840 lines
30 KiB
Idris
840 lines
30 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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import Quox.FreeVars
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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 : List (Type -> Type)
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Equal = [ErrorEff, DefsReader, NameGen]
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public export
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EqualInner : List (Type -> Type)
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EqualInner = [ErrorEff, NameGen, EqModeState]
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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 -> Eff EqualInner 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 -> Eff EqualInner 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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wrongType : Term 0 n -> Term 0 n -> Eff EqualInner 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 (IOState {}) (IOState {}) = True
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sameTyCon (IOState {}) _ = 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 (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 (STRING {}) (STRING {}) = True
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sameTyCon (STRING {}) _ = 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 empty.
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|||
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||| * a pair is empty if either element is.
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||| * `{}` is empty.
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||| * `[π.A]` is empty if `A` is.
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||| * that's it.
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public export covering
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isEmpty : Definitions -> EqContext n -> SQty -> Term 0 n ->
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Eff EqualInner Bool
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isEmpty defs ctx sg ty0 = do
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Element ty0 nc <- whnf defs ctx sg ty0.loc ty0
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let Left y = choose $ isTyConE ty0
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| Right n => pure False
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case ty0 of
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TYPE {} => pure False
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IOState {} => pure False
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Pi {arg, res, _} => pure False
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Sig {fst, snd, _} =>
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isEmpty defs ctx sg fst `orM`
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isEmpty defs (extendTy0 snd.name fst ctx) sg snd.term
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Enum {cases, _} =>
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pure $ null cases
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Eq {} => pure False
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NAT {} => pure False
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STRING {} => pure False
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BOX {ty, _} => isEmpty defs ctx sg ty
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E _ => pure 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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||| or if its domain is empty.
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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 : Definitions -> EqContext n -> SQty -> Term 0 n ->
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Eff EqualInner Bool
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isSubSing defs ctx sg ty0 = do
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Element ty0 nc <- whnf defs ctx sg ty0.loc ty0
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let Left y = choose $ isTyConE ty0
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| Right n => pure False
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case ty0 of
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TYPE {} => pure False
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IOState {} => pure False
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Pi {arg, res, _} =>
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isEmpty defs ctx sg arg `orM`
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isSubSing defs (extendTy0 res.name arg ctx) sg res.term
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Sig {fst, snd, _} =>
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isSubSing defs ctx sg fst `andM`
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isSubSing defs (extendTy0 snd.name fst ctx) sg snd.term
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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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STRING {} => pure False
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BOX {ty, _} => isSubSing defs ctx sg ty
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E _ => pure False
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||| the left argument if the current mode is `Super`; otherwise the right one.
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private %inline
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bigger : Has EqModeState fs => (left, right : Lazy a) -> Eff fs a
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bigger l r = gets $ \case Super => l; _ => r
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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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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 : Definitions -> EqContext n -> SQty -> (ty, s, t : Term 0 n) ->
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Eff EqualInner ()
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namespace Elim
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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 : Definitions -> EqContext n -> SQty -> (e, f : Elim 0 n) ->
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Eff EqualInner (Term 0 n)
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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 : Definitions -> EqContext n -> (s, t : Term 0 n) ->
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Eff EqualInner ()
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private
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0 NotRedexEq : {isRedex : RedexTest tm} -> CanWhnf tm isRedex =>
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Definitions -> EqContext n -> SQty -> Pred (tm 0 n)
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NotRedexEq defs ctx sg t = NotRedex defs (toWhnfContext ctx) sg t
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namespace Term
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private covering
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compare0' : (defs : Definitions) -> (ctx : EqContext n) -> (sg : SQty) ->
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(ty, s, t : Term 0 n) ->
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(0 _ : NotRedexEq defs ctx SZero ty) =>
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(0 _ : So (isTyConE ty)) =>
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(0 _ : NotRedexEq defs ctx sg s) =>
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(0 _ : NotRedexEq defs ctx sg t) =>
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Eff EqualInner ()
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compare0' defs ctx sg (TYPE {}) s t = compareType defs ctx s t
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compare0' defs ctx sg ty@(IOState {}) s t =
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-- Γ ⊢ e = f ⇒ IOState
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-- ----------------------
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-- Γ ⊢ e = f ⇐ IOState
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--
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-- (no canonical values, ofc)
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case (s, t) of
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(E e, E f) => ignore $ Elim.compare0 defs ctx sg e f
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(E _, _) => wrongType t.loc ctx ty t
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_ => wrongType s.loc ctx ty s
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compare0' defs ctx sg ty@(Pi {qty, arg, res, _}) s t = local_ Equal $
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-- Γ ⊢ A empty
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-- -------------------------------------------
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-- Γ ⊢ (λ x ⇒ s) = (λ x ⇒ t) ⇐ (π·x : A) → B
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if !(isEmpty defs ctx sg arg) then pure () else
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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 defs ctx' sg 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) => ignore $ Elim.compare0 defs ctx sg 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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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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eta : Loc -> Elim 0 n -> ScopeTerm 0 n -> Eff EqualInner ()
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eta loc e (S _ (N _)) = clashT loc ctx ty s t
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eta _ e (S _ (Y b)) = compare0 defs ctx' sg res.term (toLamBody e) b
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compare0' defs ctx sg 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 ≥ 0 maybe
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(Pair sFst sSnd {}, Pair tFst tSnd {}) => do
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compare0 defs ctx sg fst sFst tFst
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compare0 defs ctx sg (sub1 snd (Ann sFst fst fst.loc)) sSnd tSnd
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(E e, E f) => ignore $ Elim.compare0 defs ctx sg e f
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(E e, Pair fst snd _) => eta s.loc e fst snd
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(Pair fst snd _, E f) => eta s.loc f fst snd
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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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where
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eta : Loc -> Elim 0 n -> Term 0 n -> Term 0 n -> Eff EqualInner ()
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eta loc e s t =
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case sg of
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SZero => do
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compare0 defs ctx sg fst (E $ Fst e e.loc) s
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compare0 defs ctx sg (sub1 snd (Ann s fst s.loc)) (E $ Snd e e.loc) t
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SOne => clashT loc ctx ty s t
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compare0' defs ctx sg 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) => ignore $ Elim.compare0 defs ctx sg 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' defs ctx sg nat@(NAT {}) s t = local_ Equal $
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case (s, t) of
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-- ---------------
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-- Γ ⊢ n = n ⇐ ℕ
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(Nat x {}, Nat y {}) => unless (x == y) $ clashT s.loc ctx nat s t
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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 defs ctx sg nat s' t'
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(Nat (S x) {}, Succ t' {}) => compare0 defs ctx sg nat (Nat x s.loc) t'
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(Succ s' {}, Nat (S y) {}) => compare0 defs ctx sg nat s' (Nat y t.loc)
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(E e, E f) => ignore $ Elim.compare0 defs ctx sg e f
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(Nat 0 {}, Succ {}) => clashT s.loc ctx nat s t
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(Nat 0 {}, E _) => clashT s.loc ctx nat s t
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(Succ {}, Nat 0 {}) => 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 _, Nat 0 {}) => clashT s.loc ctx nat s t
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(E _, Succ {}) => clashT s.loc ctx nat s t
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(Nat {}, 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' defs ctx sg str@(STRING {}) s t = local_ Equal $
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case (s, t) of
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(Str x _, Str y _) => unless (x == y) $ clashT s.loc ctx str s t
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(E e, E f) => ignore $ Elim.compare0 defs ctx sg e f
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(Str {}, E _) => clashT s.loc ctx str s t
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(E _, Str {}) => clashT s.loc ctx str s t
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(Str {}, _) => wrongType t.loc ctx str t
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(E _, _) => wrongType t.loc ctx str t
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_ => wrongType s.loc ctx str s
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compare0' defs ctx sg bty@(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 defs ctx sg ty s t
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-- Γ ⊢ s = (case1 e return A of {[x] ⇒ x}) ⇐ A
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-- -----------------------------------------------
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-- Γ ⊢ [s] = e ⇐ [ρ.A]
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(Box s loc, E f) => eta s f
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(E e, Box t loc) => eta t e
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(E e, E f) => ignore $ Elim.compare0 defs ctx sg e f
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(Box {}, _) => wrongType t.loc ctx bty t
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(E _, _) => wrongType t.loc ctx bty t
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_ => wrongType s.loc ctx bty s
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where
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eta : Term 0 n -> Elim 0 n -> Eff EqualInner ()
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eta s e = do
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nm <- mnb "inner" e.loc
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let e = CaseBox One e (SN ty) (SY [< nm] (BVT 0 nm.loc)) e.loc
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compare0 defs ctx sg ty s (E e)
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compare0' defs ctx sg 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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ignore $ Elim.compare0 defs ctx sg e f
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private covering
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compareType' : (defs : Definitions) -> (ctx : EqContext n) ->
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(s, t : Term 0 n) ->
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(0 _ : NotRedexEq defs ctx SZero s) => (0 _ : So (isTyConE s)) =>
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(0 _ : NotRedexEq defs ctx SZero t) => (0 _ : So (isTyConE t)) =>
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(0 _ : So (sameTyCon s t)) =>
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Eff EqualInner ()
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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' defs 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' defs ctx a@(IOState {}) (IOState {}) =
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-- Γ ⊢ IOState <: IOState
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pure ()
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compareType' defs 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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expectEqualQ loc sQty tQty
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local flip $ compareType defs ctx sArg tArg -- contra
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compareType defs (extendTy0 sRes.name sArg ctx) sRes.term tRes.term
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compareType' defs 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 defs ctx sFst tFst
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compareType defs (extendTy0 sSnd.name sFst ctx) sSnd.term tSnd.term
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compareType' defs 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 defs (extendDim sTy.name Zero ctx) sTy.zero tTy.zero
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compareType defs (extendDim sTy.name One ctx) sTy.one tTy.one
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ty <- bigger sTy tTy
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local_ Equal $ do
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Term.compare0 defs ctx SZero ty.zero sl tl
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Term.compare0 defs ctx SZero ty.one sr tr
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compareType' defs 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' defs ctx (NAT {}) (NAT {}) =
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-- ------------
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-- Γ ⊢ ℕ <: ℕ
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pure ()
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compareType' defs ctx (STRING {}) (STRING {}) =
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-- ------------
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-- Γ ⊢ String <: String
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pure ()
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compareType' defs ctx (BOX pi a loc) (BOX rh b {}) = do
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expectEqualQ loc pi rh
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compareType defs ctx a b
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compareType' defs 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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ignore $ Elim.compare0 defs ctx SZero e f
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private
|
||
lookupFree : Has ErrorEff fs =>
|
||
Definitions -> EqContext n -> Name -> Universe -> Loc ->
|
||
Eff fs (Term 0 n)
|
||
lookupFree defs ctx x u loc =
|
||
case lookup x defs of
|
||
Nothing => throw $ NotInScope loc x
|
||
Just d => pure $ d.typeWithAt [|Z|] ctx.termLen u
|
||
|
||
|
||
export
|
||
typecaseTel : (k : TyConKind) -> BContext (arity k) -> Universe ->
|
||
CtxExtension d n (arity k + n)
|
||
typecaseTel k xs u = case k of
|
||
KTYPE => [<]
|
||
KIOState => [<]
|
||
-- A : ★ᵤ, B : 0.A → ★ᵤ
|
||
KPi =>
|
||
let [< a, b] = xs in
|
||
[< (Zero, a, TYPE u a.loc),
|
||
(Zero, b, Arr Zero (BVT 0 b.loc) (TYPE u b.loc) b.loc)]
|
||
KSig =>
|
||
let [< a, b] = xs in
|
||
[< (Zero, a, TYPE u a.loc),
|
||
(Zero, b, Arr Zero (BVT 0 b.loc) (TYPE u b.loc) b.loc)]
|
||
KEnum => [<]
|
||
-- A₀ : ★ᵤ, A₁ : ★ᵤ, A : (A₀ ≡ A₁ : ★ᵤ), L : A₀, R : A₀
|
||
KEq =>
|
||
let [< a0, a1, a, l, r] = xs in
|
||
[< (Zero, a0, TYPE u a0.loc),
|
||
(Zero, a1, TYPE u a1.loc),
|
||
(Zero, a, Eq0 (TYPE u a.loc) (BVT 1 a.loc) (BVT 0 a.loc) a.loc),
|
||
(Zero, l, BVT 2 l.loc),
|
||
(Zero, r, BVT 2 r.loc)]
|
||
KNat => [<]
|
||
KString => [<]
|
||
-- A : ★ᵤ
|
||
KBOX => let [< a] = xs in [< (Zero, a, TYPE u a.loc)]
|
||
|
||
|
||
namespace Elim
|
||
private data InnerErr : Type where
|
||
|
||
private
|
||
InnerErrEff : Type -> Type
|
||
InnerErrEff = StateL InnerErr (Maybe Error)
|
||
|
||
private
|
||
EqualElim : List (Type -> Type)
|
||
EqualElim = InnerErrEff :: EqualInner
|
||
|
||
private covering
|
||
computeElimTypeE : (defs : Definitions) -> (ctx : EqContext n) ->
|
||
(sg : SQty) ->
|
||
(e : Elim 0 n) -> (0 ne : NotRedexEq defs ctx sg e) =>
|
||
Eff EqualElim (Term 0 n)
|
||
computeElimTypeE defs ectx sg e = lift $
|
||
computeElimType defs (toWhnfContext ectx) sg e
|
||
|
||
private
|
||
putError : Has InnerErrEff fs => Error -> Eff fs ()
|
||
putError err = modifyAt InnerErr (<|> Just err)
|
||
|
||
private
|
||
try : Eff EqualInner () -> Eff EqualElim ()
|
||
try act = lift $ catch putError $ lift act {fs' = EqualElim}
|
||
|
||
private covering %inline
|
||
clashE : (defs : Definitions) -> (ctx : EqContext n) -> (sg : SQty) ->
|
||
(e, f : Elim 0 n) -> (0 nf : NotRedexEq defs ctx sg f) =>
|
||
Eff EqualElim (Term 0 n)
|
||
clashE defs ctx sg e f = do
|
||
putError $ ClashE e.loc ctx !mode e f
|
||
computeElimTypeE defs ctx sg 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 : Definitions -> EqContext n -> (k : TyConKind) ->
|
||
(ret : Term 0 n) -> (u : Universe) ->
|
||
(b1, b2 : Maybe (TypeCaseArmBody k 0 n)) ->
|
||
(def : Term 0 n) ->
|
||
Eff EqualElim ()
|
||
compareArm {b1 = Nothing, b2 = Nothing, _} = pure ()
|
||
compareArm defs ctx k ret u b1 b2 def = do
|
||
let def = SN def
|
||
left = fromMaybe def b1; right = fromMaybe def b2
|
||
names = (fromMaybe def $ b1 <|> b2).names
|
||
try $ compare0 defs (extendTyN (typecaseTel k names u) ctx)
|
||
SZero (weakT (arity k) ret) left.term right.term
|
||
|
||
private covering
|
||
compare0Inner : Definitions -> EqContext n -> (sg : SQty) ->
|
||
(e, f : Elim 0 n) -> Eff EqualElim (Term 0 n)
|
||
|
||
private covering
|
||
compare0Inner' : (defs : Definitions) -> (ctx : EqContext n) -> (sg : SQty) ->
|
||
(e, f : Elim 0 n) ->
|
||
(0 ne : NotRedexEq defs ctx sg e) ->
|
||
(0 nf : NotRedexEq defs ctx sg f) ->
|
||
Eff EqualElim (Term 0 n)
|
||
|
||
compare0Inner' defs ctx sg e@(F {}) f _ _ = do
|
||
if e == f then computeElimTypeE defs ctx sg f
|
||
else clashE defs ctx sg e f
|
||
|
||
compare0Inner' defs ctx sg e@(B {}) f _ _ = do
|
||
if e == f then computeElimTypeE defs ctx sg f
|
||
else clashE defs ctx sg 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]
|
||
compare0Inner' defs ctx sg (App e s eloc) (App f t floc) ne nf = do
|
||
ety <- compare0Inner defs ctx sg e f
|
||
(_, arg, res) <- expectPi defs ctx sg eloc ety
|
||
try $ Term.compare0 defs ctx sg arg s t
|
||
pure $ sub1 res $ Ann s arg s.loc
|
||
compare0Inner' defs ctx sg e'@(App {}) f' ne nf =
|
||
clashE defs ctx sg 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]
|
||
compare0Inner' defs ctx sg (CasePair epi e eret ebody eloc)
|
||
(CasePair fpi f fret fbody floc) ne nf =
|
||
local_ Equal $ do
|
||
ety <- compare0Inner defs ctx sg e f
|
||
(fst, snd) <- expectSig defs ctx sg eloc ety
|
||
let [< x, y] = ebody.names
|
||
try $ do
|
||
compareType defs (extendTy0 eret.name ety ctx) eret.term fret.term
|
||
Term.compare0 defs
|
||
(extendTyN [< (epi, x, fst), (epi, y, snd.term)] ctx) sg
|
||
(substCasePairRet ebody.names ety eret)
|
||
ebody.term fbody.term
|
||
expectEqualQ e.loc epi fpi
|
||
pure $ sub1 eret e
|
||
compare0Inner' defs ctx sg e'@(CasePair {}) f' ne nf =
|
||
clashE defs ctx sg e' f'
|
||
|
||
-- Ψ | Γ ⊢ e = f ⇒ (x : A) × B
|
||
-- ------------------------------
|
||
-- Ψ | Γ ⊢ fst e = fst f ⇒ A
|
||
compare0Inner' defs ctx sg (Fst e eloc) (Fst f floc) ne nf =
|
||
local_ Equal $ do
|
||
ety <- compare0Inner defs ctx sg e f
|
||
fst <$> expectSig defs ctx sg eloc ety
|
||
compare0Inner' defs ctx sg e@(Fst {}) f _ _ =
|
||
clashE defs ctx sg e f
|
||
|
||
-- Ψ | Γ ⊢ e = f ⇒ (x : A) × B
|
||
-- ------------------------------------
|
||
-- Ψ | Γ ⊢ snd e = snd f ⇒ B[fst e/x]
|
||
compare0Inner' defs ctx sg (Snd e eloc) (Snd f floc) ne nf =
|
||
local_ Equal $ do
|
||
ety <- compare0Inner defs ctx sg e f
|
||
(_, tsnd) <- expectSig defs ctx sg eloc ety
|
||
pure $ sub1 tsnd (Fst e eloc)
|
||
compare0Inner' defs ctx sg e@(Snd {}) f _ _ =
|
||
clashE defs ctx sg 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]
|
||
compare0Inner' defs ctx sg (CaseEnum epi e eret earms eloc)
|
||
(CaseEnum fpi f fret farms floc) ne nf =
|
||
local_ Equal $ do
|
||
ety <- compare0Inner defs ctx sg e f
|
||
try $
|
||
compareType defs (extendTy0 eret.name ety ctx) eret.term fret.term
|
||
for_ (SortedMap.toList earms) $ \(t, l) => do
|
||
let Just r = lookup t farms
|
||
| Nothing => putError $ TagNotIn floc t (fromList $ keys farms)
|
||
let t' = Ann (Tag t l.loc) ety l.loc
|
||
try $ Term.compare0 defs ctx sg (sub1 eret t') l r
|
||
try $ expectEqualQ eloc epi fpi
|
||
pure $ sub1 eret e
|
||
compare0Inner' defs ctx sg e@(CaseEnum {}) f _ _ = clashE defs ctx sg 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]
|
||
compare0Inner' defs ctx sg (CaseNat epi epi' e eret ezer esuc eloc)
|
||
(CaseNat fpi fpi' f fret fzer fsuc floc) ne nf =
|
||
local_ Equal $ do
|
||
ety <- compare0Inner defs ctx sg e f
|
||
let [< p, ih] = esuc.names
|
||
try $ do
|
||
compareType defs (extendTy0 eret.name ety ctx) eret.term fret.term
|
||
Term.compare0 defs ctx sg
|
||
(sub1 eret (Ann (Zero ezer.loc) (NAT ezer.loc) ezer.loc))
|
||
ezer fzer
|
||
Term.compare0 defs
|
||
(extendTyN [< (epi, p, NAT p.loc), (epi', ih, eret.term)] ctx) sg
|
||
(substCaseSuccRet esuc.names eret) esuc.term fsuc.term
|
||
expectEqualQ e.loc epi fpi
|
||
expectEqualQ e.loc epi' fpi'
|
||
pure $ sub1 eret e
|
||
compare0Inner' defs ctx sg e@(CaseNat {}) f _ _ = clashE defs ctx sg 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]
|
||
compare0Inner' defs ctx sg (CaseBox epi e eret ebody eloc)
|
||
(CaseBox fpi f fret fbody floc) ne nf =
|
||
local_ Equal $ do
|
||
ety <- compare0Inner defs ctx sg e f
|
||
(q, ty) <- expectBOX defs ctx sg eloc ety
|
||
try $ do
|
||
compareType defs (extendTy0 eret.name ety ctx) eret.term fret.term
|
||
Term.compare0 defs (extendTy (epi * q) ebody.name ty ctx) sg
|
||
(substCaseBoxRet ebody.name ety eret)
|
||
ebody.term fbody.term
|
||
expectEqualQ eloc epi fpi
|
||
pure $ sub1 eret e
|
||
compare0Inner' defs ctx sg e@(CaseBox {}) f _ _ = clashE defs ctx sg e f
|
||
|
||
-- (no neutral dim apps in a closed dctx)
|
||
compare0Inner' _ _ _ (DApp _ (K {}) _) _ ne _ =
|
||
void $ absurd $ noOr2 $ noOr2 ne
|
||
compare0Inner' _ _ _ _ (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
|
||
compare0Inner' defs ctx sg (Ann s a _) (Ann t b _) _ _ = do
|
||
ty <- bigger a b
|
||
try $ Term.compare0 defs ctx sg ty s t
|
||
pure ty
|
||
|
||
-- Ψ | Γ ⊢ A‹p₁/𝑖› <: B‹p₂/𝑖›
|
||
-- Ψ | Γ ⊢ A‹q₁/𝑖› <: B‹q₂/𝑖›
|
||
-- Ψ | Γ ⊢ s <: t ⇐ B‹p₂/𝑖›
|
||
-- -----------------------------------------------------------
|
||
-- Ψ | Γ ⊢ coe [𝑖 ⇒ A] @p₁ @q₁ s
|
||
-- <: coe [𝑖 ⇒ B] @p₂ @q₂ t ⇒ B‹q₂/𝑖›
|
||
compare0Inner' defs ctx sg (Coe ty1 p1 q1 val1 _)
|
||
(Coe ty2 p2 q2 val2 _) ne nf = do
|
||
let ty1p = dsub1 ty1 p1; ty2p = dsub1 ty2 p2
|
||
ty1q = dsub1 ty1 q1; ty2q = dsub1 ty2 q2
|
||
(ty_p, ty_q) <- bigger (ty1p, ty1q) (ty2p, ty2q)
|
||
try $ do
|
||
compareType defs ctx ty1p ty2p
|
||
compareType defs ctx ty1q ty2q
|
||
Term.compare0 defs ctx sg ty_p val1 val2
|
||
pure $ ty_q
|
||
compare0Inner' defs ctx sg e@(Coe {}) f _ _ = clashE defs ctx sg e f
|
||
|
||
-- (no neutral compositions in a closed dctx)
|
||
compare0Inner' _ _ _ (Comp {r = K {}, _}) _ ne _ = void $ absurd $ noOr2 ne
|
||
compare0Inner' _ _ _ (Comp {r = B i _, _}) _ _ _ = absurd i
|
||
compare0Inner' _ _ _ _ (Comp {r = K {}, _}) _ nf = void $ absurd $ noOr2 nf
|
||
|
||
-- (type case equality purely structural)
|
||
compare0Inner' defs ctx sg (TypeCase ty1 ret1 arms1 def1 eloc)
|
||
(TypeCase ty2 ret2 arms2 def2 floc) ne _ =
|
||
case sg `decEq` SZero of
|
||
Yes Refl => local_ Equal $ do
|
||
ety <- compare0Inner defs ctx SZero ty1 ty2
|
||
u <- expectTYPE defs ctx SZero eloc ety
|
||
try $ do
|
||
compareType defs ctx ret1 ret2
|
||
compareType defs ctx def1 def2
|
||
for_ allKinds $ \k =>
|
||
compareArm defs ctx k ret1 u
|
||
(lookupPrecise k arms1) (lookupPrecise k arms2) def1
|
||
pure ret1
|
||
No _ => do
|
||
putError $ ClashQ eloc sg.qty Zero
|
||
computeElimTypeE defs ctx sg $ TypeCase ty1 ret1 arms1 def1 eloc
|
||
compare0Inner' defs ctx sg e@(TypeCase {}) f _ _ = clashE defs ctx sg e f
|
||
|
||
-- Ψ | Γ ⊢ s <: f ⇐ A
|
||
-- --------------------------
|
||
-- Ψ | Γ ⊢ (s ∷ A) <: f ⇒ A
|
||
--
|
||
-- and vice versa
|
||
compare0Inner' defs ctx sg (Ann s a _) f _ _ = do
|
||
try $ Term.compare0 defs ctx sg a s (E f)
|
||
pure a
|
||
compare0Inner' defs ctx sg e (Ann t b _) _ _ = do
|
||
try $ Term.compare0 defs ctx sg b (E e) t
|
||
pure b
|
||
compare0Inner' defs ctx sg e@(Ann {}) f _ _ =
|
||
clashE defs ctx sg e f
|
||
|
||
compare0Inner defs ctx sg e f = do
|
||
Element e ne <- whnf defs ctx sg e.loc e
|
||
Element f nf <- whnf defs ctx sg f.loc f
|
||
ty <- compare0Inner' defs ctx sg e f ne nf
|
||
if !(lift $ isSubSing defs ctx sg ty) && isJust !(getAt InnerErr)
|
||
then putAt InnerErr Nothing
|
||
else modifyAt InnerErr $ map $ WhileComparingE ctx !mode sg e f
|
||
pure ty
|
||
|
||
|
||
namespace Term
|
||
compare0 defs ctx sg ty s t =
|
||
wrapErr (WhileComparingT ctx !mode sg ty s t) $ do
|
||
Element ty' _ <- whnf defs ctx SZero ty.loc ty
|
||
Element s' _ <- whnf defs ctx sg s.loc s
|
||
Element t' _ <- whnf defs ctx sg t.loc t
|
||
tty <- ensureTyCon ty.loc ctx ty'
|
||
compare0' defs ctx sg ty' s' t'
|
||
|
||
namespace Elim
|
||
compare0 defs ctx sg e f = do
|
||
(ty, err) <- runStateAt InnerErr Nothing $ compare0Inner defs ctx sg e f
|
||
maybe (pure ty) throw err
|
||
|
||
compareType defs ctx s t = do
|
||
Element s' _ <- whnf defs ctx SZero s.loc s
|
||
Element t' _ <- whnf defs ctx SZero t.loc t
|
||
ts <- ensureTyCon s.loc ctx s'
|
||
tt <- ensureTyCon t.loc ctx t'
|
||
st <- either pure (const $ clashTy s.loc ctx s' t') $
|
||
nchoose $ sameTyCon s' t'
|
||
compareType' defs ctx s' t'
|
||
|
||
|
||
parameters (loc : Loc) (ctx : TyContext d n)
|
||
parameters (mode : EqMode)
|
||
private
|
||
fromInner : Eff EqualInner a -> Eff Equal a
|
||
fromInner = lift . map fst . runState mode
|
||
|
||
private
|
||
eachFace : Applicative f => FreeVars d ->
|
||
(EqContext n -> DSubst d 0 -> f ()) -> f ()
|
||
eachFace fvs act =
|
||
for_ (splits loc ctx.dctx fvs) $ \th =>
|
||
act (makeEqContext ctx th) th
|
||
|
||
private
|
||
CompareAction : Nat -> Nat -> Type
|
||
CompareAction d n =
|
||
Definitions -> EqContext n -> DSubst d 0 -> Eff EqualInner ()
|
||
|
||
private
|
||
runCompare : FreeVars d -> CompareAction d n -> Eff Equal ()
|
||
runCompare fvs act = fromInner $ eachFace fvs $ act !(askAt DEFS)
|
||
|
||
private
|
||
fdvAll : HasFreeDVars t => List (t d n) -> FreeVars d
|
||
fdvAll = let Val d = ctx.dimLen in foldMap (fdvWith [|d|] ctx.termLen)
|
||
|
||
namespace Term
|
||
export covering
|
||
compare : SQty -> (ty, s, t : Term d n) -> Eff Equal ()
|
||
compare sg ty s t = runCompare (fdvAll [ty, s, t]) $ \defs, ectx, th =>
|
||
compare0 defs ectx sg (ty // th) (s // th) (t // th)
|
||
|
||
export covering
|
||
compareType : (s, t : Term d n) -> Eff Equal ()
|
||
compareType s t = runCompare (fdvAll [s, t]) $ \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 : SQty -> (e, f : Elim d n) -> Eff Equal ()
|
||
compare sg e f = runCompare (fdvAll [e, f]) $ \defs, ectx, th =>
|
||
ignore $ compare0 defs ectx sg (e // th) (f // th)
|
||
|
||
namespace Term
|
||
export covering %inline
|
||
equal, sub, super : SQty -> (ty, s, t : Term d n) -> Eff Equal ()
|
||
equal = compare Equal
|
||
sub = compare Sub
|
||
super = compare Super
|
||
|
||
export covering %inline
|
||
equalType, subtype, supertype : (s, t : Term d n) -> Eff Equal ()
|
||
equalType = compareType Equal
|
||
subtype = compareType Sub
|
||
supertype = compareType Super
|
||
|
||
namespace Elim
|
||
export covering %inline
|
||
equal, sub, super : SQty -> (e, f : Elim d n) -> Eff Equal ()
|
||
equal = compare Equal
|
||
sub = compare Sub
|
||
super = compare Super
|