756 lines
29 KiB
Idris
756 lines
29 KiB
Idris
module Quox.Equal
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import Quox.BoolExtra
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import public Quox.Typing
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import Data.Maybe
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import Quox.EffExtra
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%default total
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public export
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EqModeState : Type -> Type
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EqModeState = State EqMode
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public export
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Equal : Type -> Type
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Equal = Eff [ErrorEff, DefsReader, NameGen]
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public export
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Equal_ : Type -> Type
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Equal_ = Eff [ErrorEff, NameGen, EqModeState]
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export
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runEqualWith_ : EqMode -> NameSuf -> Equal_ a -> (Either Error a, NameSuf)
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runEqualWith_ mode suf act =
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extract $
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runNameGenWith suf $
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runExcept $
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evalState mode act
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export
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runEqual_ : EqMode -> Equal_ a -> Either Error a
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runEqual_ mode act = fst $ runEqualWith_ mode 0 act
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export
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runEqualWith : NameSuf -> Definitions -> Equal a -> (Either Error a, NameSuf)
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runEqualWith suf defs act =
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extract $
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runStateAt GEN suf $
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runReaderAt DEFS defs $
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runExcept act
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export
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runEqual : Definitions -> Equal a -> Either Error a
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runEqual defs act = fst $ runEqualWith 0 defs act
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export %inline
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mode : Has EqModeState fs => Eff fs EqMode
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mode = get
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parameters (loc : Loc) (ctx : EqContext n)
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private %inline
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clashT : Term 0 n -> Term 0 n -> Term 0 n -> Equal_ a
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clashT ty s t = throw $ ClashT loc ctx !mode ty s t
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private %inline
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clashTy : Term 0 n -> Term 0 n -> Equal_ a
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clashTy s t = throw $ ClashTy loc ctx !mode s t
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private %inline
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clashE : Elim 0 n -> Elim 0 n -> Equal_ a
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clashE e f = throw $ ClashE loc ctx !mode e f
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private %inline
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wrongType : Term 0 n -> Term 0 n -> Equal_ a
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wrongType ty s = throw $ WrongType loc ctx ty s
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public export %inline
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sameTyCon : (s, t : Term d n) ->
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(0 ts : So (isTyConE s)) => (0 tt : So (isTyConE t)) =>
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Bool
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sameTyCon (TYPE {}) (TYPE {}) = True
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sameTyCon (TYPE {}) _ = False
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sameTyCon (Pi {}) (Pi {}) = True
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sameTyCon (Pi {}) _ = False
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sameTyCon (Sig {}) (Sig {}) = True
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sameTyCon (Sig {}) _ = False
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sameTyCon (W {}) (W {}) = True
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sameTyCon (W {}) _ = False
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sameTyCon (Enum {}) (Enum {}) = True
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sameTyCon (Enum {}) _ = False
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sameTyCon (Eq {}) (Eq {}) = True
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sameTyCon (Eq {}) _ = False
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sameTyCon (Nat {}) (Nat {}) = True
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sameTyCon (Nat {}) _ = False
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sameTyCon (BOX {}) (BOX {}) = True
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sameTyCon (BOX {}) _ = False
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sameTyCon (E {}) (E {}) = True
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sameTyCon (E {}) _ = False
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||| true if a type is known to be a subsingleton purely by its form.
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||| a subsingleton is a type with only zero or one possible values.
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||| equality/subtyping accepts immediately on values of subsingleton types.
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|||
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||| * a function type is a subsingleton if its codomain is.
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||| * a pair type is a subsingleton if both its elements are.
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||| * equality types are subsingletons because of uip.
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||| * an enum type is a subsingleton if it has zero or one tags.
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||| * a box type is a subsingleton if its content is
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public export covering
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isSubSing : {n : Nat} -> Definitions -> EqContext n -> Term 0 n -> Equal_ Bool
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isSubSing defs ctx ty0 = do
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Element ty0 nc <- whnf defs ctx ty0.loc ty0
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case ty0 of
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TYPE {} => pure False
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Pi {arg, res, _} =>
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isSubSing defs (extendTy Zero res.name arg ctx) res.term
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Sig {fst, snd, _} =>
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isSubSing defs ctx fst `andM`
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isSubSing defs (extendTy Zero snd.name fst ctx) snd.term
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W {} => pure False
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Enum {cases, _} =>
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pure $ length (SortedSet.toList cases) <= 1
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Eq {} => pure True
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Nat {} => pure False
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BOX {ty, _} => isSubSing defs ctx ty
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E (Ann {tm, _}) => isSubSing defs ctx tm
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E _ => pure False
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Lam {} => pure False
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Pair {} => pure False
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Sup {} => pure False
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Tag {} => pure False
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DLam {} => pure False
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Zero {} => pure False
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Succ {} => pure False
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Box {} => pure False
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export
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ensureTyCon : Has ErrorEff fs =>
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(loc : Loc) -> (ctx : EqContext n) -> (t : Term 0 n) ->
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Eff fs (So (isTyConE t))
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ensureTyCon loc ctx t = case nchoose $ isTyConE t of
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Left y => pure y
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Right n => throw $ NotType loc (toTyContext ctx) (t // shift0 ctx.dimLen)
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||| performs the minimum work required to recompute the type of an elim.
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|||
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||| ⚠ **assumes the elim is already typechecked.** ⚠
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private covering
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computeElimTypeE : (defs : Definitions) -> EqContext n ->
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(e : Elim 0 n) -> (0 ne : NotRedex defs e) =>
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Equal_ (Term 0 n)
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computeElimTypeE defs ectx e =
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let Val n = ectx.termLen in
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lift $ computeElimType defs (toWhnfContext ectx) e
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parameters (defs : Definitions)
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mutual
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namespace Term
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||| `compare0 ctx ty s t` compares `s` and `t` at type `ty`, according to
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||| the current variance `mode`.
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|||
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||| ⚠ **assumes that `s`, `t` have already been checked against `ty`**. ⚠
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export covering %inline
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compare0 : EqContext n -> (ty, s, t : Term 0 n) -> Equal_ ()
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compare0 ctx ty s t =
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wrapErr (WhileComparingT ctx !mode ty s t) $ do
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let Val n = ctx.termLen
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Element ty' _ <- whnf defs ctx ty.loc ty
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Element s' _ <- whnf defs ctx s.loc s
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Element t' _ <- whnf defs ctx t.loc t
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tty <- ensureTyCon ty.loc ctx ty'
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compare0' ctx ty' s' t'
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||| converts an elim "Γ ⊢ e" to "Γ, x ⊢ e x", for comparing with
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||| a lambda "Γ ⊢ λx ⇒ t" that has been converted to "Γ, x ⊢ t".
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private %inline
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toLamBody : Elim d n -> Term d (S n)
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toLamBody e = E $ App (weakE 1 e) (BVT 0 e.loc) e.loc
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private covering
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compare0' : EqContext n ->
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(ty, s, t : Term 0 n) ->
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(0 _ : NotRedex defs ty) => (0 _ : So (isTyConE ty)) =>
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(0 _ : NotRedex defs s) => (0 _ : NotRedex defs t) =>
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Equal_ ()
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compare0' ctx (TYPE {}) s t = compareType ctx s t
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compare0' ctx ty@(Pi {qty, arg, res, _}) s t {n} = local_ Equal $
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case (s, t) of
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-- Γ, x : A ⊢ s = t : B
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-- -------------------------------------------
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-- Γ ⊢ (λ x ⇒ s) = (λ x ⇒ t) : (π·x : A) → B
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(Lam b1 {}, Lam b2 {}) =>
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compare0 ctx' res.term b1.term b2.term
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-- Γ, x : A ⊢ s = e x : B
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-- -----------------------------------
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-- Γ ⊢ (λ x ⇒ s) = e : (π·x : A) → B
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(E e, Lam b {}) => eta s.loc e b
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(Lam b {}, E e) => eta s.loc e b
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(E e, E f) => Elim.compare0 ctx e f
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(Lam {}, t) => wrongType t.loc ctx ty t
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(E _, t) => wrongType t.loc ctx ty t
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(s, _) => wrongType s.loc ctx ty s
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where
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ctx' : EqContext (S n)
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ctx' = extendTy qty res.name arg ctx
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eta : Loc -> Elim 0 n -> ScopeTerm 0 n -> Equal_ ()
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eta _ e (S _ (Y b)) = compare0 ctx' res.term (toLamBody e) b
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eta loc e (S _ (N _)) = clashT loc ctx ty s t
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compare0' ctx ty@(Sig {fst, snd, _}) s t = local_ Equal $
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case (s, t) of
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-- Γ ⊢ s₁ = t₁ : A Γ ⊢ s₂ = t₂ : B{s₁/x}
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-- --------------------------------------------
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-- Γ ⊢ (s₁, t₁) = (s₂, t₂) : (x : A) × B
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--
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-- [todo] η for π ≰ 1 maybe
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(Pair sFst sSnd {}, Pair tFst tSnd {}) => do
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compare0 ctx fst sFst tFst
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compare0 ctx (sub1 snd (Ann sFst fst fst.loc)) sSnd tSnd
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(E e, E f) => Elim.compare0 ctx e f
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(Pair {}, E _) => clashT s.loc ctx ty s t
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(E _, Pair {}) => clashT s.loc ctx ty s t
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(Pair {}, t) => wrongType t.loc ctx ty t
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(E _, t) => wrongType t.loc ctx ty t
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(s, _) => wrongType s.loc ctx ty s
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compare0' ctx ty@(W {shape, body, _}) s t =
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case (s, t) of
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-- Γ ⊢ s₁ = t₁ : A
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-- Γ ⊢ s₂ = t₂ : ω.B[s₁∷A/x] → (x : A) ⊲ B
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-- -----------------------------------------
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-- Γ ⊢ s₁⋄s₂ = t₁⋄t₂ : (x : A) ⊲ B
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(Sup sRoot sSub {}, Sup tRoot tSub {}) => do
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compare0 ctx shape sRoot tRoot
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let arg = sub1 body (Ann sRoot shape sRoot.loc)
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subTy = Arr Any arg ty ty.loc
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compare0 ctx subTy sSub tSub
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(E e, E f) => Elim.compare0 ctx e f
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(Sup {}, E {}) => clashT s.loc ctx ty s t
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(E {}, Sup {}) => clashT s.loc ctx ty s t
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(Sup {}, t) => wrongType t.loc ctx ty t
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(E {}, t) => wrongType t.loc ctx ty t
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(s, _) => wrongType s.loc ctx ty s
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compare0' ctx ty@(Enum {}) s t = local_ Equal $
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case (s, t) of
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-- --------------------
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-- Γ ⊢ `t = `t : {ts}
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--
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-- t ∈ ts is in the typechecker, not here, ofc
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(Tag t1 {}, Tag t2 {}) =>
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unless (t1 == t2) $ clashT s.loc ctx ty s t
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(E e, E f) => Elim.compare0 ctx e f
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(Tag {}, E _) => clashT s.loc ctx ty s t
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(E _, Tag {}) => clashT s.loc ctx ty s t
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(Tag {}, t) => wrongType t.loc ctx ty t
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(E _, t) => wrongType t.loc ctx ty t
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(s, _) => wrongType s.loc ctx ty s
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compare0' _ (Eq {}) _ _ =
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-- ✨ uip ✨
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--
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-- ----------------------------
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-- Γ ⊢ e = f : Eq [i ⇒ A] s t
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pure ()
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compare0' ctx nat@(Nat {}) s t = local_ Equal $
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case (s, t) of
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-- ---------------
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-- Γ ⊢ 0 = 0 : ℕ
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(Zero {}, Zero {}) => pure ()
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-- Γ ⊢ s = t : ℕ
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-- -------------------------
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-- Γ ⊢ succ s = succ t : ℕ
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(Succ s' {}, Succ t' {}) => compare0 ctx nat s' t'
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(E e, E f) => Elim.compare0 ctx e f
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(Zero {}, Succ {}) => clashT s.loc ctx nat s t
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(Zero {}, E _) => clashT s.loc ctx nat s t
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(Succ {}, Zero {}) => clashT s.loc ctx nat s t
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(Succ {}, E _) => clashT s.loc ctx nat s t
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(E _, Zero {}) => clashT s.loc ctx nat s t
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(E _, Succ {}) => clashT s.loc ctx nat s t
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(Zero {}, t) => wrongType t.loc ctx nat t
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(Succ {}, t) => wrongType t.loc ctx nat t
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(E _, t) => wrongType t.loc ctx nat t
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(s, _) => wrongType s.loc ctx nat s
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compare0' ctx ty@(BOX q ty' {}) s t = local_ Equal $
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case (s, t) of
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-- Γ ⊢ s = t : A
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-- -----------------------
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-- Γ ⊢ [s] = [t] : [π.A]
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(Box s' {}, Box t' {}) => compare0 ctx ty' s' t'
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(E e, E f) => Elim.compare0 ctx e f
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(Box {}, t) => wrongType t.loc ctx ty t
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(E _, t) => wrongType t.loc ctx ty t
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(s, _) => wrongType s.loc ctx ty s
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compare0' ctx ty@(E _) s t = do
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-- a neutral type can only be inhabited by neutral values
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-- e.g. an abstract value in an abstract type, bound variables, …
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let E e = s | _ => wrongType s.loc ctx ty s
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E f = t | _ => wrongType t.loc ctx ty t
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Elim.compare0 ctx e f
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||| compares two types, using the current variance `mode` for universes.
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||| fails if they are not types, even if they would happen to be equal.
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export covering %inline
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compareType : EqContext n -> (s, t : Term 0 n) -> Equal_ ()
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compareType ctx s t = do
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let Val n = ctx.termLen
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Element s' _ <- whnf defs ctx s.loc s
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Element t' _ <- whnf defs ctx t.loc t
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ts <- ensureTyCon s.loc ctx s'
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tt <- ensureTyCon t.loc ctx t'
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st <- either pure (const $ clashTy s.loc ctx s' t') $
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nchoose $ sameTyCon s' t'
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compareType' ctx s' t'
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private covering
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compareType' : EqContext n -> (s, t : Term 0 n) ->
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(0 _ : NotRedex defs s) => (0 _ : So (isTyConE s)) =>
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(0 _ : NotRedex defs t) => (0 _ : So (isTyConE t)) =>
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(0 _ : So (sameTyCon s t)) =>
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Equal_ ()
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-- equality is the same as subtyping, except with the
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-- "≤" in the TYPE rule being replaced with "="
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compareType' ctx a@(TYPE k {}) (TYPE l {}) =
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-- 𝓀 ≤ ℓ
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-- ----------------------
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-- Γ ⊢ Type 𝓀 <: Type ℓ
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expectModeU a.loc !mode k l
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compareType' ctx (Pi {qty = sQty, arg = sArg, res = sRes, loc})
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(Pi {qty = tQty, arg = tArg, res = tRes, _}) = do
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-- Γ ⊢ A₁ :> A₂ Γ, x : A₁ ⊢ B₁ <: B₂
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-- ----------------------------------------
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-- Γ ⊢ π.(x : A₁) → B₁ <: π.(x : A₂) → B₂
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--
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-- no quantity subtyping since that would need a runtime coercion
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-- e.g. if ⌊0.A → B⌋ ⇝ ⌊B⌋, then the promotion to ω.A → B would need
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-- to re-add the abstraction
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expectEqualQ loc sQty tQty
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local flip $ compareType ctx sArg tArg -- contra
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compareType (extendTy Zero sRes.name sArg ctx) sRes.term tRes.term
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compareType' ctx (Sig {fst = sFst, snd = sSnd, _})
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(Sig {fst = tFst, snd = tSnd, _}) = do
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-- Γ ⊢ A₁ <: A₂ Γ, x : A₁ ⊢ B₁ <: B₂
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-- --------------------------------------
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-- Γ ⊢ (x : A₁) × B₁ <: (x : A₂) × B₂
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compareType ctx sFst tFst
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compareType (extendTy Zero sSnd.name sFst ctx) sSnd.term tSnd.term
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compareType' ctx (W {shape = sShape, body = sBody, loc})
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(W {shape = tShape, body = tBody, _}) = do
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-- Γ ⊢ A₁ <: A₂ Γ, x : A₁ ⊢ B₁ <: B₂
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-- --------------------------------------
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-- Γ ⊢ (x : A₁) ⊲ B₁ <: (x : A₂) ⊲ B₂
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compareType ctx sShape tShape
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compareType (extendTy Zero sBody.name sShape ctx) sBody.term tBody.term
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compareType' ctx (Eq {ty = sTy, l = sl, r = sr, _})
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(Eq {ty = tTy, l = tl, r = tr, _}) = do
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-- Γ ⊢ A₁‹ε/i› <: A₂‹ε/i›
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-- Γ ⊢ l₁ = l₂ : A₁‹0/i› Γ ⊢ r₁ = r₂ : A₁‹1/i›
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-- ------------------------------------------------
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-- Γ ⊢ Eq (i ⇒ A₁) l₁ r₂ <: Eq (i ⇒ A₂) l₂ r₂
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compareType (extendDim sTy.name Zero ctx) sTy.zero tTy.zero
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compareType (extendDim sTy.name One ctx) sTy.one tTy.one
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let ty = case !mode of Super => sTy; _ => tTy
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local_ Equal $ do
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Term.compare0 ctx ty.zero sl tl
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Term.compare0 ctx ty.one sr tr
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compareType' ctx s@(Enum tags1 {}) t@(Enum tags2 {}) = do
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-- ------------------
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-- Γ ⊢ {ts} <: {ts}
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--
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-- no subtyping based on tag subsets, since that would need
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-- a runtime coercion
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unless (tags1 == tags2) $ clashTy s.loc ctx s t
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compareType' ctx (Nat {}) (Nat {}) =
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-- ------------
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-- Γ ⊢ ℕ <: ℕ
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pure ()
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compareType' ctx (BOX pi a loc) (BOX rh b {}) = do
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-- Γ ⊢ A <: B
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-- --------------------
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-- Γ ⊢ [π.A] <: [π.B]
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expectEqualQ loc pi rh
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compareType ctx a b
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compareType' ctx (E e) (E f) = do
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-- no fanciness needed here cos anything other than a neutral
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-- has been inlined by whnf
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Elim.compare0 ctx e f
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namespace Elim
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-- [fixme] the following code ends up repeating a lot of work in the
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-- computeElimType calls. the results should be shared better
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||| compare two eliminations according to the given variance `mode`.
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|||
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||| ⚠ **assumes that they have both been typechecked, and have
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||| equal types.** ⚠
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export covering %inline
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compare0 : EqContext n -> (e, f : Elim 0 n) -> Equal_ ()
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compare0 ctx e f =
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wrapErr (WhileComparingE ctx !mode e f) $ do
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let Val n = ctx.termLen
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Element e' ne <- whnf defs ctx e.loc e
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Element f' nf <- whnf defs ctx f.loc f
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unless !(isSubSing defs ctx =<< computeElimTypeE defs ctx e') $
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compare0' ctx e' f' ne nf
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private covering
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compare0' : EqContext n ->
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(e, f : Elim 0 n) ->
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(0 ne : NotRedex defs e) -> (0 nf : NotRedex defs f) ->
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Equal_ ()
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compare0' ctx e@(F x u _) f@(F y v _) _ _ =
|
||
unless (x == y && u == v) $ clashE e.loc ctx e f
|
||
compare0' ctx e@(F {}) f _ _ = clashE e.loc ctx e f
|
||
|
||
compare0' ctx e@(B i _) f@(B j _) _ _ =
|
||
unless (i == j) $ clashE e.loc ctx e f
|
||
compare0' ctx e@(B {}) f _ _ = clashE e.loc ctx e f
|
||
|
||
-- Ψ | Γ ⊢ e = f ⇒ π.(x : A) → B
|
||
-- Ψ | Γ ⊢ s = t ⇐ A
|
||
-- -------------------------------
|
||
-- Ψ | Γ ⊢ e s = f t ⇒ B[s∷A/x]
|
||
compare0' ctx (App e s eloc) (App f t floc) ne nf =
|
||
local_ Equal $ do
|
||
compare0 ctx e f
|
||
(_, arg, _) <- expectPi defs ctx eloc =<<
|
||
computeElimTypeE defs ctx e @{noOr1 ne}
|
||
Term.compare0 ctx arg s t
|
||
compare0' ctx e@(App {}) f _ _ = clashE e.loc ctx e f
|
||
|
||
-- Ψ | Γ ⊢ e = f ⇒ (x : A) × B
|
||
-- Ψ | Γ, 0.p : (x : A) × B ⊢ Q = R
|
||
-- Ψ | Γ, x : A, y : B ⊢ s = t ⇐ Q[((x, y) ∷ (x : A) × B)/p]
|
||
-- -----------------------------------------------------------
|
||
-- Ψ | Γ ⊢ caseπ e return Q of { (x, y) ⇒ s }
|
||
-- = caseπ f return R of { (x, y) ⇒ t } ⇒ Q[e/p]
|
||
compare0' ctx (CasePair epi e eret ebody eloc)
|
||
(CasePair fpi f fret fbody {}) ne nf =
|
||
local_ Equal $ do
|
||
compare0 ctx e f
|
||
ety <- computeElimTypeE defs ctx e @{noOr1 ne}
|
||
compareType (extendTy Zero eret.name ety ctx) eret.term fret.term
|
||
(fst, snd) <- expectSig defs ctx eloc ety
|
||
let [< x, y] = ebody.names
|
||
Term.compare0 (extendTyN [< (epi, x, fst), (epi, y, snd.term)] ctx)
|
||
(substCasePairRet ebody.names ety eret)
|
||
ebody.term fbody.term
|
||
expectEqualQ e.loc epi fpi
|
||
compare0' ctx e@(CasePair {}) f _ _ = clashE e.loc ctx e f
|
||
|
||
-- Ψ | Γ ⊢ e = f ⇒ (x : A) ⊲ B
|
||
-- Ψ | Γ, p : (x : A) ⊲ B ⊢ Q = R ⇐ Type
|
||
-- Ψ | Γ, x : A, y : ω.B → (x : A) ⊲ B, ih : 1.(z : B) → Q[y z/p]
|
||
-- ⊢ s = t ⇐ Q[(x⋄y ∷ (x : A) ⊲ B)/p]
|
||
-- ----------------------------------------------------------------
|
||
-- Ψ | Γ ⊢ caseπ e return Q of { x ⋄ y, ς.ih ⇒ s }
|
||
-- = caseπ f return R of { x ⋄ y, ς.ih ⇒ t } ⇒ Q[e/p]
|
||
compare0' ctx (CaseW epi epi' e eret ebody eloc)
|
||
(CaseW fpi fpi' f fret fbody floc) ne nf =
|
||
local_ Equal $ do
|
||
compare0 ctx e f
|
||
ety <- computeElimTypeE defs ctx e @{noOr1 ne}
|
||
compareType (extendTy Zero eret.name ety ctx) eret.term fret.term
|
||
(shape, tbody) <- expectW defs ctx eloc ety
|
||
let [< x, y, ih] = ebody.names
|
||
z <- mnb "z" ih.loc
|
||
let xbind = (epi, x, shape)
|
||
ybind = (epi, y, Arr Any tbody.term (weakT 1 ety) y.loc)
|
||
ihbind = (epi', ih,
|
||
PiY One z
|
||
(sub1 (weakS 2 tbody) (BV 1 x.loc))
|
||
(sub1 (weakS 3 eret) (App (BV 1 y.loc) (BVT 0 z.loc) ih.loc))
|
||
ih.loc)
|
||
ctx' = extendTyN [< xbind, ybind, ihbind] ctx
|
||
Term.compare0 ctx' (substCaseWRet ebody.names ety eret)
|
||
ebody.term fbody.term
|
||
expectEqualQ e.loc epi fpi
|
||
expectEqualQ e.loc epi' fpi'
|
||
compare0' ctx e@(CaseW {}) f _ _ = clashE e.loc ctx e f
|
||
|
||
-- Ψ | Γ ⊢ e = f ⇒ {𝐚s}
|
||
-- Ψ | Γ, x : {𝐚s} ⊢ Q = R
|
||
-- Ψ | Γ ⊢ sᵢ = tᵢ ⇐ Q[𝐚ᵢ∷{𝐚s}]
|
||
-- --------------------------------------------------
|
||
-- Ψ | Γ ⊢ caseπ e return Q of { '𝐚ᵢ ⇒ sᵢ }
|
||
-- = caseπ f return R of { '𝐚ᵢ ⇒ tᵢ } ⇒ Q[e/x]
|
||
compare0' ctx (CaseEnum epi e eret earms eloc)
|
||
(CaseEnum fpi f fret farms floc) ne nf =
|
||
local_ Equal $ do
|
||
compare0 ctx e f
|
||
ety <- computeElimTypeE defs ctx e @{noOr1 ne}
|
||
compareType (extendTy Zero eret.name ety ctx) eret.term fret.term
|
||
for_ !(expectEnum defs ctx eloc ety) $ \t => do
|
||
l <- lookupArm eloc t earms
|
||
r <- lookupArm floc t farms
|
||
compare0 ctx (sub1 eret $ Ann (Tag t l.loc) ety l.loc) l r
|
||
expectEqualQ eloc epi fpi
|
||
where
|
||
lookupArm : Loc -> TagVal -> CaseEnumArms d n -> Equal_ (Term d n)
|
||
lookupArm loc t arms = case lookup t arms of
|
||
Just arm => pure arm
|
||
Nothing => throw $ TagNotIn loc t (fromList $ keys arms)
|
||
compare0' ctx e@(CaseEnum {}) f _ _ = clashE e.loc ctx e f
|
||
|
||
-- Ψ | Γ ⊢ e = f ⇒ ℕ
|
||
-- Ψ | Γ, x : ℕ ⊢ Q = R
|
||
-- Ψ | Γ ⊢ s₀ = t₀ ⇐ Q[(0 ∷ ℕ)/x]
|
||
-- Ψ | Γ, x : ℕ, y : Q ⊢ s₁ = t₁ ⇐ Q[(succ x ∷ ℕ)/x]
|
||
-- -----------------------------------------------------
|
||
-- Ψ | Γ ⊢ caseπ e return Q of { 0 ⇒ s₀; x, π.y ⇒ s₁ }
|
||
-- = caseπ f return R of { 0 ⇒ t₀; x, π.y ⇒ t₁ }
|
||
-- ⇒ Q[e/x]
|
||
compare0' ctx (CaseNat epi epi' e eret ezer esuc eloc)
|
||
(CaseNat fpi fpi' f fret fzer fsuc floc) ne nf =
|
||
local_ Equal $ do
|
||
compare0 ctx e f
|
||
ety <- computeElimTypeE defs ctx e @{noOr1 ne}
|
||
compareType (extendTy Zero eret.name ety ctx) eret.term fret.term
|
||
compare0 ctx
|
||
(sub1 eret (Ann (Zero ezer.loc) (Nat ezer.loc) ezer.loc))
|
||
ezer fzer
|
||
let [< p, ih] = esuc.names
|
||
compare0
|
||
(extendTyN [< (epi, p, Nat p.loc), (epi', ih, eret.term)] ctx)
|
||
(substCaseSuccRet esuc.names eret) esuc.term fsuc.term
|
||
expectEqualQ e.loc epi fpi
|
||
expectEqualQ e.loc epi' fpi'
|
||
compare0' ctx e@(CaseNat {}) f _ _ = clashE e.loc ctx e f
|
||
|
||
-- Ψ | Γ ⊢ e = f ⇒ [ρ. A]
|
||
-- Ψ | Γ, x : [ρ. A] ⊢ Q = R
|
||
-- Ψ | Γ, x : A ⊢ s = t ⇐ Q[([x] ∷ [ρ. A])/x]
|
||
-- --------------------------------------------------
|
||
-- Ψ | Γ ⊢ caseπ e return Q of { [x] ⇒ s }
|
||
-- = caseπ f return R of { [x] ⇒ t } ⇒ Q[e/x]
|
||
compare0' ctx (CaseBox epi e eret ebody eloc)
|
||
(CaseBox fpi f fret fbody floc) ne nf =
|
||
local_ Equal $ do
|
||
compare0 ctx e f
|
||
ety <- computeElimTypeE defs ctx e @{noOr1 ne}
|
||
compareType (extendTy Zero eret.name ety ctx) eret.term fret.term
|
||
(q, ty) <- expectBOX defs ctx eloc ety
|
||
compare0 (extendTy (epi * q) ebody.name ty ctx)
|
||
(substCaseBoxRet ebody.name ety eret)
|
||
ebody.term fbody.term
|
||
expectEqualQ eloc epi fpi
|
||
compare0' ctx e@(CaseBox {}) f _ _ = clashE e.loc ctx e f
|
||
|
||
-- all dim apps replaced with ends by whnf
|
||
compare0' _ (DApp _ (K {}) _) _ ne _ = void $ absurd $ noOr2 $ noOr2 ne
|
||
compare0' _ _ (DApp _ (K {}) _) _ nf = void $ absurd $ noOr2 $ noOr2 nf
|
||
|
||
-- Ψ | Γ ⊢ s <: t : B
|
||
-- --------------------------------
|
||
-- Ψ | Γ ⊢ (s ∷ A) <: (t ∷ B) ⇒ B
|
||
--
|
||
-- and similar for :> and A
|
||
compare0' ctx (Ann s a _) (Ann t b _) _ _ =
|
||
let ty = case !mode of Super => a; _ => b in
|
||
Term.compare0 ctx ty s t
|
||
|
||
-- Ψ | Γ ⊢ A‹p₁/𝑖› <: B‹p₂/𝑖›
|
||
-- Ψ | Γ ⊢ A‹q₁/𝑖› <: B‹q₂/𝑖›
|
||
-- Ψ | Γ ⊢ e <: f ⇒ _
|
||
-- (non-neutral forms have the coercion already pushed in)
|
||
-- -----------------------------------------------------------
|
||
-- Ψ | Γ ⊢ coe [𝑖 ⇒ A] @p₁ @q₁ e
|
||
-- <: coe [𝑖 ⇒ B] @p₂ @q₂ f ⇒ B‹q₂/𝑖›
|
||
compare0' ctx (Coe ty1 p1 q1 (E val1) _)
|
||
(Coe ty2 p2 q2 (E val2) _) ne nf = do
|
||
compareType ctx (dsub1 ty1 p1) (dsub1 ty2 p2)
|
||
compareType ctx (dsub1 ty1 q1) (dsub1 ty2 q2)
|
||
compare0 ctx val1 val2
|
||
compare0' ctx e@(Coe {}) f _ _ = clashE e.loc ctx e f
|
||
|
||
-- (no neutral compositions in a closed dctx)
|
||
compare0' _ (Comp {r = K e _, _}) _ ne _ = void $ absurd $ noOr2 ne
|
||
compare0' _ (Comp {r = B i _, _}) _ _ _ = absurd i
|
||
compare0' _ _ (Comp {r = K _ _, _}) _ nf = void $ absurd $ noOr2 nf
|
||
|
||
-- (type case equality purely structural)
|
||
compare0' ctx (TypeCase ty1 ret1 arms1 def1 eloc)
|
||
(TypeCase ty2 ret2 arms2 def2 floc) ne _ =
|
||
local_ Equal $ do
|
||
compare0 ctx ty1 ty2
|
||
u <- expectTYPE defs ctx eloc =<<
|
||
computeElimTypeE defs ctx ty1 @{noOr1 ne}
|
||
compareType ctx ret1 ret2
|
||
compareType ctx def1 def2
|
||
for_ allKinds $ \k =>
|
||
compareArm ctx k ret1 u
|
||
(lookupPrecise k arms1) (lookupPrecise k arms2) def1
|
||
compare0' ctx e@(TypeCase {}) f _ _ = clashE e.loc ctx e f
|
||
|
||
-- Ψ | Γ ⊢ s <: f ⇐ A
|
||
-- --------------------------
|
||
-- Ψ | Γ ⊢ (s ∷ A) <: f ⇒ A
|
||
--
|
||
-- and vice versa
|
||
compare0' ctx (Ann s a _) f _ _ = Term.compare0 ctx a s (E f)
|
||
compare0' ctx e (Ann t b _) _ _ = Term.compare0 ctx b (E e) t
|
||
compare0' ctx e@(Ann {}) f _ _ = clashE e.loc ctx e f
|
||
|
||
||| compare two type-case branches, which came from the arms of the given
|
||
||| kind. `ret` is the return type of the case expression, and `u` is the
|
||
||| universe the head is in.
|
||
private covering
|
||
compareArm : EqContext n -> (k : TyConKind) ->
|
||
(ret : Term 0 n) -> (u : Universe) ->
|
||
(b1, b2 : Maybe (TypeCaseArmBody k 0 n)) ->
|
||
(def : Term 0 n) ->
|
||
Equal_ ()
|
||
compareArm {b1 = Nothing, b2 = Nothing, _} = pure ()
|
||
compareArm ctx k ret u b1 b2 def =
|
||
let def = SN def in
|
||
compareArm_ ctx k ret u (fromMaybe def b1) (fromMaybe def b2)
|
||
|
||
private covering
|
||
compareArm_ : EqContext n -> (k : TyConKind) ->
|
||
(ret : Term 0 n) -> (u : Universe) ->
|
||
(b1, b2 : TypeCaseArmBody k 0 n) ->
|
||
Equal_ ()
|
||
compareArm_ ctx KTYPE ret u b1 b2 =
|
||
compare0 ctx ret b1.term b2.term
|
||
|
||
compareArm_ ctx KPi ret u b1 b2 = do
|
||
let [< a, b] = b1.names
|
||
ctx = extendTyN
|
||
[< (Zero, a, TYPE u a.loc),
|
||
(Zero, b, Arr Zero (BVT 0 b.loc) (TYPE u b.loc) b.loc)] ctx
|
||
compare0 ctx (weakT 2 ret) b1.term b2.term
|
||
|
||
compareArm_ ctx KSig ret u b1 b2 = do
|
||
let [< a, b] = b1.names
|
||
ctx = extendTyN
|
||
[< (Zero, a, TYPE u a.loc),
|
||
(Zero, b, Arr Zero (BVT 0 b.loc) (TYPE u b.loc) b.loc)] ctx
|
||
compare0 ctx (weakT 2 ret) b1.term b2.term
|
||
|
||
compareArm_ ctx KW ret u b1 b2 = do
|
||
let [< a, b] = b1.names
|
||
ctx = extendTyN
|
||
[< (Zero, a, TYPE u a.loc),
|
||
(Zero, b, Arr Zero (BVT 0 b.loc) (TYPE u b.loc) b.loc)] ctx
|
||
compare0 ctx (weakT 2 ret) b1.term b2.term
|
||
|
||
compareArm_ ctx KEnum ret u b1 b2 =
|
||
compare0 ctx ret b1.term b2.term
|
||
|
||
compareArm_ ctx KEq ret u b1 b2 = do
|
||
let [< a0, a1, a, l, r] = b1.names
|
||
ctx = extendTyN
|
||
[< (Zero, a0, TYPE u a0.loc),
|
||
(Zero, a1, TYPE u a1.loc),
|
||
(Zero, a, Eq0 (TYPE u a.loc)
|
||
(BVT 1 a0.loc) (BVT 0 a1.loc) a.loc),
|
||
(Zero, l, BVT 2 a0.loc),
|
||
(Zero, r, BVT 2 a1.loc)] ctx
|
||
compare0 ctx (weakT 5 ret) b1.term b2.term
|
||
|
||
compareArm_ ctx KNat ret u b1 b2 =
|
||
compare0 ctx ret b1.term b2.term
|
||
|
||
compareArm_ ctx KBOX ret u b1 b2 = do
|
||
let ctx = extendTy Zero b1.name (TYPE u b1.name.loc) ctx
|
||
compare0 ctx (weakT 1 ret) b1.term b1.term
|
||
|
||
|
||
parameters (loc : Loc) (ctx : TyContext d n)
|
||
-- [todo] only split on the dvars that are actually used anywhere in
|
||
-- the calls to `splits`
|
||
|
||
parameters (mode : EqMode)
|
||
private
|
||
fromEqual_ : Equal_ a -> Equal a
|
||
fromEqual_ act = lift $ evalState mode act
|
||
|
||
private
|
||
eachFace : Applicative f => (EqContext n -> DSubst d 0 -> f ()) -> f ()
|
||
eachFace act =
|
||
for_ (splits loc ctx.dctx) $ \th => act (makeEqContext ctx th) th
|
||
|
||
private
|
||
runCompare : (Definitions -> EqContext n -> DSubst d 0 -> Equal_ ()) ->
|
||
Equal ()
|
||
runCompare act = fromEqual_ $ eachFace $ act !(askAt DEFS)
|
||
|
||
namespace Term
|
||
export covering
|
||
compare : (ty, s, t : Term d n) -> Equal ()
|
||
compare ty s t = runCompare $ \defs, ectx, th =>
|
||
compare0 defs ectx (ty // th) (s // th) (t // th)
|
||
|
||
export covering
|
||
compareType : (s, t : Term d n) -> Equal ()
|
||
compareType s t = runCompare $ \defs, ectx, th =>
|
||
compareType defs ectx (s // th) (t // th)
|
||
|
||
namespace Elim
|
||
||| you don't have to pass the type in but the arguments must still be
|
||
||| of the same type!!
|
||
export covering
|
||
compare : (e, f : Elim d n) -> Equal ()
|
||
compare e f = runCompare $ \defs, ectx, th =>
|
||
compare0 defs ectx (e // th) (f // th)
|
||
|
||
namespace Term
|
||
export covering %inline
|
||
equal, sub, super : (ty, s, t : Term d n) -> Equal ()
|
||
equal = compare Equal
|
||
sub = compare Sub
|
||
super = compare Super
|
||
|
||
export covering %inline
|
||
equalType, subtype, supertype : (s, t : Term d n) -> Equal ()
|
||
equalType = compareType Equal
|
||
subtype = compareType Sub
|
||
supertype = compareType Super
|
||
|
||
namespace Elim
|
||
export covering %inline
|
||
equal, sub, super : (e, f : Elim d n) -> Equal ()
|
||
equal = compare Equal
|
||
sub = compare Sub
|
||
super = compare Super
|