Prototype: Renamed any/none to unknown/never (#447)

* Renamed any/none to unknown/never * Pin hackage version * Update Agda version
2024-11-15 14:25:44 +08:00 · 2022-04-09 00:07:08 -05:00 · 2022-04-09 00:07:08 -05:00 · d37d0c857b
commit d37d0c857b
parent 510aed7d3f
11 changed files with 181 additions and 177 deletions
--- a/.github/workflows/prototyping.yml
+++ b/.github/workflows/prototyping.yml
@ -10,7 +10,9 @@ jobs:
  linux:
    strategy:
      matrix:
-        agda: [2.6.2.1]
+        agda: [2.6.2.2]
+        hackageDate: ["2022-04-07"]
+        hackageTime: ["23:06:28"]
    name: prototyping
    runs-on: ubuntu-latest
    steps:
@ -18,7 +20,7 @@ jobs:
    - uses: actions/cache@v2
      with:
        path: ~/.cabal/store
-        key: prototyping-${{ runner.os }}-${{ matrix.agda }}
+        key: "prototyping-${{ runner.os }}-${{ matrix.agda }}-${{ matrix.hackageDate }}-${{ matrix.hackageTime }}"
    - uses: actions/cache@v2
      id: luau-ast-cache
      with:
@ -28,12 +30,12 @@ jobs:
      run: sudo apt-get install -y cabal-install
    - name: cabal update
      working-directory: prototyping
-      run: cabal update
+      run: cabal v2-update "hackage.haskell.org,${{ matrix.hackageDate }}T${{ matrix.hackageTime }}Z"
    - name: cabal install
      working-directory: prototyping
      run: |
-        cabal install Agda-${{ matrix.agda }}
        cabal install --lib scientific vector aeson --package-env .
+        cabal install --allow-newer Agda-${{ matrix.agda }}
    - name: check targets
      working-directory: prototyping
      run: |
--- a/prototyping/Luau/StrictMode.agda
+++ b/prototyping/Luau/StrictMode.agda
@ -5,7 +5,7 @@ module Luau.StrictMode where
 open import Agda.Builtin.Equality using (_≡_)
 open import FFI.Data.Maybe using (just; nothing)
 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; +; -; *; /; <; >; <=; >=; ··)
-open import Luau.Type using (Type; strict; nil; number; string; boolean; none; any; _⇒_; _∪_; _∩_; tgt)
+open import Luau.Type using (Type; strict; nil; number; string; boolean; _⇒_; _∪_; _∩_; tgt)
 open import Luau.Subtyping using (_≮:_)
 open import Luau.Heap using (Heap; function_is_end) renaming (_[_] to _[_]ᴴ)
 open import Luau.VarCtxt using (VarCtxt; ∅; _⋒_; _↦_; _⊕_↦_; _⊝_) renaming (_[_] to _[_]ⱽ)
--- a/prototyping/Luau/Subtyping.agda
+++ b/prototyping/Luau/Subtyping.agda
@ -1,6 +1,6 @@
 {-# OPTIONS --rewriting #-}

-open import Luau.Type using (Type; Scalar; nil; number; string; boolean; none; any; _⇒_; _∪_; _∩_)
+open import Luau.Type using (Type; Scalar; nil; number; string; boolean; never; unknown; _⇒_; _∪_; _∩_)
 open import Properties.Equality using (_≢_)

 module Luau.Subtyping where
@ -29,7 +29,7 @@ data Language where
  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
+  unknown : ∀ {t} → Language unknown t

 data ¬Language where

@ -42,7 +42,7 @@ data ¬Language where
  _,_ : ∀ {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
+  never : ∀ {t} → ¬Language never t

 -- Subtyping as language inclusion

--- a/prototyping/Luau/Type.agda
+++ b/prototyping/Luau/Type.agda
@ -9,8 +9,8 @@ open import FFI.Data.Maybe using (Maybe; just; nothing)
 data Type : Set where
  nil : Type
  _⇒_ : Type → Type → Type
-  none : Type
-  any : Type
+  never : Type
+  unknown : Type
  boolean : Type
  number : Type
  string : Type
@ -29,8 +29,8 @@ lhs (T ⇒ _) = T
 lhs (T ∪ _) = T
 lhs (T ∩ _) = T
 lhs nil = nil
-lhs none = none
-lhs any = any
+lhs never = never
+lhs unknown = unknown
 lhs number = number
 lhs boolean = boolean
 lhs string = string
@ -40,8 +40,8 @@ rhs (_ ⇒ T) = T
 rhs (_ ∪ T) = T
 rhs (_ ∩ T) = T
 rhs nil = nil
-rhs none = none
-rhs any = any
+rhs never = never
+rhs unknown = unknown
 rhs number = number
 rhs boolean = boolean
 rhs string = string
@ -49,16 +49,16 @@ rhs string = string
 _≡ᵀ_ : ∀ (T U : Type) → Dec(T ≡ U)
 nil ≡ᵀ nil = yes refl
 nil ≡ᵀ (S ⇒ T) = no (λ ())
-nil ≡ᵀ none = no (λ ())
-nil ≡ᵀ any = no (λ ())
+nil ≡ᵀ never = no (λ ())
+nil ≡ᵀ unknown = no (λ ())
 nil ≡ᵀ number = no (λ ())
 nil ≡ᵀ boolean = no (λ ())
 nil ≡ᵀ (S ∪ T) = no (λ ())
 nil ≡ᵀ (S ∩ T) = no (λ ())
 nil ≡ᵀ string = no (λ ())
 (S ⇒ T) ≡ᵀ string = no (λ ())
-none ≡ᵀ string = no (λ ())
-any ≡ᵀ string = no (λ ())
+never ≡ᵀ string = no (λ ())
+unknown ≡ᵀ string = no (λ ())
 boolean ≡ᵀ string = no (λ ())
 number ≡ᵀ string = no (λ ())
 (S ∪ T) ≡ᵀ string = no (λ ())
@ -68,48 +68,48 @@ number ≡ᵀ string = no (λ ())
 (S ⇒ T) ≡ᵀ (S ⇒ T) | yes refl | yes refl = yes refl
 (S ⇒ T) ≡ᵀ (U ⇒ V) | _ | no p = no (λ q → p (cong rhs q))
 (S ⇒ T) ≡ᵀ (U ⇒ V) | no p | _ = no (λ q → p (cong lhs q))
-(S ⇒ T) ≡ᵀ none = no (λ ())
-(S ⇒ T) ≡ᵀ any = no (λ ())
+(S ⇒ T) ≡ᵀ never = no (λ ())
+(S ⇒ T) ≡ᵀ unknown = no (λ ())
 (S ⇒ T) ≡ᵀ number = no (λ ())
 (S ⇒ T) ≡ᵀ boolean = no (λ ())
 (S ⇒ T) ≡ᵀ (U ∪ V) = no (λ ())
 (S ⇒ T) ≡ᵀ (U ∩ V) = no (λ ())
-none ≡ᵀ nil = no (λ ())
-none ≡ᵀ (U ⇒ V) = no (λ ())
-none ≡ᵀ none = yes refl
-none ≡ᵀ any = no (λ ())
-none ≡ᵀ number = no (λ ())
-none ≡ᵀ boolean = no (λ ())
-none ≡ᵀ (U ∪ V) = no (λ ())
-none ≡ᵀ (U ∩ V) = no (λ ())
-any ≡ᵀ nil = no (λ ())
-any ≡ᵀ (U ⇒ V) = no (λ ())
-any ≡ᵀ none = no (λ ())
-any ≡ᵀ any = yes refl
-any ≡ᵀ number = no (λ ())
-any ≡ᵀ boolean = no (λ ())
-any ≡ᵀ (U ∪ V) = no (λ ())
-any ≡ᵀ (U ∩ V) = no (λ ())
+never ≡ᵀ nil = no (λ ())
+never ≡ᵀ (U ⇒ V) = no (λ ())
+never ≡ᵀ never = yes refl
+never ≡ᵀ unknown = no (λ ())
+never ≡ᵀ number = no (λ ())
+never ≡ᵀ boolean = no (λ ())
+never ≡ᵀ (U ∪ V) = no (λ ())
+never ≡ᵀ (U ∩ V) = no (λ ())
+unknown ≡ᵀ nil = no (λ ())
+unknown ≡ᵀ (U ⇒ V) = no (λ ())
+unknown ≡ᵀ never = no (λ ())
+unknown ≡ᵀ unknown = yes refl
+unknown ≡ᵀ number = no (λ ())
+unknown ≡ᵀ boolean = no (λ ())
+unknown ≡ᵀ (U ∪ V) = no (λ ())
+unknown ≡ᵀ (U ∩ V) = no (λ ())
 number ≡ᵀ nil = no (λ ())
 number ≡ᵀ (T ⇒ U) = no (λ ())
-number ≡ᵀ none = no (λ ())
-number ≡ᵀ any = no (λ ())
+number ≡ᵀ never = no (λ ())
+number ≡ᵀ unknown = no (λ ())
 number ≡ᵀ number = yes refl
 number ≡ᵀ boolean = no (λ ())
 number ≡ᵀ (T ∪ U) = no (λ ())
 number ≡ᵀ (T ∩ U) = no (λ ())
 boolean ≡ᵀ nil = no (λ ())
 boolean ≡ᵀ (T ⇒ U) = no (λ ())
-boolean ≡ᵀ none = no (λ ())
-boolean ≡ᵀ any = no (λ ())
+boolean ≡ᵀ never = no (λ ())
+boolean ≡ᵀ unknown = no (λ ())
 boolean ≡ᵀ boolean = yes refl
 boolean ≡ᵀ number = no (λ ())
 boolean ≡ᵀ (T ∪ U) = no (λ ())
 boolean ≡ᵀ (T ∩ U) = no (λ ())
 string ≡ᵀ nil = no (λ ())
 string ≡ᵀ (x ⇒ x₁) = no (λ ())
-string ≡ᵀ none = no (λ ())
-string ≡ᵀ any = no (λ ())
+string ≡ᵀ never = no (λ ())
+string ≡ᵀ unknown = no (λ ())
 string ≡ᵀ boolean = no (λ ())
 string ≡ᵀ number = no (λ ())
 string ≡ᵀ string = yes refl
@ -117,8 +117,8 @@ string ≡ᵀ (U ∪ V) = no (λ ())
 string ≡ᵀ (U ∩ V) = no (λ ())
 (S ∪ T) ≡ᵀ nil = no (λ ())
 (S ∪ T) ≡ᵀ (U ⇒ V) = no (λ ())
-(S ∪ T) ≡ᵀ none = no (λ ())
-(S ∪ T) ≡ᵀ any = no (λ ())
+(S ∪ T) ≡ᵀ never = no (λ ())
+(S ∪ T) ≡ᵀ unknown = no (λ ())
 (S ∪ T) ≡ᵀ number = no (λ ())
 (S ∪ T) ≡ᵀ boolean = no (λ ())
 (S ∪ T) ≡ᵀ (U ∪ V) with (S ≡ᵀ U) | (T ≡ᵀ V) 
@ -128,8 +128,8 @@ string ≡ᵀ (U ∩ V) = no (λ ())
 (S ∪ T) ≡ᵀ (U ∩ V) = no (λ ())
 (S ∩ T) ≡ᵀ nil = no (λ ())
 (S ∩ T) ≡ᵀ (U ⇒ V) = no (λ ())
-(S ∩ T) ≡ᵀ none = no (λ ())
-(S ∩ T) ≡ᵀ any = no (λ ())
+(S ∩ T) ≡ᵀ never = no (λ ())
+(S ∩ T) ≡ᵀ unknown = no (λ ())
 (S ∩ T) ≡ᵀ number = no (λ ())
 (S ∩ T) ≡ᵀ boolean = no (λ ())
 (S ∩ T) ≡ᵀ (U ∪ V) = no (λ ())
@ -151,29 +151,29 @@ data Mode : Set where
  nonstrict : Mode

 src : Mode → Type → Type
-src m nil = none
-src m number = none
-src m boolean = none
-src m string = none
+src m nil = never
+src m number = never
+src m boolean = never
+src m string = never
 src m (S ⇒ T) = S
 -- In nonstrict mode, functions are covaraiant, in strict mode they're contravariant
 src strict    (S ∪ T) = (src strict S) ∩ (src strict T)
 src nonstrict (S ∪ T) = (src nonstrict S) ∪ (src nonstrict T)
 src strict    (S ∩ T) = (src strict S) ∪ (src strict T)
 src nonstrict (S ∩ T) = (src nonstrict S) ∩ (src nonstrict T)
-src strict none = any
-src nonstrict none = none
-src strict any = none
-src nonstrict any = any
+src strict never = unknown
+src nonstrict never = never
+src strict unknown = never
+src nonstrict unknown = unknown

 tgt : Type → Type
-tgt nil = none
+tgt nil = never
 tgt (S ⇒ T) = T
-tgt none = none
-tgt any = any
-tgt number = none
-tgt boolean = none
-tgt string = none
+tgt never = never
+tgt unknown = unknown
+tgt number = never
+tgt boolean = never
+tgt string = never
 tgt (S ∪ T) = (tgt S) ∪ (tgt T)
 tgt (S ∩ T) = (tgt S) ∩ (tgt T)

--- a/prototyping/Luau/Type/FromJSON.agda
+++ b/prototyping/Luau/Type/FromJSON.agda
@ -2,7 +2,7 @@

 module Luau.Type.FromJSON where

-open import Luau.Type using (Type; nil; _⇒_; _∪_; _∩_; any; number; string)
+open import Luau.Type using (Type; nil; _⇒_; _∪_; _∩_; unknown; never; number; string)

 open import Agda.Builtin.List using (List; _∷_; [])
 open import Agda.Builtin.Bool using (true; false)
@ -42,7 +42,9 @@ typeFromJSON (object o) | just (string "AstTypeFunction") | nothing | nothing =

 typeFromJSON (object o) | just (string "AstTypeReference") with lookup name o
 typeFromJSON (object o) | just (string "AstTypeReference") | just (string "nil") = Right nil
-typeFromJSON (object o) | just (string "AstTypeReference") | just (string "any") = Right any
+typeFromJSON (object o) | just (string "AstTypeReference") | just (string "any") = Right unknown -- not quite right
+typeFromJSON (object o) | just (string "AstTypeReference") | just (string "unknown") = Right unknown
+typeFromJSON (object o) | just (string "AstTypeReference") | just (string "never") = Right never
 typeFromJSON (object o) | just (string "AstTypeReference") | just (string "number") = Right number
 typeFromJSON (object o) | just (string "AstTypeReference") | just (string "string") = Right string
 typeFromJSON (object o) | just (string "AstTypeReference") | _ = Left "Unknown referenced type"
--- a/prototyping/Luau/Type/ToString.agda
+++ b/prototyping/Luau/Type/ToString.agda
@ -1,7 +1,7 @@
 module Luau.Type.ToString where

 open import FFI.Data.String using (String; _++_)
-open import Luau.Type using (Type; nil; _⇒_; none; any; number; boolean; string; _∪_; _∩_; normalizeOptional)
+open import Luau.Type using (Type; nil; _⇒_; never; unknown; number; boolean; string; _∪_; _∩_; normalizeOptional)

 {-# TERMINATING #-}
 typeToString : Type → String
@ -10,8 +10,8 @@ typeToStringᴵ : Type → String

 typeToString nil = "nil"
 typeToString (S ⇒ T) = "(" ++ (typeToString S) ++ ") -> " ++ (typeToString T)
-typeToString none = "none"
-typeToString any = "any"
+typeToString never = "never"
+typeToString unknown = "unknown"
 typeToString number = "number"
 typeToString boolean = "boolean"
 typeToString string = "string"
--- a/prototyping/Luau/TypeCheck.agda
+++ b/prototyping/Luau/TypeCheck.agda
@ -10,7 +10,7 @@ open import Luau.Syntax using (Expr; Stat; Block; BinaryOperator; yes; nil; addr
 open import Luau.Var using (Var)
 open import Luau.Addr using (Addr)
 open import Luau.Heap using (Heap; Object; function_is_end) renaming (_[_] to _[_]ᴴ)
-open import Luau.Type using (Type; Mode; nil; any; number; boolean; string; _⇒_; tgt)
+open import Luau.Type using (Type; Mode; nil; unknown; number; boolean; string; _⇒_; tgt)
 open import Luau.VarCtxt using (VarCtxt; ∅; _⋒_; _↦_; _⊕_↦_; _⊝_) renaming (_[_] to _[_]ⱽ)
 open import FFI.Data.Vector using (Vector)
 open import FFI.Data.Maybe using (Maybe; just; nothing)
@ -19,9 +19,9 @@ open import Properties.Product using (_×_; _,_)
 src : Type → Type
 src = Luau.Type.src m

-orAny : Maybe Type → Type
-orAny nothing = any
-orAny (just T) = T
+orUnknown : Maybe Type → Type
+orUnknown nothing = unknown
+orUnknown (just T) = T

 srcBinOp : BinaryOperator → Type
 srcBinOp + = number
@ -30,8 +30,8 @@ srcBinOp * = number
 srcBinOp / = number
 srcBinOp < = number
 srcBinOp > = number
-srcBinOp == = any
-srcBinOp ~= = any
+srcBinOp == = unknown
+srcBinOp ~= = unknown
 srcBinOp <= = number
 srcBinOp >= = number
 srcBinOp ·· = string
@ -89,7 +89,7 @@ data _⊢ᴱ_∈_ where

  var : ∀ {x T Γ} →

-    T ≡ orAny(Γ [ x ]ⱽ) →
+    T ≡ orUnknown(Γ [ x ]ⱽ) →
    ----------------
    Γ ⊢ᴱ (var x) ∈ T

--- a/prototyping/Properties/StrictMode.agda
+++ b/prototyping/Properties/StrictMode.agda
@ -9,10 +9,10 @@ open import FFI.Data.Maybe using (Maybe; just; nothing)
 open import Luau.Heap using (Heap; Object; function_is_end; defn; alloc; ok; next; lookup-not-allocated) renaming (_≡_⊕_↦_ to _≡ᴴ_⊕_↦_; _[_] to _[_]ᴴ; ∅ to ∅ᴴ)
 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)
 open import Luau.Substitution using (_[_/_]ᴮ; _[_/_]ᴱ; _[_/_]ᴮunless_; var_[_/_]ᴱwhenever_)
-open import Luau.Subtyping using (_≮:_; witness; any; none; scalar; function; scalar-function; scalar-function-ok; scalar-function-err; scalar-scalar; function-scalar; function-ok; function-err; left; right; _,_; Tree; Language; ¬Language)
+open import Luau.Subtyping using (_≮:_; witness; unknown; never; scalar; function; scalar-function; scalar-function-ok; scalar-function-err; scalar-scalar; function-scalar; function-ok; function-err; left; right; _,_; Tree; Language; ¬Language)
 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; ==; ~=)
-open import Luau.Type using (Type; strict; nil; number; boolean; string; _⇒_; none; any; _∩_; _∪_; tgt; _≡ᵀ_; _≡ᴹᵀ_)
-open import Luau.TypeCheck(strict) using (_⊢ᴮ_∈_; _⊢ᴱ_∈_; _⊢ᴴᴮ_▷_∈_; _⊢ᴴᴱ_▷_∈_; nil; var; addr; app; function; block; done; return; local; orAny; srcBinOp; tgtBinOp)
+open import Luau.Type using (Type; strict; nil; number; boolean; string; _⇒_; never; unknown; _∩_; _∪_; tgt; _≡ᵀ_; _≡ᴹᵀ_)
+open import Luau.TypeCheck(strict) using (_⊢ᴮ_∈_; _⊢ᴱ_∈_; _⊢ᴴᴮ_▷_∈_; _⊢ᴴᴱ_▷_∈_; nil; var; addr; app; function; block; done; return; local; orUnknown; srcBinOp; tgtBinOp)
 open import Luau.Var using (_≡ⱽ_)
 open import Luau.Addr using (_≡ᴬ_)
 open import Luau.VarCtxt using (VarCtxt; ∅; _⋒_; _↦_; _⊕_↦_; _⊝_; ⊕-lookup-miss; ⊕-swap; ⊕-over) renaming (_[_] to _[_]ⱽ)
@ -22,7 +22,7 @@ open import Properties.Equality using (_≢_; sym; cong; trans; subst₁)
 open import Properties.Dec using (Dec; yes; no)
 open import Properties.Contradiction using (CONTRADICTION; ¬)
 open import Properties.Functions using (_∘_)
-open import Properties.Subtyping using (any-≮:; ≡-trans-≮:; ≮:-trans-≡; none-tgt-≮:; tgt-none-≮:; src-any-≮:; any-src-≮:; ≮:-trans; ≮:-refl; scalar-≢-impl-≮:; function-≮:-scalar; scalar-≮:-function; function-≮:-none; any-≮:-scalar; scalar-≮:-none; any-≮:-none)
+open import Properties.Subtyping using (unknown-≮:; ≡-trans-≮:; ≮:-trans-≡; never-tgt-≮:; tgt-never-≮:; src-unknown-≮:; unknown-src-≮:; ≮:-trans; ≮:-refl; scalar-≢-impl-≮:; function-≮:-scalar; scalar-≮:-function; function-≮:-never; unknown-≮:-scalar; scalar-≮:-never; unknown-≮:-never)
 open import Properties.TypeCheck(strict) using (typeOfᴼ; typeOfᴹᴼ; typeOfⱽ; typeOfᴱ; typeOfᴮ; typeCheckᴱ; typeCheckᴮ; typeCheckᴼ; typeCheckᴴ)
 open import Luau.OpSem using (_⟦_⟧_⟶_; _⊢_⟶*_⊣_; _⊢_⟶ᴮ_⊣_; _⊢_⟶ᴱ_⊣_; app₁; app₂; function; beta; return; block; done; local; subst; binOp₀; binOp₁; binOp₂; refl; step; +; -; *; /; <; >; ==; ~=; <=; >=; ··)
 open import Luau.RuntimeError using (BinOpError; RuntimeErrorᴱ; RuntimeErrorᴮ; FunctionMismatch; BinOpMismatch₁; BinOpMismatch₂; UnboundVariable; SEGV; app₁; app₂; bin₁; bin₂; block; local; return; +; -; *; /; <; >; <=; >=; ··)
@ -68,12 +68,12 @@ 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 (addr a)) (snoc {a = a} defn) p | yes refl = unknown-≮: p
+heap-weakeningᴱ Γ H (val (addr a)) (snoc {a = b} q) p | no r = ≡-trans-≮: (cong orUnknown (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 = none-tgt-≮: (heap-weakeningᴱ Γ H M h (tgt-none-≮: p))
+heap-weakeningᴱ Γ H (M $ N) h p = never-tgt-≮: (heap-weakeningᴱ Γ H M h (tgt-never-≮: 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
@ -94,11 +94,11 @@ 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-none-≮: p))
+substitutivityᴱ H (M $ N) v x p = mapL never-tgt-≮: (substitutivityᴱ H M v x (tgt-never-≮: 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 (≮:-trans q)
-substitutivityᴱ-whenever H v x y (no p) q = Left (≡-trans-≮: (cong orAny (sym (⊕-lookup-miss x y _ _ p))) q)
+substitutivityᴱ-whenever H v x y (no p) q = Left (≡-trans-≮: (cong orUnknown (sym (⊕-lookup-miss x y _ _ p))) q)

 substitutivityᴮ H (function f ⟨ var y ∈ T ⟩∈ U is C end ∙ B) v x p = substitutivityᴮ-unless H B v x f (x ≡ⱽ f) p
 substitutivityᴮ H (local var y ∈ T ← M ∙ B) v x p = substitutivityᴮ-unless H B v x y (x ≡ⱽ y) p
@ -125,9 +125,9 @@ 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-none-≮: p))
-reflect-subtypingᴱ H (M $ N) (app₂ v s) p = Left (none-tgt-≮: (heap-weakeningᴱ ∅ H M (rednᴱ⊑ s) (tgt-none-≮: 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 (M $ N) (app₁ s) p = mapLR never-tgt-≮: app₁ (reflect-subtypingᴱ H M s (tgt-never-≮: p))
+reflect-subtypingᴱ H (M $ N) (app₂ v s) p = Left (never-tgt-≮: (heap-weakeningᴱ ∅ H M (rednᴱ⊑ s) (tgt-never-≮: 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 orUnknown (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 (≮:-trans p))
@ -152,8 +152,8 @@ reflect-substitutionᴱ H (var y) v x W = reflect-substitutionᴱ-whenever H v x
 reflect-substitutionᴱ H (val (addr a)) v x (UnallocatedAddress r) = Left (UnallocatedAddress r)
 reflect-substitutionᴱ H (M $ N) v x (FunctionCallMismatch p) with substitutivityᴱ H N v x p
 reflect-substitutionᴱ H (M $ N) v x (FunctionCallMismatch p) | Right W = Right (Right W)
-reflect-substitutionᴱ H (M $ N) v x (FunctionCallMismatch p) | Left q with substitutivityᴱ H M v x (src-any-≮: q)
-reflect-substitutionᴱ H (M $ N) v x (FunctionCallMismatch p) | Left q | Left r = Left ((FunctionCallMismatch ∘ any-src-≮: q) r)
+reflect-substitutionᴱ H (M $ N) v x (FunctionCallMismatch p) | Left q with substitutivityᴱ H M v x (src-unknown-≮: q)
+reflect-substitutionᴱ H (M $ N) v x (FunctionCallMismatch p) | Left q | Left r = Left ((FunctionCallMismatch ∘ unknown-src-≮: q) r)
 reflect-substitutionᴱ H (M $ N) v x (FunctionCallMismatch p) | Left q | Right W = Right (Right W)
 reflect-substitutionᴱ H (M $ N) v x (app₁ W) = mapL app₁ (reflect-substitutionᴱ H M v x W)
 reflect-substitutionᴱ H (M $ N) v x (app₂ W) = mapL app₂ (reflect-substitutionᴱ H N v x W)
@ -187,7 +187,7 @@ 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-weakeningᴱ Γ H N h (any-src-≮: p (heap-weakeningᴱ Γ H M h (src-any-≮: p))))
+reflect-weakeningᴱ Γ H (M $ N) h (FunctionCallMismatch p) = FunctionCallMismatch (heap-weakeningᴱ Γ H N h (unknown-src-≮: p (heap-weakeningᴱ Γ H M h (src-unknown-≮: 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 (heap-weakeningᴱ Γ H M h p)
@ -214,19 +214,19 @@ reflect-weakeningᴼ H (just function f ⟨ var x ∈ T ⟩∈ U is B end) h (fu
 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-weakeningᴱ ∅ H N (rednᴱ⊑ s) ∘ any-src-≮: p) (Left ∘ app₁) (reflect-subtypingᴱ H M s (src-any-≮: p))
+reflectᴱ H (M $ N) (app₁ s) (FunctionCallMismatch p) = cond (Left ∘ FunctionCallMismatch ∘ heap-weakeningᴱ ∅ H N (rednᴱ⊑ s) ∘ unknown-src-≮: p) (Left ∘ app₁) (reflect-subtypingᴱ H M s (src-unknown-≮: 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 (λ r → Left (FunctionCallMismatch (any-src-≮: r (heap-weakeningᴱ ∅ H M (rednᴱ⊑ s) (src-any-≮: r))))) (Left ∘ app₂) (reflect-subtypingᴱ H N s q)
+reflectᴱ H (M $ N) (app₂ p s) (FunctionCallMismatch q) = cond (λ r → Left (FunctionCallMismatch (unknown-src-≮: r (heap-weakeningᴱ ∅ H M (rednᴱ⊑ s) (src-unknown-≮: r))))) (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 
 reflectᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (BlockMismatch q) | Left r = Right (addr a p (FunctionDefnMismatch r))
-reflectᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (BlockMismatch q) | Right r = Left (FunctionCallMismatch (≮:-trans-≡ r ((cong src (cong orAny (cong typeOfᴹᴼ (sym p)))))))
+reflectᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (BlockMismatch q) | Right r = Left (FunctionCallMismatch (≮:-trans-≡ r ((cong src (cong orUnknown (cong typeOfᴹᴼ (sym p)))))))
 reflectᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (block₁ W′) with reflect-substitutionᴮ _ B v x W′
 reflectᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (block₁ W′) | Left W = Right (addr a p (function₁ W))
 reflectᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (block₁ W′) | Right (Left W) = Left (app₂ W)
-reflectᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (block₁ W′) | Right (Right q) = Left (FunctionCallMismatch (≮:-trans-≡ q (cong src (cong orAny (cong typeOfᴹᴼ (sym p))))))
+reflectᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (block₁ W′) | Right (Right q) = Left (FunctionCallMismatch (≮:-trans-≡ q (cong src (cong orUnknown (cong typeOfᴹᴼ (sym p))))))
 reflectᴱ H (block var b ∈ T is B end) (block s) (BlockMismatch p) = Left (cond BlockMismatch block₁ (reflect-subtypingᴮ H B s p))
 reflectᴱ H (block var b ∈ T is B end) (block s) (block₁ W′) = mapL block₁ (reflectᴮ H B s W′)
 reflectᴱ H (block var b ∈ T is B end) (return v) W′ = Left (block₁ (return W′))
@ -283,8 +283,8 @@ reflect* H B (step s t) W = cond (reflectᴮ H B s) (reflectᴴᴮ H B s) (refle
 isntNumber : ∀ H v → (valueType v ≢ number) → (typeOfᴱ H ∅ (val v) ≮: number)
 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 (addr a) p | (just (function f ⟨ var x ∈ T ⟩∈ U is B end) , q) = ≡-trans-≮: (cong orUnknown (cong typeOfᴹᴼ q)) (function-≮:-scalar number)
+isntNumber H (addr a) p | (nothing , q) = ≡-trans-≮: (cong orUnknown (cong typeOfᴹᴼ q)) (unknown-≮:-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 ())
@ -292,8 +292,8 @@ isntNumber H (string x) p = scalar-≢-impl-≮: string number (λ ())
 isntString : ∀ H v → (valueType v ≢ string) → (typeOfᴱ H ∅ (val v) ≮: string)
 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 (addr a) p | (just (function f ⟨ var x ∈ T ⟩∈ U is B end) , q) = ≡-trans-≮: (cong orUnknown (cong typeOfᴹᴼ q)) (function-≮:-scalar string)
+isntString H (addr a) p | (nothing , q) = ≡-trans-≮: (cong orUnknown (cong typeOfᴹᴼ q)) (unknown-≮:-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)
@ -305,14 +305,14 @@ isntFunction H (number x) p = scalar-≮:-function number
 isntFunction H (bool x) p = scalar-≮:-function boolean
 isntFunction H (string x) p = scalar-≮:-function string

-isntEmpty : ∀ H v → (typeOfᴱ H ∅ (val v) ≮: none)
-isntEmpty H nil = scalar-≮:-none nil
+isntEmpty : ∀ H v → (typeOfᴱ H ∅ (val v) ≮: never)
+isntEmpty H nil = scalar-≮:-never nil
 isntEmpty H (addr a) with remember (H [ a ]ᴴ)
-isntEmpty H (addr a) | (just (function f ⟨ var x ∈ T ⟩∈ U is B end) , p) = ≡-trans-≮: (cong orAny (cong typeOfᴹᴼ p)) function-≮:-none
-isntEmpty H (addr a) | (nothing , p) = ≡-trans-≮: (cong orAny (cong typeOfᴹᴼ p)) any-≮:-none
-isntEmpty H (number x) = scalar-≮:-none number
-isntEmpty H (bool x) = scalar-≮:-none boolean
-isntEmpty H (string x) = scalar-≮:-none string
+isntEmpty H (addr a) | (just (function f ⟨ var x ∈ T ⟩∈ U is B end) , p) = ≡-trans-≮: (cong orUnknown (cong typeOfᴹᴼ p)) function-≮:-never
+isntEmpty H (addr a) | (nothing , p) = ≡-trans-≮: (cong orUnknown (cong typeOfᴹᴼ p)) unknown-≮:-never
+isntEmpty H (number x) = scalar-≮:-never number
+isntEmpty H (bool x) = scalar-≮:-never boolean
+isntEmpty H (string x) = scalar-≮:-never string

 runtimeBinOpWarning : ∀ H {op} v → BinOpError op (valueType v) → (typeOfᴱ H ∅ (val v) ≮: srcBinOp op)
 runtimeBinOpWarning H v (+ p) = isntNumber H v p
@ -330,7 +330,7 @@ runtimeWarningᴮ : ∀ H B → RuntimeErrorᴮ H B → Warningᴮ H (typeCheck

 runtimeWarningᴱ H (var x) UnboundVariable = UnboundVariable refl
 runtimeWarningᴱ H (val (addr a)) (SEGV p) = UnallocatedAddress p
-runtimeWarningᴱ H (M $ N) (FunctionMismatch v w p) = FunctionCallMismatch (any-src-≮: (isntEmpty H w) (isntFunction H v p))
+runtimeWarningᴱ H (M $ N) (FunctionMismatch v w p) = FunctionCallMismatch (unknown-src-≮: (isntEmpty H w) (isntFunction H v p))
 runtimeWarningᴱ H (M $ N) (app₁ err) = app₁ (runtimeWarningᴱ H M err)
 runtimeWarningᴱ H (M $ N) (app₂ err) = app₂ (runtimeWarningᴱ H N err)
 runtimeWarningᴱ H (block var b ∈ T is B end) (block err) = block₁ (runtimeWarningᴮ H B err)
--- a/prototyping/Properties/Subtyping.agda
+++ b/prototyping/Properties/Subtyping.agda
@ -4,8 +4,8 @@ module Properties.Subtyping where

 open import Agda.Builtin.Equality using (_≡_; refl)
 open import FFI.Data.Either using (Either; Left; Right; mapLR; swapLR; cond)
-open import Luau.Subtyping using (_<:_; _≮:_; Tree; Language; ¬Language; witness; any; none; 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; strict; nil; number; string; boolean; none; any; _⇒_; _∪_; _∩_; 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; strict; nil; number; string; boolean; never; unknown; _⇒_; _∪_; _∩_; tgt)
 open import Properties.Contradiction using (CONTRADICTION; ¬)
 open import Properties.Equality using (_≢_)
 open import Properties.Functions using (_∘_)
@ -47,8 +47,8 @@ dec-language (T₁ ⇒ T₂) (scalar s) = Left (function-scalar s)
 dec-language (T₁ ⇒ T₂) function = Right function
 dec-language (T₁ ⇒ T₂) (function-ok t) = mapLR function-ok function-ok (dec-language T₂ t)
 dec-language (T₁ ⇒ T₂) (function-err t) = mapLR function-err function-err (swapLR (dec-language T₁ t))
-dec-language none t = Left none
-dec-language any t = Right any
+dec-language never t = Left never
+dec-language unknown t = Right unknown
 dec-language (T₁ ∪ T₂) t = cond (λ p → cond (Left ∘ _,_ p) (Right ∘ right) (dec-language T₂ t)) (Right ∘ left) (dec-language T₁ t)
 dec-language (T₁ ∩ T₂) t = cond (Left ∘ left) (λ p → cond (Left ∘ right) (Right ∘ _,_ p) (dec-language T₂ t)) (dec-language T₁ t)

@ -60,7 +60,7 @@ language-comp t (left p) (q₁ , q₂) = language-comp t p q₁
 language-comp t (right p) (q₁ , q₂) = language-comp t p q₂
 language-comp (scalar s) (scalar-scalar s p₁ p₂) (scalar s) = p₂ refl
 language-comp (scalar s) (function-scalar s) (scalar s) = language-comp function (scalar-function s) function
-language-comp (scalar s) none (scalar ())
+language-comp (scalar s) never (scalar ())
 language-comp function (scalar-function ()) function
 language-comp (function-ok t) (scalar-function-ok ()) (function-ok q)
 language-comp (function-ok t) (function-ok p) (function-ok q) = language-comp t p q
@ -104,11 +104,11 @@ function-≮:-scalar s = witness function function (scalar-function s)
 scalar-≮:-function : ∀ {S T U} → (Scalar U) → (U ≮: (S ⇒ T))
 scalar-≮:-function s = witness (scalar s) (scalar s) (function-scalar s)

-any-≮:-scalar : ∀ {U} → (Scalar U) → (any ≮: U)
-any-≮:-scalar s = witness (function-ok (scalar s)) any (scalar-function-ok s)
+unknown-≮:-scalar : ∀ {U} → (Scalar U) → (unknown ≮: U)
+unknown-≮:-scalar s = witness (function-ok (scalar s)) unknown (scalar-function-ok s)

-scalar-≮:-none : ∀ {U} → (Scalar U) → (U ≮: none)
-scalar-≮:-none s = witness (scalar s) (scalar s) none
+scalar-≮:-never : ∀ {U} → (Scalar U) → (U ≮: never)
+scalar-≮:-never s = witness (scalar s) (scalar s) never

 scalar-≢-impl-≮: : ∀ {T U} → (Scalar T) → (Scalar U) → (T ≢ U) → (T ≮: U)
 scalar-≢-impl-≮: s₁ s₂ p = witness (scalar s₁) (scalar s₁) (scalar-scalar s₁ s₂ p)
@ -117,8 +117,8 @@ scalar-≢-impl-≮: s₁ s₂ p = witness (scalar s₁) (scalar s₁) (scalar-s
 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 = none} (scalar ())
-tgt-function-ok {T = any} p = any
+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 ())
@ -131,7 +131,7 @@ 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 any = any
+function-ok-tgt unknown = unknown

 skalar-function-ok : ∀ {t} → (¬Language skalar (function-ok t))
 skalar-function-ok = (scalar-function-ok number , (scalar-function-ok string , (scalar-function-ok nil , scalar-function-ok boolean)))
@ -142,22 +142,22 @@ skalar-scalar boolean = right (right (right (scalar boolean)))
 skalar-scalar string = right (left (scalar string))
 skalar-scalar nil = right (right (left (scalar nil)))

-tgt-none-≮: : ∀ {T U} → (tgt T ≮: U) → (T ≮: (skalar ∪ (none ⇒ U)))
-tgt-none-≮: (witness t p q) = witness (function-ok t) (tgt-function-ok p) (skalar-function-ok , function-ok q)
+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)

-none-tgt-≮: : ∀ {T U} → (T ≮: (skalar ∪ (none ⇒ U))) → (tgt T ≮: U)
-none-tgt-≮: (witness (scalar s) p (q₁ , q₂)) = CONTRADICTION (≮:-refl (witness (scalar s) (skalar-scalar s) q₁))
-none-tgt-≮: (witness function p (q₁ , scalar-function ()))
-none-tgt-≮: (witness (function-ok t) p (q₁ , function-ok q₂)) = witness t (function-ok-tgt p) q₂
-none-tgt-≮: (witness (function-err (scalar s)) p (q₁ , function-err (scalar ())))
+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 ())))

 -- Properties of src
 function-err-src : ∀ {T t} → (¬Language (src T) t) → Language T (function-err t)
-function-err-src {T = nil} none = scalar-function-err nil
+function-err-src {T = nil} never = scalar-function-err nil
 function-err-src {T = T₁ ⇒ T₂} p = function-err p
-function-err-src {T = none} (scalar-scalar number () p)
-function-err-src {T = none} (scalar-function-ok ())
-function-err-src {T = any} none = any
+function-err-src {T = never} (scalar-scalar number () p)
+function-err-src {T = never} (scalar-function-ok ())
+function-err-src {T = unknown} never = unknown
 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
@ -168,8 +168,8 @@ function-err-src {T = T₁ ∩ T₂} (p₁ , p₂) = function-err-src p₁ , fun
 ¬function-err-src : ∀ {T t} → (Language (src T) t) → ¬Language T (function-err t)
 ¬function-err-src {T = nil} (scalar ())
 ¬function-err-src {T = T₁ ⇒ T₂} p = function-err p
-¬function-err-src {T = none} any = none
-¬function-err-src {T = any} (scalar ())
+¬function-err-src {T = never} unknown = never
+¬function-err-src {T = unknown} (scalar ())
 ¬function-err-src {T = boolean} (scalar ())
 ¬function-err-src {T = number} (scalar ())
 ¬function-err-src {T = string} (scalar ())
@ -178,53 +178,53 @@ function-err-src {T = T₁ ∩ T₂} (p₁ , p₂) = function-err-src p₁ , fun
 ¬function-err-src {T = T₁ ∩ T₂} (right p) = right (¬function-err-src p)

 src-¬function-err : ∀ {T t} → Language T (function-err t) → (¬Language (src T) t)
-src-¬function-err {T = nil} p = none
+src-¬function-err {T = nil} p = never
 src-¬function-err {T = T₁ ⇒ T₂} (function-err p) = p
-src-¬function-err {T = none} (scalar-function-err ())
-src-¬function-err {T = any} p = none
-src-¬function-err {T = boolean} p = none
-src-¬function-err {T = number} p = none
-src-¬function-err {T = string} p = none
+src-¬function-err {T = never} (scalar-function-err ())
+src-¬function-err {T = unknown} p = never
+src-¬function-err {T = boolean} p = never
+src-¬function-err {T = number} p = never
+src-¬function-err {T = string} p = never
 src-¬function-err {T = T₁ ∪ T₂} (left p) = left (src-¬function-err p)
 src-¬function-err {T = T₁ ∪ T₂} (right p) = right (src-¬function-err p)
 src-¬function-err {T = T₁ ∩ T₂} (p₁ , p₂) = (src-¬function-err p₁ , src-¬function-err p₂)

 src-¬scalar : ∀ {S T t} (s : Scalar S) → Language T (scalar s) → (¬Language (src T) t)
-src-¬scalar number (scalar number) = none
-src-¬scalar boolean (scalar boolean) = none
-src-¬scalar string (scalar string) = none
-src-¬scalar nil (scalar nil) = none
+src-¬scalar number (scalar number) = never
+src-¬scalar boolean (scalar boolean) = never
+src-¬scalar string (scalar string) = never
+src-¬scalar nil (scalar nil) = never
 src-¬scalar s (left p) = left (src-¬scalar s p)
 src-¬scalar s (right p) = right (src-¬scalar s p)
 src-¬scalar s (p₁ , p₂) = (src-¬scalar s p₁ , src-¬scalar s p₂)
-src-¬scalar s any = none
+src-¬scalar s unknown = never

-src-any-≮: : ∀ {T U} → (T ≮: src U) → (U ≮: (T ⇒ any))
-src-any-≮: (witness t p q) = witness (function-err t) (function-err-src q) (¬function-err-src p)
+src-unknown-≮: : ∀ {T U} → (T ≮: src U) → (U ≮: (T ⇒ unknown))
+src-unknown-≮: (witness t p q) = witness (function-err t) (function-err-src q) (¬function-err-src p)

-any-src-≮: : ∀ {S T U} → (U ≮: S) → (T ≮: (U ⇒ any)) → (U ≮: src T)
-any-src-≮: (witness t x x₁) (witness (scalar s) p (function-scalar s)) = witness t x (src-¬scalar s p)
-any-src-≮: r (witness (function-ok (scalar s)) p (function-ok (scalar-scalar s () q)))
-any-src-≮: r (witness (function-ok (function-ok _)) p (function-ok (scalar-function-ok ())))
-any-src-≮: r (witness (function-err t) p (function-err q)) = witness t q (src-¬function-err 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 any and none
-any-≮: : ∀ {T U} → (T ≮: U) → (any ≮: U)
-any-≮: (witness t p q) = witness t any q
+-- Properties of unknown and never
+unknown-≮: : ∀ {T U} → (T ≮: U) → (unknown ≮: U)
+unknown-≮: (witness t p q) = witness t unknown q

-none-≮: : ∀ {T U} → (T ≮: U) → (T ≮: none)
-none-≮: (witness t p q) = witness t p none
+never-≮: : ∀ {T U} → (T ≮: U) → (T ≮: never)
+never-≮: (witness t p q) = witness t p never

-any-≮:-none : (any ≮: none)
-any-≮:-none = witness (scalar nil) any none
+unknown-≮:-never : (unknown ≮: never)
+unknown-≮:-never = witness (scalar nil) unknown never

-function-≮:-none : ∀ {T U} → ((T ⇒ U) ≮: none)
-function-≮:-none = witness function function none
+function-≮:-never : ∀ {T U} → ((T ⇒ U) ≮: never)
+function-≮:-never = witness function function never

 -- A Gentle Introduction To Semantic Subtyping (https://www.cduce.org/papers/gentle.pdf)
 -- defines a "set-theoretic" model (sec 2.5)
 -- Unfortunately we don't quite have this property, due to uninhabited types,
-- for example (none -> T) is equivalent to (none -> U)
+-- for example (never -> T) is equivalent to (never -> U)
 -- when types are interpreted as sets of syntactic values.

 _⊆_ : ∀ {A : Set} → (A → Set) → (A → Set) → Set
@ -258,7 +258,7 @@ not-quite-set-theoretic-only-if : ∀ {S₁ T₁ S₂ T₂} →

  -- We don't quite have that this is a set-theoretic model
  -- it's only true when Language T₁ and ¬Language T₂ t₂ are inhabited
-  -- in particular it's not true when T₁ is none, or T₂ is any.
+  -- in particular it's not true when T₁ is never, or T₂ is unknown.
  ∀ s₂ t₂ → Language S₂ s₂ → ¬Language T₂ t₂ →

  -- This is the "only if" part of being a set-theoretic model
@ -285,11 +285,11 @@ not-quite-set-theoretic-only-if {S₁} {T₁} {S₂} {T₂} s₂ t₂ S₂s₂

 -- A counterexample when the argument type is empty.

-set-theoretic-counterexample-one : (∀ Q → Q ⊆ Comp((Language none) ⊗ Comp(Language number)) → Q ⊆ Comp((Language none) ⊗ Comp(Language string)))
+set-theoretic-counterexample-one : (∀ Q → Q ⊆ Comp((Language never) ⊗ Comp(Language number)) → Q ⊆ Comp((Language never) ⊗ Comp(Language string)))
 set-theoretic-counterexample-one Q q ((scalar s) , u) Qtu (scalar () , p)
 set-theoretic-counterexample-one Q q ((function-err t) , u) Qtu (scalar-function-err () , p)

-set-theoretic-counterexample-two : (none ⇒ number) ≮: (none ⇒ string)
+set-theoretic-counterexample-two : (never ⇒ number) ≮: (never ⇒ string)
 set-theoretic-counterexample-two = witness
  (function-ok (scalar number)) (function-ok (scalar number))
  (function-ok (scalar-scalar number string (λ ())))
@ -298,14 +298,14 @@ set-theoretic-counterexample-two = witness
 -- The reason why this is connected to overloaded functions is that currently we have that the type of
 -- f(x) is (tgt T) where f:T. Really we should have the type depend on the type of x, that is use (tgt T U),
 -- where U is the type of x. In particular (tgt (S => T) (U & V)) should be the same as (tgt ((S&U) => T) V)
-- and tgt(none => T) should be any. For example
+-- and tgt(never => T) should be unknown. For example
 --
 -- tgt((number => string) & (string => bool))(number)
 -- is tgt(number => string)(number) & tgt(string => bool)(number)
-- is tgt(number => string)(number) & tgt(string => bool)(number&any)
-- is tgt(number => string)(number) & tgt(string&number => bool)(any)
-- is tgt(number => string)(number) & tgt(none => bool)(any)
-- is string & any
+-- is tgt(number => string)(number) & tgt(string => bool)(number&unknown)
+-- is tgt(number => string)(number) & tgt(string&number => bool)(unknown)
+-- is tgt(number => string)(number) & tgt(never => bool)(unknown)
+-- is string & unknown
 -- is string
 --
 -- there's some discussion of this in the Gentle Introduction paper.
--- a/prototyping/Properties/TypeCheck.agda
+++ b/prototyping/Properties/TypeCheck.agda
@ -8,9 +8,9 @@ open import Agda.Builtin.Equality using (_≡_; refl)
 open import Agda.Builtin.Bool using (Bool; true; false)
 open import FFI.Data.Maybe using (Maybe; just; nothing)
 open import FFI.Data.Either using (Either)
-open import Luau.TypeCheck(m) using (_⊢ᴱ_∈_; _⊢ᴮ_∈_; ⊢ᴼ_; ⊢ᴴ_; _⊢ᴴᴱ_▷_∈_; _⊢ᴴᴮ_▷_∈_; nil; var; addr; number; bool; string; app; function; block; binexp; done; return; local; nothing; orAny; tgtBinOp)
+open import Luau.TypeCheck(m) using (_⊢ᴱ_∈_; _⊢ᴮ_∈_; ⊢ᴼ_; ⊢ᴴ_; _⊢ᴴᴱ_▷_∈_; _⊢ᴴᴮ_▷_∈_; nil; var; addr; number; bool; string; app; function; block; binexp; done; return; local; nothing; orUnknown; tgtBinOp)
 open import Luau.Syntax using (Block; Expr; Value; BinaryOperator; yes; nil; addr; number; bool; string; val; var; binexp; _$_; function_is_end; block_is_end; _∙_; return; done; local_←_; _⟨_⟩; _⟨_⟩∈_; var_∈_; name; fun; arg; +; -; *; /; <; >; ==; ~=; <=; >=)
-open import Luau.Type using (Type; nil; any; none; number; boolean; string; _⇒_; tgt)
+open import Luau.Type using (Type; nil; unknown; never; number; boolean; string; _⇒_; tgt)
 open import Luau.RuntimeType using (RuntimeType; nil; number; function; string; valueType)
 open import Luau.VarCtxt using (VarCtxt; ∅; _↦_; _⊕_↦_; _⋒_; _⊝_) renaming (_[_] to _[_]ⱽ)
 open import Luau.Addr using (Addr)
@ -42,8 +42,8 @@ typeOfⱽ H (string x) = just string
 typeOfᴱ : Heap yes → VarCtxt → (Expr yes) → Type
 typeOfᴮ : Heap yes → VarCtxt → (Block yes) → Type

-typeOfᴱ H Γ (var x) = orAny(Γ [ x ]ⱽ)
-typeOfᴱ H Γ (val v) = orAny(typeOfⱽ H v)
+typeOfᴱ H Γ (var x) = orUnknown(Γ [ x ]ⱽ)
+typeOfᴱ H Γ (val v) = orUnknown(typeOfⱽ H v)
 typeOfᴱ H Γ (M $ N) = tgt(typeOfᴱ H Γ M)
 typeOfᴱ H Γ (function f ⟨ var x ∈ S ⟩∈ T is B end) = S ⇒ T
 typeOfᴱ H Γ (block var b ∈ T is B end) = T
@ -54,7 +54,7 @@ typeOfᴮ H Γ (local var x ∈ T ← M ∙ B) = typeOfᴮ H (Γ ⊕ x ↦ T) B
 typeOfᴮ H Γ (return M ∙ B) = typeOfᴱ H Γ M
 typeOfᴮ H Γ done = nil

-mustBeFunction : ∀ H Γ v → (none ≢ src (typeOfᴱ H Γ (val v))) → (function ≡ valueType(v))
+mustBeFunction : ∀ H Γ v → (never ≢ src (typeOfᴱ H Γ (val v))) → (function ≡ valueType(v))
 mustBeFunction H Γ nil p = CONTRADICTION (p refl)
 mustBeFunction H Γ (addr a) p = refl
 mustBeFunction H Γ (number n) p = CONTRADICTION (p refl)
@ -64,17 +64,17 @@ mustBeFunction H Γ (string x) p = CONTRADICTION (p refl)

 mustBeNumber : ∀ H Γ v → (typeOfᴱ H Γ (val v) ≡ number) → (valueType(v) ≡ number)
 mustBeNumber H Γ (addr a) p with remember (H [ a ]ᴴ)
-mustBeNumber H Γ (addr a) p | (just O , q) with trans (cong orAny (cong typeOfᴹᴼ (sym q))) p
+mustBeNumber H Γ (addr a) p | (just O , q) with trans (cong orUnknown (cong typeOfᴹᴼ (sym q))) p
 mustBeNumber H Γ (addr a) p | (just function f ⟨ var x ∈ T ⟩∈ U is B end , q) | ()
-mustBeNumber H Γ (addr a) p | (nothing , q) with trans (cong orAny (cong typeOfᴹᴼ (sym q))) p
+mustBeNumber H Γ (addr a) p | (nothing , q) with trans (cong orUnknown (cong typeOfᴹᴼ (sym q))) p
 mustBeNumber H Γ (addr a) p | nothing , q | ()
 mustBeNumber H Γ (number n) p = refl

 mustBeString : ∀ H Γ v → (typeOfᴱ H Γ (val v) ≡ string) → (valueType(v) ≡ string)
 mustBeString H Γ (addr a) p with remember (H [ a ]ᴴ)
-mustBeString H Γ (addr a) p | (just O , q) with trans (cong orAny (cong typeOfᴹᴼ (sym q))) p
+mustBeString H Γ (addr a) p | (just O , q) with trans (cong orUnknown (cong typeOfᴹᴼ (sym q))) p
 mustBeString H Γ (addr a) p | (just function f ⟨ var x ∈ T ⟩∈ U is B end , q) | ()
-mustBeString H Γ (addr a) p | (nothing , q) with trans (cong orAny (cong typeOfᴹᴼ (sym q))) p
+mustBeString H Γ (addr a) p | (nothing , q) with trans (cong orUnknown (cong typeOfᴹᴼ (sym q))) p
 mustBeString H Γ (addr a) p | (nothing , q) | ()
 mustBeString H Γ (string x) p = refl

@ -83,7 +83,7 @@ typeCheckᴮ : ∀ H Γ B → (Γ ⊢ᴮ B ∈ (typeOfᴮ H Γ B))

 typeCheckᴱ H Γ (var x) = var refl
 typeCheckᴱ H Γ (val nil) = nil
-typeCheckᴱ H Γ (val (addr a)) = addr (orAny (typeOfᴹᴼ (H [ a ]ᴴ)))
+typeCheckᴱ H Γ (val (addr a)) = addr (orUnknown (typeOfᴹᴼ (H [ a ]ᴴ)))
 typeCheckᴱ H Γ (val (number n)) = number
 typeCheckᴱ H Γ (val (bool b)) = bool
 typeCheckᴱ H Γ (val (string x)) = string
--- a/prototyping/Tests/PrettyPrinter/smoke_test/out.txt
+++ b/prototyping/Tests/PrettyPrinter/smoke_test/out.txt
@ -10,10 +10,10 @@ local function comp(f)
 end
 local id2 = comp(id)(id)
 local nil2 = id2(nil)
-local a : any = nil
+local a : unknown = nil
 local b : nil = nil
 local c : (nil) -> nil = nil
-local d : (any & nil) = nil
-local e : any? = nil
+local d : (unknown & nil) = nil
+local e : unknown? = nil
 local f : number = 123.0
 return id2(nil2)