ v / name x ]ᴮ) (subst v)
stepᴮ H (local x ← M ∙ B) | error E = error (local x E)
stepᴮ H (return M ∙ B) with stepᴱ H M
stepᴮ H (return M ∙ B) | step H′ M′ D = step H′ (return M′ ∙ B) (return D)