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ajeffrey@roblox.com
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commit
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3 changed files with 219 additions and 217 deletions
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@ -5,10 +5,11 @@ module Luau.StrictMode where
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open import Agda.Builtin.Equality using (_≡_)
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open import FFI.Data.Maybe using (just; nothing)
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open import Luau.Syntax using (Expr; Stat; Block; BinaryOperator; yes; nil; addr; var; binexp; var_∈_; _⟨_⟩∈_; function_is_end; _$_; block_is_end; local_←_; _∙_; done; return; name; +; -; *; /; <; >; <=; >=; ··)
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open import Luau.Type using (Type; strict; nil; number; string; _⇒_; tgt)
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open import Luau.Type using (Type; strict; nil; number; string; boolean; none; any; _⇒_; _∪_; _∩_; tgt)
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open import Luau.Heap using (Heap; function_is_end) renaming (_[_] to _[_]ᴴ)
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open import Luau.VarCtxt using (VarCtxt; ∅; _⋒_; _↦_; _⊕_↦_; _⊝_) renaming (_[_] to _[_]ⱽ)
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open import Luau.TypeCheck(strict) using (_⊢ᴮ_∈_; _⊢ᴱ_∈_; ⊢ᴴ_; ⊢ᴼ_; _⊢ᴴᴱ_▷_∈_; _⊢ᴴᴮ_▷_∈_; var; addr; app; binexp; block; return; local; function)
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open import Luau.TypeCheck(strict) using (_⊢ᴮ_∈_; _⊢ᴱ_∈_; ⊢ᴴ_; ⊢ᴼ_; _⊢ᴴᴱ_▷_∈_; _⊢ᴴᴮ_▷_∈_; var; addr; app; binexp; block; return; local; function; srcBinOp)
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open import Properties.Contradiction using (¬)
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open import Properties.Equality using (_≢_)
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open import Properties.TypeCheck(strict) using (typeCheckᴮ)
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open import Properties.Product using (_,_)
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@ -16,22 +17,53 @@ open import Properties.Product using (_,_)
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src : Type → Type
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src = Luau.Type.src strict
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data _<:_ (T U : Type) : Set where
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temp : (T ≡ U) → (T <: U)
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data Scalar : Type → Set where
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number : Scalar number
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boolean : Scalar boolean
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string : Scalar string
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nil : Scalar nil
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data Tree : Set where
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scalar : ∀ {T} → Scalar T → Tree
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function-ok : Tree → Tree
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function-err : Tree → Tree
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data Language : Type → Tree → Set
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data ¬Language : Type → Tree → Set
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data Language where
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scalar : ∀ {T} → (s : Scalar T) → Language T (scalar s)
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function-ok : ∀ {T U u} → (Language U u) → Language (T ⇒ U) (function-ok u)
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function-err : ∀ {T U t} → (¬Language T t) → Language (T ⇒ U) (function-err t)
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left : ∀ {T U t} → Language T t → Language (T ∪ U) t
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right : ∀ {T U u} → Language U u → Language (T ∪ U) u
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_,_ : ∀ {T U t} → Language T t → Language U t → Language (T ∩ U) t
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any : ∀ {t} → Language any t
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data ¬Language where
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scalar-scalar : ∀ {S T} → (s : Scalar S) → (Scalar T) → (S ≢ T) → ¬Language T (scalar s)
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scalar-function-ok : ∀ {S u} → (Scalar S) → ¬Language S (function-ok u)
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scalar-function-err : ∀ {S t} → (Scalar S) → ¬Language S (function-err t)
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function-scalar : ∀ {S T U} (s : Scalar S) → ¬Language (T ⇒ U) (scalar s)
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function-ok : ∀ {T U u} → (¬Language U u) → ¬Language (T ⇒ U) (function-ok u)
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function-err : ∀ {T U t} → (Language T t) → ¬Language (T ⇒ U) (function-err t)
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_,_ : ∀ {T U t} → ¬Language T t → ¬Language U t → ¬Language (T ∪ U) t
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left : ∀ {T U t} → ¬Language T t → ¬Language (T ∩ U) t
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right : ∀ {T U u} → ¬Language U u → ¬Language (T ∩ U) u
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none : ∀ {t} → ¬Language none t
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data _≮:_ (T U : Type) : Set where
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temp : (T ≢ U) → (T ≮: U)
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data BinOpWarning : BinaryOperator → Type → Set where
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+ : ∀ {T} → (T ≮: number) → BinOpWarning + T
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- : ∀ {T} → (T ≮: number) → BinOpWarning - T
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* : ∀ {T} → (T ≮: number) → BinOpWarning * T
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/ : ∀ {T} → (T ≮: number) → BinOpWarning / T
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< : ∀ {T} → (T ≮: number) → BinOpWarning < T
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> : ∀ {T} → (T ≮: number) → BinOpWarning > T
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<= : ∀ {T} → (T ≮: number) → BinOpWarning <= T
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>= : ∀ {T} → (T ≮: number) → BinOpWarning >= T
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·· : ∀ {T} → (T ≮: string) → BinOpWarning ·· T
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witness : ∀ t →
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Language T t →
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¬Language U t →
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-----------------
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T ≮: U
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data Warningᴱ (H : Heap yes) {Γ} : ∀ {M T} → (Γ ⊢ᴱ M ∈ T) → Set
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data Warningᴮ (H : Heap yes) {Γ} : ∀ {B T} → (Γ ⊢ᴮ B ∈ T) → Set
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@ -70,13 +102,13 @@ data Warningᴱ H {Γ} where
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BinOpMismatch₁ : ∀ {op M N T U} {D₁ : Γ ⊢ᴱ M ∈ T} {D₂ : Γ ⊢ᴱ N ∈ U} →
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BinOpWarning op T →
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(T ≮: srcBinOp op) →
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------------------------------
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Warningᴱ H (binexp {op} D₁ D₂)
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BinOpMismatch₂ : ∀ {op M N T U} {D₁ : Γ ⊢ᴱ M ∈ T} {D₂ : Γ ⊢ᴱ N ∈ U} →
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BinOpWarning op U →
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(U ≮: srcBinOp op) →
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------------------------------
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Warningᴱ H (binexp {op} D₁ D₂)
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@ -144,8 +176,7 @@ data Warningᴮ H {Γ} where
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FunctionDefnMismatch : ∀ {f x B C T U V W} {D₁ : (Γ ⊕ x ↦ T) ⊢ᴮ C ∈ V} {D₂ : (Γ ⊕ f ↦ (T ⇒ U)) ⊢ᴮ B ∈ W} →
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(V ≮: U
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) →
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(V ≮: U) →
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-------------------------------------
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Warningᴮ H (function D₁ D₂)
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@ -23,6 +23,19 @@ orAny : Maybe Type → Type
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orAny nothing = any
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orAny (just T) = T
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srcBinOp : BinaryOperator → Type
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srcBinOp + = number
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srcBinOp - = number
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srcBinOp * = number
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srcBinOp / = number
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srcBinOp < = number
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srcBinOp > = number
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srcBinOp == = any
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srcBinOp ~= = any
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srcBinOp <= = number
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srcBinOp >= = number
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srcBinOp ·· = string
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tgtBinOp : BinaryOperator → Type
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tgtBinOp + = number
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tgtBinOp - = number
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@ -7,11 +7,11 @@ open import Agda.Builtin.Equality using (_≡_; refl)
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open import FFI.Data.Either using (Either; Left; Right)
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open import FFI.Data.Maybe using (Maybe; just; nothing)
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open import Luau.Heap using (Heap; Object; function_is_end; defn; alloc; ok; next; lookup-not-allocated) renaming (_≡_⊕_↦_ to _≡ᴴ_⊕_↦_; _[_] to _[_]ᴴ; ∅ to ∅ᴴ)
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open import Luau.StrictMode using (Warningᴱ; Warningᴮ; Warningᴼ; Warningᴴ; UnallocatedAddress; UnboundVariable; FunctionCallMismatch; app₁; app₂; BinOpWarning; BinOpMismatch₁; BinOpMismatch₂; bin₁; bin₂; BlockMismatch; block₁; return; LocalVarMismatch; local₁; local₂; FunctionDefnMismatch; function₁; function₂; heap; expr; block; addr; +; -; *; /; <; >; <=; >=; ··; _<:_; _≮:_)
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open import Luau.StrictMode using (Warningᴱ; Warningᴮ; Warningᴼ; Warningᴴ; UnallocatedAddress; UnboundVariable; FunctionCallMismatch; app₁; app₂; BinOpMismatch₁; BinOpMismatch₂; bin₁; bin₂; BlockMismatch; block₁; return; LocalVarMismatch; local₁; local₂; FunctionDefnMismatch; function₁; function₂; heap; expr; block; addr; _≮:_; witness; any; none; nil; number; string; boolean; scalar; scalar-function-ok; scalar-function-err; scalar-scalar; function-scalar; function-ok; function-err; left; right; _,_; Tree; Language; ¬Language; Scalar)
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open import Luau.Substitution using (_[_/_]ᴮ; _[_/_]ᴱ; _[_/_]ᴮunless_; var_[_/_]ᴱwhenever_)
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open import Luau.Syntax using (Expr; yes; var; val; var_∈_; _⟨_⟩∈_; _$_; addr; number; bool; string; binexp; nil; function_is_end; block_is_end; done; return; local_←_; _∙_; fun; arg; name; ==; ~=)
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open import Luau.Type using (Type; strict; nil; number; boolean; string; _⇒_; none; any; tgt; _≡ᵀ_; _≡ᴹᵀ_)
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open import Luau.TypeCheck(strict) using (_⊢ᴮ_∈_; _⊢ᴱ_∈_; _⊢ᴴᴮ_▷_∈_; _⊢ᴴᴱ_▷_∈_; nil; var; addr; app; function; block; done; return; local; orAny; tgtBinOp)
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open import Luau.Type using (Type; strict; nil; number; boolean; string; _⇒_; none; any; _∩_; _∪_; tgt; _≡ᵀ_; _≡ᴹᵀ_)
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open import Luau.TypeCheck(strict) using (_⊢ᴮ_∈_; _⊢ᴱ_∈_; _⊢ᴴᴮ_▷_∈_; _⊢ᴴᴱ_▷_∈_; nil; var; addr; app; function; block; done; return; local; orAny; srcBinOp; tgtBinOp)
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open import Luau.Var using (_≡ⱽ_)
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open import Luau.Addr using (_≡ᴬ_)
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open import Luau.VarCtxt using (VarCtxt; ∅; _⋒_; _↦_; _⊕_↦_; _⊝_; ⊕-lookup-miss; ⊕-swap; ⊕-over) renaming (_[_] to _[_]ⱽ)
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@ -23,7 +23,7 @@ open import Properties.Contradiction using (CONTRADICTION; ¬)
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open import Properties.TypeCheck(strict) using (typeOfᴼ; typeOfᴹᴼ; typeOfⱽ; typeOfᴱ; typeOfᴮ; typeCheckᴱ; typeCheckᴮ; typeCheckᴼ; typeCheckᴴ)
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open import Luau.OpSem using (_⟦_⟧_⟶_; _⊢_⟶*_⊣_; _⊢_⟶ᴮ_⊣_; _⊢_⟶ᴱ_⊣_; app₁; app₂; function; beta; return; block; done; local; subst; binOp₀; binOp₁; binOp₂; refl; step; +; -; *; /; <; >; ==; ~=; <=; >=; ··)
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open import Luau.RuntimeError using (BinOpError; RuntimeErrorᴱ; RuntimeErrorᴮ; FunctionMismatch; BinOpMismatch₁; BinOpMismatch₂; UnboundVariable; SEGV; app₁; app₂; bin₁; bin₂; block; local; return; +; -; *; /; <; >; <=; >=; ··)
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open import Luau.RuntimeType using (valueType; number; string; function)
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open import Luau.RuntimeType using (RuntimeType; valueType; number; string; boolean; nil; function)
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-- Move these! --
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swapLR : ∀ {A B} → Either A B → Either B A
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@ -86,37 +86,67 @@ lookup-⊑-nothing {H} a (snoc defn) p with a ≡ᴬ next H
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lookup-⊑-nothing {H} a (snoc defn) p | yes refl = refl
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lookup-⊑-nothing {H} a (snoc o) p | no q = trans (lookup-not-allocated o q) p
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-- For the moment subtyping is just syntactic equality, with any as top but this will change!
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dec-language : ∀ T t → Either (¬Language T t) (Language T t)
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dec-language = {!!}
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<:-refl : ∀ T → (T <: T)
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<:-refl T = {!!}
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<:-any : ∀ T → (T <: any)
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<:-any = {!!}
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≮:-antirefl : ∀ T → ¬(T ≮: T)
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≮:-antirefl = {!!}
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≮:-antirefl : ∀ {T} → ¬(T ≮: T)
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≮:-antirefl (witness (scalar s) (scalar s) (scalar-scalar s t p)) = CONTRADICTION (p refl)
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≮:-antirefl (witness (function-ok t) (function-ok p) (function-ok q)) = ≮:-antirefl (witness t p q)
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≮:-antirefl (witness (function-err t) (function-err p) (function-err q)) = ≮:-antirefl (witness t q p)
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≮:-antirefl (witness t (left p) (q₁ , q₂)) = ≮:-antirefl (witness t p q₁)
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≮:-antirefl (witness t (right p) (q₁ , q₂)) = ≮:-antirefl (witness t p q₂)
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≮:-antirefl (witness t (p₁ , p₂) (left q)) = ≮:-antirefl (witness t p₁ q)
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≮:-antirefl (witness t (p₁ , p₂) (right q)) = ≮:-antirefl (witness t p₂ q)
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≮:-antirefl (witness (scalar s) any (scalar-scalar s () t))
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≮:-antirefl (witness (function-ok t) any (scalar-function-ok ()))
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≮:-antirefl (witness (function-err t) any (scalar-function-err ()))
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≮:-antitrans : ∀ {S T U} → (S ≮: U) → Either (S ≮: T) (T ≮: U)
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≮:-antitrans = {!!}
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≮:-antitrans {T = T} (witness t p q) = mapLR (witness t p) (λ z → witness t z q) (dec-language T t)
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<:-trans-≮: : ∀ {S T U} → (S <: T) → (S ≮: U) → (T ≮: U)
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<:-trans-≮: = {!!}
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any-≮: : ∀ {T U} → (T ≮: U) → (any ≮: U)
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any-≮: (witness t p q) = witness t any q
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≮:-trans-<: : ∀ {S T U} → (S ≮: U) → (T <: U) → (S ≮: T)
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≮:-trans-<: = {!!}
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none-≮: : ∀ {T U} → (T ≮: U) → (T ≮: none)
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none-≮: (witness t p q) = witness t p none
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src-contravariant : ∀ {T U} → (T <: U) → (src U <: src T)
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src-contravariant = {!!}
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skalar = number ∪ (string ∪ (nil ∪ boolean))
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tgt-covariant : ∀ {T U} → (T <: U) → (tgt T <: tgt U)
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tgt-covariant = {!!}
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tgt-function-ok : ∀ {T t} → (Language (tgt T) t) → Language T (function-ok t)
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tgt-function-ok {T = nil} (scalar ())
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tgt-function-ok {T = T₁ ⇒ T₂} p = function-ok p
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tgt-function-ok {T = none} (scalar ())
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tgt-function-ok {T = any} p = any
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tgt-function-ok {T = boolean} (scalar ())
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tgt-function-ok {T = number} (scalar ())
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tgt-function-ok {T = string} (scalar ())
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tgt-function-ok {T = T₁ ∪ T₂} (left p) = left (tgt-function-ok p)
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tgt-function-ok {T = T₁ ∪ T₂} (right p) = right (tgt-function-ok p)
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tgt-function-ok {T = T₁ ∩ T₂} (p₁ , p₂) = (tgt-function-ok p₁ , tgt-function-ok p₂)
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tgt-≮: : ∀ {T U} → (tgt T ≮: tgt U) → (T ≮: U)
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tgt-≮: = {!!}
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function-ok-tgt : ∀ {T t} → Language T (function-ok t) → (Language (tgt T) t)
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function-ok-tgt (function-ok p) = p
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function-ok-tgt (left p) = left (function-ok-tgt p)
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function-ok-tgt (right p) = right (function-ok-tgt p)
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function-ok-tgt (p₁ , p₂) = (function-ok-tgt p₁ , function-ok-tgt p₂)
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function-ok-tgt any = any
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none-tgt-≮: : ∀ {T U} → (T ≮: (none ⇒ U)) → (tgt T ≮: U)
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none-tgt-≮: = {!!}
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skalar-function-ok : ∀ {t} → (¬Language skalar (function-ok t))
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skalar-function-ok = (scalar-function-ok number , (scalar-function-ok string , (scalar-function-ok nil , scalar-function-ok boolean)))
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skalar-scalar : ∀ {T} (s : Scalar T) → (Language skalar (scalar s))
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skalar-scalar number = left (scalar number)
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skalar-scalar boolean = right (right (right (scalar boolean)))
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skalar-scalar string = right (left (scalar string))
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skalar-scalar nil = right (right (left (scalar nil)))
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tgt-src-≮: : ∀ {T U} → (tgt T ≮: U) → (T ≮: (skalar ∪ (none ⇒ U)))
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tgt-src-≮: (witness t p q) = witness (function-ok t) (tgt-function-ok p) (skalar-function-ok , function-ok q)
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src-tgt-≮: : ∀ {T U} → (T ≮: (skalar ∪ (none ⇒ U))) → (tgt T ≮: U)
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src-tgt-≮: (witness (scalar s) p (q₁ , q₂)) = CONTRADICTION (≮:-antirefl (witness (scalar s) (skalar-scalar s) q₁))
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src-tgt-≮: (witness (function-ok t) p (q₁ , function-ok q₂)) = witness t (function-ok-tgt p) q₂
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src-tgt-≮: (witness (function-err (scalar s)) p (q₁ , function-err (scalar ())))
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src-≮: : ∀ {T U} → (src T ≮: src U) → (U ≮: T)
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src-≮: = {!!}
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@ -124,6 +154,18 @@ src-≮: = {!!}
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any-src-≮: : ∀ {T U} → (T ≮: (U ⇒ any)) → (U ≮: src T)
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any-src-≮: = {!!}
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function-≮:-scalar : ∀ {S T U} → (Scalar U) → ((S ⇒ T) ≮: U)
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function-≮:-scalar = {!!}
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scalar-≮:-function : ∀ {S T U} → (Scalar U) → (U ≮: (S ⇒ T))
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scalar-≮:-function s = witness (scalar s) (scalar s) (function-scalar s)
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any-≮:-scalar : ∀ {U} → (Scalar U) → (any ≮: U)
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any-≮:-scalar s = witness (function-ok (scalar s)) any (scalar-function-ok s)
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scalar-≢-impl-≮: : ∀ {T U} → (Scalar T) → (Scalar U) → (T ≢ U) → (T ≮: U)
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scalar-≢-impl-≮: s₁ s₂ p = witness (scalar s₁) (scalar s₁) (scalar-scalar s₁ s₂ p)
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-- The rest of the proof just depends on those properties
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≮:-trans-≡ : ∀ {S T U} → (S ≮: T) → (T ≡ U) → (S ≮: U)
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@ -132,47 +174,26 @@ any-src-≮: = {!!}
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≡-trans-≮: : ∀ {S T U} → (S ≡ T) → (T ≮: U) → (S ≮: U)
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≡-trans-≮: refl p = p
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≡-impl-<: : ∀ {T U} → (T ≡ U) → (T <: U)
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≡-impl-<: {T} refl = <:-refl T
|
||||
heap-weakeningᴱ : ∀ Γ H M {H′ U} → (H ⊑ H′) → (typeOfᴱ H′ Γ M ≮: U) → (typeOfᴱ H Γ M ≮: U)
|
||||
heap-weakeningᴱ Γ H (var x) h p = p
|
||||
heap-weakeningᴱ Γ H (val nil) h p = p
|
||||
heap-weakeningᴱ Γ H (val (addr a)) refl p = p
|
||||
heap-weakeningᴱ Γ H (val (addr a)) (snoc {a = b} q) p with a ≡ᴬ b
|
||||
heap-weakeningᴱ Γ H (val (addr a)) (snoc {a = a} defn) p | yes refl = any-≮: p
|
||||
heap-weakeningᴱ Γ H (val (addr a)) (snoc {a = b} q) p | no r = ≡-trans-≮: (cong orAny (cong typeOfᴹᴼ (lookup-not-allocated q r))) p
|
||||
heap-weakeningᴱ Γ H (val (number x)) h p = p
|
||||
heap-weakeningᴱ Γ H (val (bool x)) h p = p
|
||||
heap-weakeningᴱ Γ H (val (string x)) h p = p
|
||||
heap-weakeningᴱ Γ H (M $ N) h p = src-tgt-≮: (heap-weakeningᴱ Γ H M h (tgt-src-≮: p))
|
||||
heap-weakeningᴱ Γ H (function f ⟨ var x ∈ T ⟩∈ U is B end) h p = p
|
||||
heap-weakeningᴱ Γ H (block var b ∈ T is B end) h p = p
|
||||
heap-weakeningᴱ Γ H (binexp M op N) h p = p
|
||||
|
||||
heap-weakeningᴱ : ∀ Γ H M {H′} → (H ⊑ H′) → (typeOfᴱ H′ Γ M <: typeOfᴱ H Γ M)
|
||||
heap-weakeningᴮ : ∀ Γ H B {H′} → (H ⊑ H′) → (typeOfᴮ H′ Γ B <: typeOfᴮ H Γ B)
|
||||
|
||||
heap-weakeningᴱ Γ H (var x) h = <:-refl (typeOfᴱ H Γ (var x))
|
||||
heap-weakeningᴱ Γ H (val nil) h = <:-refl nil
|
||||
heap-weakeningᴱ Γ H (val (addr a)) refl = <:-refl (typeOfᴱ H Γ (val (addr a)))
|
||||
heap-weakeningᴱ Γ H (val (addr a)) (snoc {a = b} defn) with a ≡ᴬ b
|
||||
heap-weakeningᴱ Γ H (val (addr a)) (snoc {a = a} {O = O} defn) | yes refl = <:-any (typeOfᴼ O)
|
||||
heap-weakeningᴱ Γ H (val (addr a)) (snoc {a = b} p) | no q = ≡-impl-<: (cong orAny (cong typeOfᴹᴼ (sym (lookup-not-allocated p q))))
|
||||
heap-weakeningᴱ Γ H (val (number n)) h = <:-refl number
|
||||
heap-weakeningᴱ Γ H (val (bool b)) h = <:-refl boolean
|
||||
heap-weakeningᴱ Γ H (val (string x)) h = <:-refl string
|
||||
heap-weakeningᴱ Γ H (binexp M op N) h = <:-refl (typeOfᴱ H Γ (binexp M op N))
|
||||
heap-weakeningᴱ Γ H (M $ N) h = tgt-covariant (heap-weakeningᴱ Γ H M h)
|
||||
heap-weakeningᴱ Γ H (function f ⟨ var x ∈ T ⟩∈ U is B end) h = <:-refl (T ⇒ U)
|
||||
heap-weakeningᴱ Γ H (block var b ∈ T is B end) h = <:-refl T
|
||||
heap-weakeningᴮ Γ H (function f ⟨ var x ∈ T ⟩∈ U is C end ∙ B) h = heap-weakeningᴮ (Γ ⊕ f ↦ (T ⇒ U)) H B h
|
||||
heap-weakeningᴮ Γ H (local var x ∈ T ← M ∙ B) h = heap-weakeningᴮ (Γ ⊕ x ↦ T) H B h
|
||||
heap-weakeningᴮ Γ H (return M ∙ B) h = heap-weakeningᴱ Γ H M h
|
||||
heap-weakeningᴮ Γ H (done) h = <:-refl nil
|
||||
|
||||
heap-weakening-≮:ᴱ : ∀ Γ H M {H′ U} → (H ⊑ H′) → (typeOfᴱ H′ Γ M ≮: U) → (typeOfᴱ H Γ M ≮: U)
|
||||
heap-weakening-≮:ᴱ Γ H M h p = <:-trans-≮: (heap-weakeningᴱ Γ H M h) p
|
||||
|
||||
heap-weakening-≮:ᴮ : ∀ Γ H B {H′ U} → (H ⊑ H′) → (typeOfᴮ H′ Γ B ≮: U) → (typeOfᴮ H Γ B ≮: U)
|
||||
heap-weakening-≮:ᴮ Γ H B h p = <:-trans-≮: (heap-weakeningᴮ Γ H B h) p
|
||||
|
||||
-- none-not-obj : ∀ O → none ≢ typeOfᴼ O
|
||||
-- none-not-obj (function f ⟨ var x ∈ T ⟩∈ U is B end) ()
|
||||
|
||||
-- typeOf-val-not-none : ∀ {H Γ} v → OrWarningᴱ H (typeCheckᴱ H Γ (val v)) (typeOfᴱ H Γ (val v) ≮: none)
|
||||
-- typeOf-val-not-none nil = ok {!!}
|
||||
-- typeOf-val-not-none (number n) = ok {!!}
|
||||
-- typeOf-val-not-none (bool b) = ok {!!}
|
||||
-- typeOf-val-not-none (string x) = ok {!!}
|
||||
-- typeOf-val-not-none {H = H} (addr a) with remember (H [ a ]ᴴ)
|
||||
-- typeOf-val-not-none {H = H} (addr a) | (just O , p) = ok {!!}
|
||||
-- typeOf-val-not-none {H = H} (addr a) | (nothing , p) = warning (UnallocatedAddress p)
|
||||
heap-weakeningᴮ : ∀ Γ H B {H′ U} → (H ⊑ H′) → (typeOfᴮ H′ Γ B ≮: U) → (typeOfᴮ H Γ B ≮: U)
|
||||
heap-weakeningᴮ Γ H (function f ⟨ var x ∈ T ⟩∈ U is C end ∙ B) h p = heap-weakeningᴮ (Γ ⊕ f ↦ (T ⇒ U)) H B h p
|
||||
heap-weakeningᴮ Γ H (local var x ∈ T ← M ∙ B) h p = heap-weakeningᴮ (Γ ⊕ x ↦ T) H B h p
|
||||
heap-weakeningᴮ Γ H (return M ∙ B) h p = heap-weakeningᴱ Γ H M h p
|
||||
heap-weakeningᴮ Γ H done h p = p
|
||||
|
||||
substitutivityᴱ : ∀ {Γ T U} H M v x → (typeOfᴱ H Γ (M [ v / x ]ᴱ) ≮: U) → Either (typeOfᴱ H (Γ ⊕ x ↦ T) M ≮: U) (typeOfᴱ H ∅ (val v) ≮: T)
|
||||
substitutivityᴱ-whenever : ∀ {Γ T U} H v x y (r : Dec(x ≡ y)) → (typeOfᴱ H Γ (var y [ v / x ]ᴱwhenever r) ≮: U) → Either (typeOfᴱ H (Γ ⊕ x ↦ T) (var y) ≮: U) (typeOfᴱ H ∅ (val v) ≮: T)
|
||||
|
|
@ -184,7 +205,7 @@ substitutivityᴮ-unless-no : ∀ {Γ Γ′ T V} H B v x y (r : x ≢ y) → (Γ
|
|||
substitutivityᴱ H (var y) v x p = substitutivityᴱ-whenever H v x y (x ≡ⱽ y) p
|
||||
substitutivityᴱ H (val w) v x p = Left p
|
||||
substitutivityᴱ H (binexp M op N) v x p = Left p
|
||||
substitutivityᴱ H (M $ N) v x p = mapL none-tgt-≮: (substitutivityᴱ H M v x (tgt-≮: p))
|
||||
substitutivityᴱ H (M $ N) v x p = mapL src-tgt-≮: (substitutivityᴱ H M v x (tgt-src-≮: p))
|
||||
substitutivityᴱ H (function f ⟨ var y ∈ T ⟩∈ U is B end) v x p = Left p
|
||||
substitutivityᴱ H (block var b ∈ T is B end) v x p = Left p
|
||||
substitutivityᴱ-whenever H v x x (yes refl) q = swapLR (≮:-antitrans q)
|
||||
|
|
@ -199,114 +220,35 @@ substitutivityᴮ-unless H B v x y (no p) q = substitutivityᴮ-unless-no H B v
|
|||
substitutivityᴮ-unless-yes H B v x y refl refl p = Left p
|
||||
substitutivityᴮ-unless-no H B v x y p refl q = substitutivityᴮ H B v x q
|
||||
|
||||
-- substitutivityᴱ-src : ∀ {Γ T} H M N v x → (typeOfᴱ H Γ (N [ v / x ]ᴱ) ≮: src(typeOfᴱ H Γ (M [ v / x ]ᴱ))) → Either (typeOfᴱ H (Γ ⊕ x ↦ T) N ≮: src(typeOfᴱ H (Γ ⊕ x ↦ T) M)) (Either (Warningᴱ H (typeCheckᴱ H ∅ (val v))) (typeOfᴱ H ∅ (val v) ≮: T))
|
||||
-- substitutivityᴱ-src = {!!}
|
||||
|
||||
|
||||
-- substitutivityᴱ H (var y) v x p with x ≡ⱽ y
|
||||
-- substitutivityᴱ H (var y) v x p | yes q = substitutivityᴱ-whenever-yes H v x y q p
|
||||
-- substitutivityᴱ H (var y) v x p | no q = substitutivityᴱ-whenever-no H v x y q p
|
||||
-- substitutivityᴱ H (val w) v x p = refl
|
||||
-- substitutivityᴱ H (binexp M op N) v x p = refl
|
||||
-- substitutivityᴱ H (M $ N) v x p = cong tgt (substitutivityᴱ H M v x p)
|
||||
-- substitutivityᴱ H (function f ⟨ var y ∈ T ⟩∈ U is B end) v x p = refl
|
||||
-- substitutivityᴱ H (block var b ∈ T is B end) v x p = refl
|
||||
-- substitutivityᴱ-whenever-yes H v x x refl q = cong orAny q
|
||||
-- substitutivityᴱ-whenever-no H v x y p q = cong orAny ( sym (⊕-lookup-miss x y _ _ p))
|
||||
-- substitutivityᴮ H (function f ⟨ var y ∈ T ⟩∈ U is C end ∙ B) v x p with x ≡ⱽ f
|
||||
-- substitutivityᴮ H (function f ⟨ var y ∈ T ⟩∈ U is C end ∙ B) v x p | yes q = substitutivityᴮ-unless-yes H B v x f q p (⊕-over q)
|
||||
-- substitutivityᴮ H (function f ⟨ var y ∈ T ⟩∈ U is C end ∙ B) v x p | no q = substitutivityᴮ-unless-no H B v x f q p (⊕-swap q)
|
||||
-- substitutivityᴮ H (local var y ∈ T ← M ∙ B) v x p with x ≡ⱽ y
|
||||
-- substitutivityᴮ H (local var y ∈ T ← M ∙ B) v x p | yes q = substitutivityᴮ-unless-yes H B v x y q p (⊕-over q)
|
||||
-- substitutivityᴮ H (local var y ∈ T ← M ∙ B) v x p | no q = substitutivityᴮ-unless-no H B v x y q p (⊕-swap q)
|
||||
-- substitutivityᴮ H (return M ∙ B) v x p = substitutivityᴱ H M v x p
|
||||
-- substitutivityᴮ H done v x p = refl
|
||||
-- substitutivityᴮ-unless-yes H B v x x refl q refl = refl
|
||||
-- substitutivityᴮ-unless-no H B v x y p q refl = substitutivityᴮ H B v x q
|
||||
|
||||
-- binOpPreservation : ∀ H {op v w x} → (v ⟦ op ⟧ w ⟶ x) → (tgtBinOp op ≡ typeOfᴱ H ∅ (val x))
|
||||
-- binOpPreservation H (+ m n) = refl
|
||||
-- binOpPreservation H (- m n) = refl
|
||||
-- binOpPreservation H (/ m n) = refl
|
||||
-- binOpPreservation H (* m n) = refl
|
||||
-- binOpPreservation H (< m n) = refl
|
||||
-- binOpPreservation H (> m n) = refl
|
||||
-- binOpPreservation H (<= m n) = refl
|
||||
-- binOpPreservation H (>= m n) = refl
|
||||
-- binOpPreservation H (== v w) = refl
|
||||
-- binOpPreservation H (~= v w) = refl
|
||||
-- binOpPreservation H (·· v w) = refl
|
||||
|
||||
-- <:-BinOpWarning : ∀ op {T U} → (T <: U) → BinOpWarning op T → BinOpWarning op U
|
||||
-- <:-BinOpWarning = {!!}
|
||||
|
||||
-- preservationᴱ : ∀ H M {H′ M′} → (H ⊢ M ⟶ᴱ M′ ⊣ H′) → Either (typeOfᴱ H′ ∅ M′ <: typeOfᴱ H ∅ M) (Either (Warningᴱ H (typeCheckᴱ H ∅ M)) (Warningᴴ H (typeCheckᴴ H)))
|
||||
-- preservationᴮ : ∀ H B {H′ B′} → (H ⊢ B ⟶ᴮ B′ ⊣ H′) → Either (typeOfᴮ H′ ∅ B′ <: typeOfᴮ H ∅ B) (Either (Warningᴮ H (typeCheckᴮ H ∅ B)) (Warningᴴ H (typeCheckᴴ H)))
|
||||
|
||||
-- preservationᴱ = {!!}
|
||||
-- preservationᴮ = {!!}
|
||||
|
||||
-- preservationᴱ H (function f ⟨ var x ∈ T ⟩∈ U is B end) (function a defn) = ok refl
|
||||
-- preservationᴱ H (M $ N) (app₁ s) with preservationᴱ H M s
|
||||
-- preservationᴱ H (M $ N) (app₁ s) | ok p = ok (cong tgt p)
|
||||
-- preservationᴱ H (M $ N) (app₁ s) | warning (expr W) = warning (expr (app₁ W))
|
||||
-- preservationᴱ H (M $ N) (app₁ s) | warning (heap W) = warning (heap W)
|
||||
-- preservationᴱ H (M $ N) (app₂ p s) with heap-weakeningᴱ H M (rednᴱ⊑ s)
|
||||
-- preservationᴱ H (M $ N) (app₂ p s) | ok q = ok (cong tgt q)
|
||||
-- preservationᴱ H (M $ N) (app₂ p s) | warning W = warning (expr (app₁ W))
|
||||
-- preservationᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ S ⟩∈ T is B end) v refl p) with remember (typeOfⱽ H v)
|
||||
-- preservationᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ S ⟩∈ T is B end) v refl p) | (just U , q) with S ≡ᵀ U | T ≡ᵀ typeOfᴮ H (x ↦ S) B
|
||||
-- preservationᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ S ⟩∈ T is B end) v refl p) | (just U , q) | yes refl | yes refl = ok (cong tgt (cong orAny (cong typeOfᴹᴼ p)))
|
||||
-- preservationᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ S ⟩∈ T is B end) v refl p) | (just U , q) | yes refl | no r = warning (heap (addr a p (FunctionDefnMismatch {!!})))
|
||||
-- preservationᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ S ⟩∈ T is B end) v refl p) | (just U , q) | no r | _ = warning (expr (FunctionCallMismatch {!!}))
|
||||
-- preservationᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ S ⟩∈ T is B end) v refl p) | (nothing , q) with typeOf-val-not-none v
|
||||
-- preservationᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ S ⟩∈ T is B end) v refl p) | (nothing , q) | ok r = {!!}
|
||||
-- preservationᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ S ⟩∈ T is B end) v refl p) | (nothing , q) | warning W = warning (expr (app₂ W))
|
||||
-- preservationᴱ H (block var b ∈ T is B end) (block s) = ok refl
|
||||
-- preservationᴱ H (block var b ∈ T is return M ∙ B end) (return v) with T ≡ᵀ typeOfᴱ H ∅ (val v)
|
||||
-- preservationᴱ H (block var b ∈ T is return M ∙ B end) (return v) | yes p = ok p
|
||||
-- preservationᴱ H (block var b ∈ T is return M ∙ B end) (return v) | no p = warning (expr (BlockMismatch p))
|
||||
-- preservationᴱ H (block var b ∈ T is done end) (done) with T ≡ᵀ nil
|
||||
-- preservationᴱ H (block var b ∈ T is done end) (done) | yes p = ok p
|
||||
-- preservationᴱ H (block var b ∈ T is done end) (done) | no p = warning (expr (BlockMismatch p))
|
||||
-- preservationᴱ H (binexp M op N) (binOp₀ s) = ok (binOpPreservation H s)
|
||||
-- preservationᴱ H (binexp M op N) (binOp₁ s) = ok refl
|
||||
-- preservationᴱ H (binexp M op N) (binOp₂ s) = ok refl
|
||||
|
||||
-- preservationᴮ H (local var x ∈ T ← M ∙ B) (local s) with heap-weakeningᴮ H B (rednᴱ⊑ s)
|
||||
-- preservationᴮ H (local var x ∈ T ← M ∙ B) (local s) | ok p = ok p
|
||||
-- preservationᴮ H (local var x ∈ T ← M ∙ B) (local s) | warning W = warning (block (local₂ W))
|
||||
-- preservationᴮ H (local var x ∈ T ← M ∙ B) (subst v) with remember (typeOfⱽ H v)
|
||||
-- preservationᴮ H (local var x ∈ T ← M ∙ B) (subst v) | (just U , p) with T ≡ᵀ U
|
||||
-- preservationᴮ H (local var x ∈ T ← M ∙ B) (subst v) | (just T , p) | yes refl = ok (substitutivityᴮ H B v x (sym p))
|
||||
-- preservationᴮ H (local var x ∈ T ← M ∙ B) (subst v) | (just U , p) | no q = warning (block (LocalVarMismatch {!!}))
|
||||
-- preservationᴮ H (local var x ∈ T ← M ∙ B) (subst v) | (nothing , p) with typeOf-val-not-none v
|
||||
-- preservationᴮ H (local var x ∈ T ← M ∙ B) (subst v) | (nothing , p) | ok q = {!!}
|
||||
-- preservationᴮ H (local var x ∈ T ← M ∙ B) (subst v) | (nothing , p) | warning W = warning (block (local₁ W))
|
||||
-- preservationᴮ H (function f ⟨ var x ∈ T ⟩∈ U is C end ∙ B) (function a defn) with heap-weakeningᴮ H B (snoc defn)
|
||||
-- preservationᴮ H (function f ⟨ var x ∈ T ⟩∈ U is C end ∙ B) (function a defn) | ok r = ok (trans r (substitutivityᴮ _ B (addr a) f refl))
|
||||
-- preservationᴮ H (function f ⟨ var x ∈ T ⟩∈ U is C end ∙ B) (function a defn) | warning W = warning (block (function₂ W))
|
||||
-- preservationᴮ H (return M ∙ B) (return s) with preservationᴱ H M s
|
||||
-- preservationᴮ H (return M ∙ B) (return s) | ok p = ok p
|
||||
-- preservationᴮ H (return M ∙ B) (return s) | warning (expr W) = warning (block (return W))
|
||||
-- preservationᴮ H (return M ∙ B) (return s) | warning (heap W) = warning (heap W)
|
||||
binOpPreservation : ∀ H {op v w x} → (v ⟦ op ⟧ w ⟶ x) → (tgtBinOp op ≡ typeOfᴱ H ∅ (val x))
|
||||
binOpPreservation H (+ m n) = refl
|
||||
binOpPreservation H (- m n) = refl
|
||||
binOpPreservation H (/ m n) = refl
|
||||
binOpPreservation H (* m n) = refl
|
||||
binOpPreservation H (< m n) = refl
|
||||
binOpPreservation H (> m n) = refl
|
||||
binOpPreservation H (<= m n) = refl
|
||||
binOpPreservation H (>= m n) = refl
|
||||
binOpPreservation H (== v w) = refl
|
||||
binOpPreservation H (~= v w) = refl
|
||||
binOpPreservation H (·· v w) = refl
|
||||
|
||||
reflect-subtypingᴱ : ∀ H M {H′ M′ T} → (H ⊢ M ⟶ᴱ M′ ⊣ H′) → (typeOfᴱ H′ ∅ M′ ≮: T) → Either (typeOfᴱ H ∅ M ≮: T) (Warningᴱ H (typeCheckᴱ H ∅ M))
|
||||
reflect-subtypingᴮ : ∀ H B {H′ B′ T} → (H ⊢ B ⟶ᴮ B′ ⊣ H′) → (typeOfᴮ H′ ∅ B′ ≮: T) → Either (typeOfᴮ H ∅ B ≮: T) (Warningᴮ H (typeCheckᴮ H ∅ B))
|
||||
|
||||
reflect-subtypingᴱ H (M $ N) (app₁ s) p = mapLR none-tgt-≮: app₁ (reflect-subtypingᴱ H M s (tgt-≮: p))
|
||||
reflect-subtypingᴱ H (M $ N) (app₂ v s) p = Left (none-tgt-≮: (heap-weakening-≮:ᴱ ∅ H M (rednᴱ⊑ s) (tgt-≮: p)))
|
||||
reflect-subtypingᴱ H (M $ N) (app₁ s) p = mapLR src-tgt-≮: app₁ (reflect-subtypingᴱ H M s (tgt-src-≮: p))
|
||||
reflect-subtypingᴱ H (M $ N) (app₂ v s) p = Left (src-tgt-≮: (heap-weakeningᴱ ∅ H M (rednᴱ⊑ s) (tgt-src-≮: p)))
|
||||
reflect-subtypingᴱ H (M $ N) (beta (function f ⟨ var y ∈ T ⟩∈ U is B end) v refl q) p = Left (≡-trans-≮: (cong tgt (cong orAny (cong typeOfᴹᴼ q))) p)
|
||||
reflect-subtypingᴱ H (function f ⟨ var x ∈ T ⟩∈ U is B end) (function a defn) p = Left p
|
||||
reflect-subtypingᴱ H (block var b ∈ T is B end) (block s) p = Left p
|
||||
reflect-subtypingᴱ H (block var b ∈ T is return (val v) ∙ B end) (return v) p = mapR BlockMismatch (swapLR (≮:-antitrans p))
|
||||
reflect-subtypingᴱ H (block var b ∈ T is done end) done p = mapR BlockMismatch (swapLR (≮:-antitrans p))
|
||||
reflect-subtypingᴱ H (binexp M op N) (binOp₀ s) p = {!!}
|
||||
reflect-subtypingᴱ H (binexp M op N) (binOp₀ s) p = Left (≡-trans-≮: (binOpPreservation H s) p)
|
||||
reflect-subtypingᴱ H (binexp M op N) (binOp₁ s) p = Left p
|
||||
reflect-subtypingᴱ H (binexp M op N) (binOp₂ s) p = Left p
|
||||
|
||||
reflect-subtypingᴮ H (function f ⟨ var x ∈ T ⟩∈ U is C end ∙ B) (function a defn) p = mapLR (heap-weakening-≮:ᴮ _ _ B (snoc defn)) (CONTRADICTION ∘ (≮:-antirefl (T ⇒ U))) (substitutivityᴮ _ B (addr a) f p)
|
||||
reflect-subtypingᴮ H (local var x ∈ T ← M ∙ B) (local s) p = Left (heap-weakening-≮:ᴮ (x ↦ T) H B (rednᴱ⊑ s) p)
|
||||
reflect-subtypingᴮ H (function f ⟨ var x ∈ T ⟩∈ U is C end ∙ B) (function a defn) p = mapLR (heap-weakeningᴮ _ _ B (snoc defn)) (CONTRADICTION ∘ ≮:-antirefl) (substitutivityᴮ _ B (addr a) f p)
|
||||
reflect-subtypingᴮ H (local var x ∈ T ← M ∙ B) (local s) p = Left (heap-weakeningᴮ (x ↦ T) H B (rednᴱ⊑ s) p)
|
||||
reflect-subtypingᴮ H (local var x ∈ T ← M ∙ B) (subst v) p = mapR LocalVarMismatch (substitutivityᴮ H B v x p)
|
||||
reflect-subtypingᴮ H (return M ∙ B) (return s) p = mapR return (reflect-subtypingᴱ H M s p)
|
||||
|
||||
|
|
@ -330,10 +272,10 @@ reflect-substitutionᴱ H (function f ⟨ var y ∈ T ⟩∈ U is B end) v x (Fu
|
|||
reflect-substitutionᴱ H (function f ⟨ var y ∈ T ⟩∈ U is B end) v x (function₁ W) = mapL function₁ (reflect-substitutionᴮ-unless H B v x y (x ≡ⱽ y) W)
|
||||
reflect-substitutionᴱ H (block var b ∈ T is B end) v x (BlockMismatch q) = mapLR BlockMismatch Right (substitutivityᴮ H B v x q)
|
||||
reflect-substitutionᴱ H (block var b ∈ T is B end) v x (block₁ W′) = mapL block₁ (reflect-substitutionᴮ H B v x W′)
|
||||
reflect-substitutionᴱ H (binexp M op N) x v (BinOpMismatch₁ q) = {!!}
|
||||
reflect-substitutionᴱ H (binexp M op N) x v (BinOpMismatch₂ q) = {!!}
|
||||
reflect-substitutionᴱ H (binexp M op N) x v (bin₁ W) = mapL bin₁ (reflect-substitutionᴱ H M x v W)
|
||||
reflect-substitutionᴱ H (binexp M op N) x v (bin₂ W) = mapL bin₂ (reflect-substitutionᴱ H N x v W)
|
||||
reflect-substitutionᴱ H (binexp M op N) v x (BinOpMismatch₁ q) = mapLR BinOpMismatch₁ Right (substitutivityᴱ H M v x q)
|
||||
reflect-substitutionᴱ H (binexp M op N) v x (BinOpMismatch₂ q) = mapLR BinOpMismatch₂ Right (substitutivityᴱ H N v x q)
|
||||
reflect-substitutionᴱ H (binexp M op N) v x (bin₁ W) = mapL bin₁ (reflect-substitutionᴱ H M v x W)
|
||||
reflect-substitutionᴱ H (binexp M op N) v x (bin₂ W) = mapL bin₂ (reflect-substitutionᴱ H N v x W)
|
||||
|
||||
reflect-substitutionᴱ-whenever H a x x (yes refl) (UnallocatedAddress p) = Right (Left (UnallocatedAddress p))
|
||||
reflect-substitutionᴱ-whenever H v x y (no p) (UnboundVariable q) = Left (UnboundVariable (trans (sym (⊕-lookup-miss x y _ _ p)) q))
|
||||
|
|
@ -356,37 +298,37 @@ reflect-weakeningᴮ : ∀ Γ H B {H′} → (H ⊑ H′) → Warningᴮ H′ (t
|
|||
|
||||
reflect-weakeningᴱ Γ H (var x) h (UnboundVariable p) = (UnboundVariable p)
|
||||
reflect-weakeningᴱ Γ H (val (addr a)) h (UnallocatedAddress p) = UnallocatedAddress (lookup-⊑-nothing a h p)
|
||||
reflect-weakeningᴱ Γ H (M $ N) h (FunctionCallMismatch p) = FunctionCallMismatch (heap-weakening-≮:ᴱ Γ H N h (any-src-≮: (heap-weakening-≮:ᴱ Γ H M h (src-≮: p))))
|
||||
reflect-weakeningᴱ Γ H (M $ N) h (FunctionCallMismatch p) = FunctionCallMismatch (heap-weakeningᴱ Γ H N h (any-src-≮: (heap-weakeningᴱ Γ H M h (src-≮: p))))
|
||||
reflect-weakeningᴱ Γ H (M $ N) h (app₁ W) = app₁ (reflect-weakeningᴱ Γ H M h W)
|
||||
reflect-weakeningᴱ Γ H (M $ N) h (app₂ W) = app₂ (reflect-weakeningᴱ Γ H N h W)
|
||||
reflect-weakeningᴱ Γ H (binexp M op N) h (BinOpMismatch₁ p) = BinOpMismatch₁ {!!} -- (<:-BinOpWarning op (heap-weakeningᴱ Γ H M h) p)
|
||||
reflect-weakeningᴱ Γ H (binexp M op N) h (BinOpMismatch₂ p) = BinOpMismatch₂ {!!} -- (<:-BinOpWarning op (heap-weakeningᴱ Γ H N h) p)
|
||||
reflect-weakeningᴱ Γ H (binexp M op N) h (BinOpMismatch₁ p) = BinOpMismatch₁ (heap-weakeningᴱ Γ H M h p)
|
||||
reflect-weakeningᴱ Γ H (binexp M op N) h (BinOpMismatch₂ p) = BinOpMismatch₂ (heap-weakeningᴱ Γ H N h p)
|
||||
reflect-weakeningᴱ Γ H (binexp M op N) h (bin₁ W′) = bin₁ (reflect-weakeningᴱ Γ H M h W′)
|
||||
reflect-weakeningᴱ Γ H (binexp M op N) h (bin₂ W′) = bin₂ (reflect-weakeningᴱ Γ H N h W′)
|
||||
reflect-weakeningᴱ Γ H (function f ⟨ var y ∈ T ⟩∈ U is B end) h (FunctionDefnMismatch p) = FunctionDefnMismatch {!!} -- (<:-trans-≮: (heap-weakeningᴮ (Γ ⊕ y ↦ T) H B h) p)
|
||||
reflect-weakeningᴱ Γ H (function f ⟨ var y ∈ T ⟩∈ U is B end) h (FunctionDefnMismatch p) = FunctionDefnMismatch (heap-weakeningᴮ (Γ ⊕ y ↦ T) H B h p)
|
||||
reflect-weakeningᴱ Γ H (function f ⟨ var y ∈ T ⟩∈ U is B end) h (function₁ W) = function₁ (reflect-weakeningᴮ (Γ ⊕ y ↦ T) H B h W)
|
||||
reflect-weakeningᴱ Γ H (block var b ∈ T is B end) h (BlockMismatch p) = BlockMismatch {!!} -- (<:-trans-≮: (heap-weakeningᴮ Γ H B h) p)
|
||||
reflect-weakeningᴱ Γ H (block var b ∈ T is B end) h (BlockMismatch p) = BlockMismatch (heap-weakeningᴮ Γ H B h p)
|
||||
reflect-weakeningᴱ Γ H (block var b ∈ T is B end) h (block₁ W) = block₁ (reflect-weakeningᴮ Γ H B h W)
|
||||
|
||||
reflect-weakeningᴮ Γ H (return M ∙ B) h (return W) = return (reflect-weakeningᴱ Γ H M h W)
|
||||
reflect-weakeningᴮ Γ H (local var y ∈ T ← M ∙ B) h (LocalVarMismatch p) = LocalVarMismatch (heap-weakening-≮:ᴱ Γ H M h p)
|
||||
reflect-weakeningᴮ Γ H (local var y ∈ T ← M ∙ B) h (LocalVarMismatch p) = LocalVarMismatch (heap-weakeningᴱ Γ H M h p)
|
||||
reflect-weakeningᴮ Γ H (local var y ∈ T ← M ∙ B) h (local₁ W) = local₁ (reflect-weakeningᴱ Γ H M h W)
|
||||
reflect-weakeningᴮ Γ H (local var y ∈ T ← M ∙ B) h (local₂ W) = local₂ (reflect-weakeningᴮ (Γ ⊕ y ↦ T) H B h W)
|
||||
reflect-weakeningᴮ Γ H (function f ⟨ var x ∈ T ⟩∈ U is C end ∙ B) h (FunctionDefnMismatch p) = FunctionDefnMismatch (heap-weakening-≮:ᴮ (Γ ⊕ x ↦ T) H C h p)
|
||||
reflect-weakeningᴮ Γ H (function f ⟨ var x ∈ T ⟩∈ U is C end ∙ B) h (FunctionDefnMismatch p) = FunctionDefnMismatch (heap-weakeningᴮ (Γ ⊕ x ↦ T) H C h p)
|
||||
reflect-weakeningᴮ Γ H (function f ⟨ var x ∈ T ⟩∈ U is C end ∙ B) h (function₁ W) = function₁ (reflect-weakeningᴮ (Γ ⊕ x ↦ T) H C h W)
|
||||
reflect-weakeningᴮ Γ H (function f ⟨ var x ∈ T ⟩∈ U is C end ∙ B) h (function₂ W) = function₂ (reflect-weakeningᴮ (Γ ⊕ f ↦ (T ⇒ U)) H B h W)
|
||||
|
||||
reflect-weakeningᴼ : ∀ H O {H′} → (H ⊑ H′) → Warningᴼ H′ (typeCheckᴼ H′ O) → Warningᴼ H (typeCheckᴼ H O)
|
||||
reflect-weakeningᴼ H (just function f ⟨ var x ∈ T ⟩∈ U is B end) h (FunctionDefnMismatch p) = FunctionDefnMismatch (heap-weakening-≮:ᴮ (x ↦ T) H B h p)
|
||||
reflect-weakeningᴼ H (just function f ⟨ var x ∈ T ⟩∈ U is B end) h (FunctionDefnMismatch p) = FunctionDefnMismatch (heap-weakeningᴮ (x ↦ T) H B h p)
|
||||
reflect-weakeningᴼ H (just function f ⟨ var x ∈ T ⟩∈ U is B end) h (function₁ W) = function₁ (reflect-weakeningᴮ (x ↦ T) H B h W)
|
||||
|
||||
reflectᴱ : ∀ H M {H′ M′} → (H ⊢ M ⟶ᴱ M′ ⊣ H′) → Warningᴱ H′ (typeCheckᴱ H′ ∅ M′) → Either (Warningᴱ H (typeCheckᴱ H ∅ M)) (Warningᴴ H (typeCheckᴴ H))
|
||||
reflectᴮ : ∀ H B {H′ B′} → (H ⊢ B ⟶ᴮ B′ ⊣ H′) → Warningᴮ H′ (typeCheckᴮ H′ ∅ B′) → Either (Warningᴮ H (typeCheckᴮ H ∅ B)) (Warningᴴ H (typeCheckᴴ H))
|
||||
|
||||
reflectᴱ H (M $ N) (app₁ s) (FunctionCallMismatch p) = cond (Left ∘ FunctionCallMismatch ∘ heap-weakening-≮:ᴱ ∅ H N (rednᴱ⊑ s) ∘ any-src-≮:) (Left ∘ app₁) (reflect-subtypingᴱ H M s (src-≮: p))
|
||||
reflectᴱ H (M $ N) (app₁ s) (FunctionCallMismatch p) = cond (Left ∘ FunctionCallMismatch ∘ heap-weakeningᴱ ∅ H N (rednᴱ⊑ s) ∘ any-src-≮:) (Left ∘ app₁) (reflect-subtypingᴱ H M s (src-≮: p))
|
||||
reflectᴱ H (M $ N) (app₁ s) (app₁ W′) = mapL app₁ (reflectᴱ H M s W′)
|
||||
reflectᴱ H (M $ N) (app₁ s) (app₂ W′) = Left (app₂ (reflect-weakeningᴱ ∅ H N (rednᴱ⊑ s) W′))
|
||||
reflectᴱ H (M $ N) (app₂ p s) (FunctionCallMismatch q) = cond (Left ∘ FunctionCallMismatch ∘ any-src-≮: ∘ heap-weakening-≮:ᴱ ∅ H M (rednᴱ⊑ s) ∘ src-≮:) (Left ∘ app₂) (reflect-subtypingᴱ H N s q)
|
||||
reflectᴱ H (M $ N) (app₂ p s) (FunctionCallMismatch q) = cond (Left ∘ FunctionCallMismatch ∘ any-src-≮: ∘ heap-weakeningᴱ ∅ H M (rednᴱ⊑ s) ∘ src-≮:) (Left ∘ app₂) (reflect-subtypingᴱ H N s q)
|
||||
reflectᴱ H (M $ N) (app₂ p s) (app₁ W′) = Left (app₁ (reflect-weakeningᴱ ∅ H M (rednᴱ⊑ s) W′))
|
||||
reflectᴱ H (M $ N) (app₂ p s) (app₂ W′) = mapL app₂ (reflectᴱ H N s W′)
|
||||
reflectᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (BlockMismatch q) with substitutivityᴮ H B v x q
|
||||
|
|
@ -401,12 +343,12 @@ reflectᴱ H (block var b ∈ T is B end) (block s) (block₁ W′) = mapL block
|
|||
reflectᴱ H (block var b ∈ T is B end) (return v) W′ = Left (block₁ (return W′))
|
||||
reflectᴱ H (function f ⟨ var x ∈ T ⟩∈ U is B end) (function a defn) (UnallocatedAddress ())
|
||||
reflectᴱ H (binexp M op N) (binOp₀ ()) (UnallocatedAddress p)
|
||||
reflectᴱ H (binexp M op N) (binOp₁ s) (BinOpMismatch₁ p) = Left (BinOpMismatch₁ {!!}) -- (<:-BinOpWarning op (preservationᴱ H M s) p))
|
||||
reflectᴱ H (binexp M op N) (binOp₁ s) (BinOpMismatch₂ p) = Left (BinOpMismatch₂ {!!}) -- (<:-BinOpWarning op (heap-weakeningᴱ ∅ H N (rednᴱ⊑ s)) p))
|
||||
reflectᴱ H (binexp M op N) (binOp₁ s) (BinOpMismatch₁ p) = Left (cond BinOpMismatch₁ bin₁ (reflect-subtypingᴱ H M s p))
|
||||
reflectᴱ H (binexp M op N) (binOp₁ s) (BinOpMismatch₂ p) = Left (BinOpMismatch₂ (heap-weakeningᴱ ∅ H N (rednᴱ⊑ s) p))
|
||||
reflectᴱ H (binexp M op N) (binOp₁ s) (bin₁ W′) = mapL bin₁ (reflectᴱ H M s W′)
|
||||
reflectᴱ H (binexp M op N) (binOp₁ s) (bin₂ W′) = Left (bin₂ (reflect-weakeningᴱ ∅ H N (rednᴱ⊑ s) W′))
|
||||
reflectᴱ H (binexp M op N) (binOp₂ s) (BinOpMismatch₁ p) = Left (BinOpMismatch₁ {!!}) -- (<:-BinOpWarning op (heap-weakeningᴱ ∅ H M (rednᴱ⊑ s)) p))
|
||||
reflectᴱ H (binexp M op N) (binOp₂ s) (BinOpMismatch₂ p) = Left (BinOpMismatch₂ {!!}) -- (<:-BinOpWarning op (preservationᴱ H N s) p))
|
||||
reflectᴱ H (binexp M op N) (binOp₂ s) (BinOpMismatch₁ p) = Left (BinOpMismatch₁ (heap-weakeningᴱ ∅ H M (rednᴱ⊑ s) p))
|
||||
reflectᴱ H (binexp M op N) (binOp₂ s) (BinOpMismatch₂ p) = Left (cond BinOpMismatch₂ bin₂ (reflect-subtypingᴱ H N s p))
|
||||
reflectᴱ H (binexp M op N) (binOp₂ s) (bin₁ W′) = Left (bin₁ (reflect-weakeningᴱ ∅ H M (rednᴱ⊑ s) W′))
|
||||
reflectᴱ H (binexp M op N) (binOp₂ s) (bin₂ W′) = mapL bin₂ (reflectᴱ H N s W′)
|
||||
|
||||
|
|
@ -417,7 +359,7 @@ reflectᴮ H (local var x ∈ T ← M ∙ B) (subst v) W′ = Left (cond local
|
|||
reflectᴮ H (function f ⟨ var y ∈ T ⟩∈ U is C end ∙ B) (function a defn) W′ with reflect-substitutionᴮ _ B (addr a) f W′
|
||||
reflectᴮ H (function f ⟨ var y ∈ T ⟩∈ U is C end ∙ B) (function a defn) W′ | Left W = Left (function₂ (reflect-weakeningᴮ (f ↦ (T ⇒ U)) H B (snoc defn) W))
|
||||
reflectᴮ H (function f ⟨ var y ∈ T ⟩∈ U is C end ∙ B) (function a defn) W′ | Right (Left (UnallocatedAddress ()))
|
||||
reflectᴮ H (function f ⟨ var y ∈ T ⟩∈ U is C end ∙ B) (function a defn) W′ | Right (Right p) = CONTRADICTION (≮:-antirefl (T ⇒ U) p)
|
||||
reflectᴮ H (function f ⟨ var y ∈ T ⟩∈ U is C end ∙ B) (function a defn) W′ | Right (Right p) = CONTRADICTION (≮:-antirefl p)
|
||||
reflectᴮ H (return M ∙ B) (return s) (return W′) = mapL return (reflectᴱ H M s W′)
|
||||
|
||||
reflectᴴᴱ : ∀ H M {H′ M′} → (H ⊢ M ⟶ᴱ M′ ⊣ H′) → Warningᴴ H′ (typeCheckᴴ H′) → Either (Warningᴱ H (typeCheckᴱ H ∅ M)) (Warningᴴ H (typeCheckᴴ H))
|
||||
|
|
@ -427,7 +369,7 @@ reflectᴴᴱ H (M $ N) (app₁ s) W = mapL app₁ (reflectᴴᴱ H M s W)
|
|||
reflectᴴᴱ H (M $ N) (app₂ v s) W = mapL app₂ (reflectᴴᴱ H N s W)
|
||||
reflectᴴᴱ H (M $ N) (beta O v refl p) W = Right W
|
||||
reflectᴴᴱ H (function f ⟨ var x ∈ T ⟩∈ U is B end) (function a p) (addr b refl W) with b ≡ᴬ a
|
||||
reflectᴴᴱ H (function f ⟨ var x ∈ T ⟩∈ U is B end) (function a defn) (addr b refl (FunctionDefnMismatch p)) | yes refl = Left (FunctionDefnMismatch (heap-weakening-≮:ᴮ (x ↦ T) H B (snoc defn) p))
|
||||
reflectᴴᴱ H (function f ⟨ var x ∈ T ⟩∈ U is B end) (function a defn) (addr b refl (FunctionDefnMismatch p)) | yes refl = Left (FunctionDefnMismatch (heap-weakeningᴮ (x ↦ T) H B (snoc defn) p))
|
||||
reflectᴴᴱ H (function f ⟨ var x ∈ T ⟩∈ U is B end) (function a defn) (addr b refl (function₁ W)) | yes refl = Left (function₁ (reflect-weakeningᴮ (x ↦ T) H B (snoc defn) W))
|
||||
reflectᴴᴱ H (function f ⟨ var x ∈ T ⟩∈ U is B end) (function a p) (addr b refl W) | no q = Right (addr b (lookup-not-allocated p q) (reflect-weakeningᴼ H _ (snoc p) W))
|
||||
reflectᴴᴱ H (block var b ∈ T is B end) (block s) W = mapL block₁ (reflectᴴᴮ H B s W)
|
||||
|
|
@ -438,7 +380,7 @@ reflectᴴᴱ H (binexp M op N) (binOp₁ s) W = mapL bin₁ (reflectᴴᴱ H M
|
|||
reflectᴴᴱ H (binexp M op N) (binOp₂ s) W = mapL bin₂ (reflectᴴᴱ H N s W)
|
||||
|
||||
reflectᴴᴮ H (function f ⟨ var x ∈ T ⟩∈ U is C end ∙ B) (function a p) (addr b refl W) with b ≡ᴬ a
|
||||
reflectᴴᴮ H (function f ⟨ var x ∈ T ⟩∈ U is C end ∙ B) (function a defn) (addr b refl (FunctionDefnMismatch p)) | yes refl = Left (FunctionDefnMismatch (heap-weakening-≮:ᴮ (x ↦ T) H C (snoc defn) p))
|
||||
reflectᴴᴮ H (function f ⟨ var x ∈ T ⟩∈ U is C end ∙ B) (function a defn) (addr b refl (FunctionDefnMismatch p)) | yes refl = Left (FunctionDefnMismatch (heap-weakeningᴮ (x ↦ T) H C (snoc defn) p))
|
||||
reflectᴴᴮ H (function f ⟨ var x ∈ T ⟩∈ U is C end ∙ B) (function a defn) (addr b refl (function₁ W)) | yes refl = Left (function₁ (reflect-weakeningᴮ (x ↦ T) H C (snoc defn) W))
|
||||
reflectᴴᴮ H (function f ⟨ var x ∈ T ⟩∈ U is C end ∙ B) (function a p) (addr b refl W) | no q = Right (addr b (lookup-not-allocated p q) (reflect-weakeningᴼ H _ (snoc p) W))
|
||||
reflectᴴᴮ H (local var x ∈ T ← M ∙ B) (local s) W = mapL local₁ (reflectᴴᴱ H M s W)
|
||||
|
|
@ -450,24 +392,40 @@ reflect* H B refl W = W
|
|||
reflect* H B (step s t) W = cond (reflectᴮ H B s) (reflectᴴᴮ H B s) (reflect* _ _ t W)
|
||||
|
||||
isntNumber : ∀ H v → (valueType v ≢ number) → (typeOfᴱ H ∅ (val v) ≮: number)
|
||||
isntNumber = {!!}
|
||||
isntNumber H nil p = scalar-≢-impl-≮: nil number (λ ())
|
||||
isntNumber H (addr a) p with remember (H [ a ]ᴴ)
|
||||
isntNumber H (addr a) p | (just (function f ⟨ var x ∈ T ⟩∈ U is B end) , q) = ≡-trans-≮: (cong orAny (cong typeOfᴹᴼ q)) (function-≮:-scalar number)
|
||||
isntNumber H (addr a) p | (nothing , q) = ≡-trans-≮: (cong orAny (cong typeOfᴹᴼ q)) (any-≮:-scalar number)
|
||||
isntNumber H (number x) p = CONTRADICTION (p refl)
|
||||
isntNumber H (bool x) p = scalar-≢-impl-≮: boolean number (λ ())
|
||||
isntNumber H (string x) p = scalar-≢-impl-≮: string number (λ ())
|
||||
|
||||
isntString : ∀ H v → (valueType v ≢ string) → (typeOfᴱ H ∅ (val v) ≮: string)
|
||||
isntString = {!!}
|
||||
isntString H nil p = scalar-≢-impl-≮: nil string (λ ())
|
||||
isntString H (addr a) p with remember (H [ a ]ᴴ)
|
||||
isntString H (addr a) p | (just (function f ⟨ var x ∈ T ⟩∈ U is B end) , q) = ≡-trans-≮: (cong orAny (cong typeOfᴹᴼ q)) (function-≮:-scalar string)
|
||||
isntString H (addr a) p | (nothing , q) = ≡-trans-≮: (cong orAny (cong typeOfᴹᴼ q)) (any-≮:-scalar string)
|
||||
isntString H (number x) p = scalar-≢-impl-≮: number string (λ ())
|
||||
isntString H (bool x) p = scalar-≢-impl-≮: boolean string (λ ())
|
||||
isntString H (string x) p = CONTRADICTION (p refl)
|
||||
|
||||
isntFunction : ∀ H v {T U} → (valueType v ≢ function) → (typeOfᴱ H ∅ (val v) ≮: (T ⇒ U))
|
||||
isntFunction = {!!}
|
||||
isntFunction H nil p = scalar-≮:-function nil
|
||||
isntFunction H (addr a) p = CONTRADICTION (p refl)
|
||||
isntFunction H (number x) p = scalar-≮:-function number
|
||||
isntFunction H (bool x) p = scalar-≮:-function boolean
|
||||
isntFunction H (string x) p = scalar-≮:-function string
|
||||
|
||||
runtimeBinOpWarning : ∀ H {op} v → BinOpError op (valueType v) → BinOpWarning op (orAny (typeOfⱽ H v))
|
||||
runtimeBinOpWarning H v (+ p) = + (isntNumber H v p)
|
||||
runtimeBinOpWarning H v (- p) = - (isntNumber H v p)
|
||||
runtimeBinOpWarning H v (* p) = * (isntNumber H v p)
|
||||
runtimeBinOpWarning H v (/ p) = / (isntNumber H v p)
|
||||
runtimeBinOpWarning H v (< p) = < (isntNumber H v p)
|
||||
runtimeBinOpWarning H v (> p) = > (isntNumber H v p)
|
||||
runtimeBinOpWarning H v (<= p) = <= (isntNumber H v p)
|
||||
runtimeBinOpWarning H v (>= p) = >= (isntNumber H v p)
|
||||
runtimeBinOpWarning H v (·· p) = ·· (isntString H v p)
|
||||
runtimeBinOpWarning : ∀ H {op} v → BinOpError op (valueType v) → (typeOfᴱ H ∅ (val v) ≮: srcBinOp op)
|
||||
runtimeBinOpWarning H v (+ p) = isntNumber H v p
|
||||
runtimeBinOpWarning H v (- p) = isntNumber H v p
|
||||
runtimeBinOpWarning H v (* p) = isntNumber H v p
|
||||
runtimeBinOpWarning H v (/ p) = isntNumber H v p
|
||||
runtimeBinOpWarning H v (< p) = isntNumber H v p
|
||||
runtimeBinOpWarning H v (> p) = isntNumber H v p
|
||||
runtimeBinOpWarning H v (<= p) = isntNumber H v p
|
||||
runtimeBinOpWarning H v (>= p) = isntNumber H v p
|
||||
runtimeBinOpWarning H v (·· p) = isntString H v p
|
||||
|
||||
runtimeWarningᴱ : ∀ H M → RuntimeErrorᴱ H M → Warningᴱ H (typeCheckᴱ H ∅ M)
|
||||
runtimeWarningᴮ : ∀ H B → RuntimeErrorᴮ H B → Warningᴮ H (typeCheckᴮ H ∅ B)
|
||||
|
|
@ -487,6 +445,6 @@ runtimeWarningᴮ H (local var x ∈ T ← M ∙ B) (local err) = local₁ (runt
|
|||
runtimeWarningᴮ H (return M ∙ B) (return err) = return (runtimeWarningᴱ H M err)
|
||||
|
||||
wellTypedProgramsDontGoWrong : ∀ H′ B B′ → (∅ᴴ ⊢ B ⟶* B′ ⊣ H′) → (RuntimeErrorᴮ H′ B′) → Warningᴮ ∅ᴴ (typeCheckᴮ ∅ᴴ ∅ B)
|
||||
wellTypedProgramsDontGoWrong H′ B B′ t err with reflect* ∅ᴴ B t {!!}
|
||||
wellTypedProgramsDontGoWrong H′ B B′ t err with reflect* ∅ᴴ B t (Left (runtimeWarningᴮ H′ B′ err))
|
||||
wellTypedProgramsDontGoWrong H′ B B′ t err | Right (addr a refl ())
|
||||
wellTypedProgramsDontGoWrong H′ B B′ t err | Left W = W
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue