393 lines
14 KiB
Idris
393 lines
14 KiB
Idris
module Quox.Equal
|
||
|
||
import public Quox.Typing
|
||
import public Control.Monad.Either
|
||
import public Control.Monad.Reader
|
||
import Data.Maybe
|
||
|
||
|
||
public export
|
||
record CmpContext where
|
||
constructor MkCmpContext
|
||
mode : EqMode
|
||
|
||
|
||
public export
|
||
0 HasCmpContext : (Type -> Type) -> Type
|
||
HasCmpContext = MonadReader CmpContext
|
||
|
||
public export
|
||
0 CanEqual : (q : Type) -> (Type -> Type) -> Type
|
||
CanEqual q m = (HasErr q m, HasCmpContext m)
|
||
|
||
|
||
|
||
private %inline
|
||
mode : HasCmpContext m => m EqMode
|
||
mode = asks mode
|
||
|
||
private %inline
|
||
clashT : CanEqual q m => Term q d n -> Term q d n -> Term q d n -> m a
|
||
clashT ty s t = throwError $ ClashT !mode ty s t
|
||
|
||
private %inline
|
||
clashE : CanEqual q m => Elim q d n -> Elim q d n -> m a
|
||
clashE e f = throwError $ ClashE !mode e f
|
||
|
||
|
||
||| true if a term is syntactically a type, or is neutral.
|
||
|||
|
||
||| this function *doesn't* push substitutions, because its main use is as a
|
||
||| `So` argument to skip cases that are already known to be nonsense. and
|
||
||| the substitutions have already been pushed.
|
||
public export %inline
|
||
isTyCon : (t : Term {}) -> Bool
|
||
isTyCon (TYPE {}) = True
|
||
isTyCon (Pi {}) = True
|
||
isTyCon (Lam {}) = False
|
||
isTyCon (Sig {}) = True
|
||
isTyCon (Pair {}) = False
|
||
isTyCon (Eq {}) = True
|
||
isTyCon (DLam {}) = False
|
||
isTyCon (E {}) = True
|
||
isTyCon (CloT {}) = False
|
||
isTyCon (DCloT {}) = False
|
||
|
||
public export %inline
|
||
sameTyCon : (s, t : Term q d n) ->
|
||
(0 ts : So (isTyCon s)) => (0 tt : So (isTyCon t)) =>
|
||
Bool
|
||
sameTyCon (TYPE {}) (TYPE {}) = True
|
||
sameTyCon (TYPE {}) _ = False
|
||
sameTyCon (Pi {}) (Pi {}) = True
|
||
sameTyCon (Pi {}) _ = False
|
||
sameTyCon (Sig {}) (Sig {}) = True
|
||
sameTyCon (Sig {}) _ = False
|
||
sameTyCon (Eq {}) (Eq {}) = True
|
||
sameTyCon (Eq {}) _ = False
|
||
sameTyCon (E {}) (E {}) = True
|
||
sameTyCon (E {}) _ = False
|
||
|
||
|
||
parameters (defs : Definitions' q g)
|
||
||| true if a type is known to be a subsingleton purely by its form.
|
||
||| a subsingleton is a type with only zero or one possible values.
|
||
||| equality/subtyping accepts immediately on values of subsingleton types.
|
||
|||
|
||
||| * a function type is a subsingleton if its codomain is.
|
||
||| * a pair type is a subsingleton if both its elements are.
|
||
||| * all equality types are subsingletons because uip is admissible by
|
||
||| boundary separation.
|
||
public export
|
||
isSubSing : Term q 0 n -> Bool
|
||
isSubSing ty =
|
||
let Element ty nc = whnf defs ty in
|
||
case ty of
|
||
TYPE _ => False
|
||
Pi {res, _} => isSubSing res.term
|
||
Lam {} => False
|
||
Sig {fst, snd, _} => isSubSing fst && isSubSing snd.term
|
||
Pair {} => False
|
||
Eq {} => True
|
||
DLam {} => False
|
||
E (s :# _) => isSubSing s
|
||
E _ => False
|
||
|
||
|
||
parameters {auto _ : HasErr q m}
|
||
export %inline
|
||
ensure : (a -> Error q) -> (p : a -> Bool) -> (t : a) -> m (So (p t))
|
||
ensure e p t = case nchoose $ p t of
|
||
Left y => pure y
|
||
Right _ => throwError $ e t
|
||
|
||
export %inline
|
||
ensureTyCon : HasErr q m => (t : Term q d n) -> m (So (isTyCon t))
|
||
ensureTyCon = ensure NotType isTyCon
|
||
|
||
parameters (defs : Definitions' q _) {auto _ : (CanEqual q m, Eq q)}
|
||
mutual
|
||
namespace Term
|
||
||| `compare0 ctx ty s t` compares `s` and `t` at type `ty`, according to
|
||
||| the current variance `mode`.
|
||
|||
|
||
||| ⚠ **assumes that `s`, `t` have already been checked against `ty`**. ⚠
|
||
export covering %inline
|
||
compare0 : TContext q 0 n -> (ty, s, t : Term q 0 n) -> m ()
|
||
compare0 ctx ty s t =
|
||
wrapErr (WhileComparingT (MkTyContext new ctx) !mode ty s t) $ do
|
||
let Element ty nty = whnf defs ty
|
||
Element s ns = whnf defs s
|
||
Element t nt = whnf defs t
|
||
tty <- ensureTyCon ty
|
||
compare0' ctx ty s t
|
||
|
||
||| converts an elim "Γ ⊢ e" to "Γ, x ⊢ e x", for comparing with
|
||
||| a lambda "Γ ⊢ λx ⇒ t" that has been converted to "Γ, x ⊢ t".
|
||
private %inline
|
||
toLamBody : Elim q d n -> Term q d (S n)
|
||
toLamBody e = E $ weakE e :@ BVT 0
|
||
|
||
private covering
|
||
compare0' : TContext q 0 n ->
|
||
(ty, s, t : Term q 0 n) ->
|
||
(0 nty : NotRedex defs ty) => (0 tty : So (isTyCon ty)) =>
|
||
(0 ns : NotRedex defs s) => (0 nt : NotRedex defs t) =>
|
||
m ()
|
||
compare0' ctx (TYPE _) s t = compareType ctx s t
|
||
|
||
compare0' ctx ty@(Pi {arg, res, _}) s t {n} = local {mode := Equal} $
|
||
case (s, t) of
|
||
-- Γ, x : A ⊢ s = t : B
|
||
-- -----------------------------------------
|
||
-- Γ ⊢ (λx ⇒ s) = (λx ⇒ t) : (π·x : A) → B
|
||
(Lam _ b1, Lam _ b2) => compare0 ctx' res.term b1.term b2.term
|
||
|
||
-- Γ, x : A ⊢ s = e x : B
|
||
-- ----------------------------------
|
||
-- Γ ⊢ (λx ⇒ s) = e : (π·x : A) → B
|
||
(E e, Lam _ b) => eta e b
|
||
(Lam _ b, E e) => eta e b
|
||
|
||
(E e, E f) => Elim.compare0 ctx e f
|
||
_ => throwError $ WrongType ty s t
|
||
where
|
||
ctx' : TContext q 0 (S n)
|
||
ctx' = ctx :< arg
|
||
|
||
eta : Elim q 0 n -> ScopeTerm q 0 n -> m ()
|
||
eta e (TUsed b) = compare0 ctx' res.term (toLamBody e) b
|
||
eta e (TUnused _) = clashT ty s t
|
||
|
||
compare0' ctx ty@(Sig {fst, snd, _}) s t = local {mode := Equal} $
|
||
case (s, t) of
|
||
-- Γ ⊢ s₁ = t₁ : A Γ ⊢ s₂ = t₂ : B{s₁/x}
|
||
-- -------------------------------------------
|
||
-- Γ ⊢ (s₁,t₁) = (s₂,t₂) : (x : A) × B
|
||
--
|
||
-- [todo] η for π ≥ 0 maybe
|
||
(Pair sFst sSnd, Pair tFst tSnd) => do
|
||
compare0 ctx fst sFst tFst
|
||
compare0 ctx (sub1 snd (sFst :# fst)) sSnd tSnd
|
||
|
||
_ => throwError $ WrongType ty s t
|
||
|
||
compare0' _ (Eq {}) _ _ =
|
||
-- ✨ uip ✨
|
||
--
|
||
-- Γ ⊢ e = f : Eq [i ⇒ A] s t
|
||
pure ()
|
||
|
||
compare0' ctx ty@(E _) s t = do
|
||
-- a neutral type can only be inhabited by neutral values
|
||
-- e.g. an abstract value in an abstract type, bound variables, …
|
||
E e <- pure s | _ => throwError $ WrongType ty s t
|
||
E f <- pure t | _ => throwError $ WrongType ty s t
|
||
Elim.compare0 ctx e f
|
||
|
||
||| compares two types, using the current variance `mode` for universes.
|
||
||| fails if they are not types, even if they would happen to be equal.
|
||
export covering %inline
|
||
compareType : TContext q 0 n -> (s, t : Term q 0 n) -> m ()
|
||
compareType ctx s t = do
|
||
let Element s ns = whnf defs s
|
||
Element t nt = whnf defs t
|
||
ts <- ensureTyCon s
|
||
tt <- ensureTyCon t
|
||
st <- either pure (const $ clashT (TYPE UAny) s t) $
|
||
nchoose $ sameTyCon s t
|
||
compareType' ctx s t
|
||
|
||
private covering
|
||
compareType' : TContext q 0 n -> (s, t : Term q 0 n) ->
|
||
(0 ns : NotRedex defs s) => (0 ts : So (isTyCon s)) =>
|
||
(0 nt : NotRedex defs t) => (0 tt : So (isTyCon t)) =>
|
||
(0 st : So (sameTyCon s t)) =>
|
||
m ()
|
||
-- equality is the same as subtyping, except with the
|
||
-- "≤" in the TYPE rule being replaced with "="
|
||
compareType' ctx (TYPE k) (TYPE l) =
|
||
-- 𝓀 ≤ ℓ
|
||
-- ----------------------
|
||
-- Γ ⊢ Type 𝓀 <: Type ℓ
|
||
expectModeU !mode k l
|
||
|
||
compareType' ctx (Pi {qty = sQty, arg = sArg, res = sRes, _})
|
||
(Pi {qty = tQty, arg = tArg, res = tRes, _}) = do
|
||
-- Γ ⊢ A₁ :> A₂ Γ, x : A₁ ⊢ B₁ <: B₂
|
||
-- ----------------------------------------
|
||
-- Γ ⊢ (π·x : A₁) → B₁ <: (π·x : A₂) → B₂
|
||
expectEqualQ sQty tQty
|
||
local {mode $= flip} $ compareType ctx sArg tArg -- contra
|
||
compareType (ctx :< sArg) sRes.term tRes.term
|
||
|
||
compareType' ctx (Sig {fst = sFst, snd = sSnd, _})
|
||
(Sig {fst = tFst, snd = tSnd, _}) = do
|
||
-- Γ ⊢ A₁ <: A₂ Γ, x : A₁ ⊢ B₁ <: B₂
|
||
-- --------------------------------------
|
||
-- Γ ⊢ (x : A₁) × B₁ <: (x : A₂) × B₂
|
||
compareType ctx sFst tFst
|
||
compareType (ctx :< sFst) sSnd.term tSnd.term
|
||
|
||
compareType' ctx (Eq {ty = sTy, l = sl, r = sr, _})
|
||
(Eq {ty = tTy, l = tl, r = tr, _}) = do
|
||
-- Γ ⊢ A₁‹ε/i› <: A₂‹ε/i›
|
||
-- Γ ⊢ l₁ = l₂ : A₁‹𝟎/i› Γ ⊢ r₁ = r₂ : A₁‹𝟏/i›
|
||
-- ------------------------------------------------
|
||
-- Γ ⊢ Eq [i ⇒ A₁] l₁ r₂ <: Eq [i ⇒ A₂] l₂ r₂
|
||
compareType ctx sTy.zero tTy.zero
|
||
compareType ctx sTy.one tTy.one
|
||
local {mode := Equal} $ do
|
||
Term.compare0 ctx sTy.zero sl tl
|
||
Term.compare0 ctx sTy.one sr tr
|
||
|
||
compareType' ctx (E e) (E f) = do
|
||
-- no fanciness needed here cos anything other than a neutral
|
||
-- has been inlined by whnf
|
||
Elim.compare0 ctx e f
|
||
|
||
||| performs the minimum work required to recompute the type of an elim.
|
||
|||
|
||
||| ⚠ **assumes the elim is already typechecked.** ⚠
|
||
private covering
|
||
computeElimType : TContext q 0 n -> (e : Elim q 0 n) ->
|
||
(0 ne : NotRedex defs e) ->
|
||
m (Term q 0 n)
|
||
computeElimType ctx (F x) _ = do
|
||
defs <- lookupFree' defs x
|
||
pure $ defs.type.get
|
||
computeElimType ctx (B i) _ = do
|
||
pure $ ctx !! i
|
||
computeElimType ctx (f :@ s) ne = do
|
||
(_, arg, res) <- expectPi defs !(computeElimType ctx f (noOr1 ne))
|
||
pure $ sub1 res (s :# arg)
|
||
computeElimType ctx (CasePair {pair, ret, _}) _ = do
|
||
pure $ sub1 ret pair
|
||
computeElimType ctx (f :% p) ne = do
|
||
(ty, _, _) <- expectEq defs !(computeElimType ctx f (noOr1 ne))
|
||
pure $ dsub1 ty p
|
||
computeElimType ctx (_ :# ty) _ = do
|
||
pure ty
|
||
|
||
private covering
|
||
replaceEnd : TContext q 0 n ->
|
||
(e : Elim q 0 n) -> DimConst -> (0 ne : NotRedex defs e) ->
|
||
m (Elim q 0 n)
|
||
replaceEnd ctx e p ne = do
|
||
(ty, l, r) <- expectEq defs !(computeElimType ctx e ne)
|
||
pure $ ends l r p :# dsub1 ty (K p)
|
||
|
||
namespace Elim
|
||
-- [fixme] the following code ends up repeating a lot of work in the
|
||
-- computeElimType calls. the results should be shared better
|
||
|
||
||| compare two eliminations according to the given variance `mode`.
|
||
|||
|
||
||| ⚠ **assumes that they have both been typechecked, and have
|
||
||| equal types.** ⚠
|
||
export covering %inline
|
||
compare0 : TContext q 0 n -> (e, f : Elim q 0 n) -> m ()
|
||
compare0 ctx e f =
|
||
wrapErr (WhileComparingE (MkTyContext new ctx) !mode e f) $ do
|
||
let Element e ne = whnf defs e
|
||
Element f nf = whnf defs f
|
||
-- [fixme] there is a better way to do this "isSubSing" stuff for sure
|
||
unless (isSubSing defs !(computeElimType ctx e ne)) $
|
||
compare0' ctx e f ne nf
|
||
|
||
private covering
|
||
compare0' : TContext q 0 n ->
|
||
(e, f : Elim q 0 n) ->
|
||
(0 ne : NotRedex defs e) -> (0 nf : NotRedex defs f) ->
|
||
m ()
|
||
-- replace applied equalities with the appropriate end first
|
||
-- e.g. e : Eq [i ⇒ A] s t ⊢ e 𝟎 = s : A‹𝟎/i›
|
||
--
|
||
-- [todo] maybe have typed whnf and do this (and η???) there instead
|
||
compare0' ctx (e :% K p) f ne nf =
|
||
compare0 ctx !(replaceEnd ctx e p $ noOr1 ne) f
|
||
compare0' ctx e (f :% K q) ne nf =
|
||
compare0 ctx e !(replaceEnd ctx f q $ noOr1 nf)
|
||
|
||
compare0' _ e@(F x) f@(F y) _ _ = unless (x == y) $ clashE e f
|
||
compare0' _ e@(F _) f _ _ = clashE e f
|
||
|
||
compare0' ctx e@(B i) f@(B j) _ _ = unless (i == j) $ clashE e f
|
||
compare0' _ e@(B _) f _ _ = clashE e f
|
||
|
||
compare0' ctx (e :@ s) (f :@ t) ne nf =
|
||
local {mode := Equal} $ do
|
||
compare0 ctx e f
|
||
(_, arg, _) <- expectPi defs !(computeElimType ctx e (noOr1 ne))
|
||
Term.compare0 ctx arg s t
|
||
compare0' _ e@(_ :@ _) f _ _ = clashE e f
|
||
|
||
compare0' ctx (CasePair epi e _ eret _ _ ebody)
|
||
(CasePair fpi f _ fret _ _ fbody) ne nf =
|
||
local {mode := Equal} $ do
|
||
compare0 ctx e f
|
||
ety <- computeElimType ctx e (noOr1 ne)
|
||
compareType (ctx :< ety) eret.term fret.term
|
||
(fst, snd) <- expectSig defs ety
|
||
Term.compare0 (ctx :< fst :< snd.term) (substCasePairRet ety eret)
|
||
ebody.term fbody.term
|
||
unless (epi == fpi) $ throwError $ ClashQ epi fpi
|
||
compare0' _ e@(CasePair {}) f _ _ = clashE e f
|
||
|
||
compare0' ctx (s :# a) (t :# _) _ _ = Term.compare0 ctx a s t
|
||
compare0' ctx (s :# a) f _ _ = Term.compare0 ctx a s (E f)
|
||
compare0' ctx e (t :# b) _ _ = Term.compare0 ctx b (E e) t
|
||
compare0' _ e@(_ :# _) f _ _ = clashE e f
|
||
|
||
|
||
parameters {auto _ : (HasDefs' q _ m, HasErr q m, Eq q)} (ctx : TyContext q d n)
|
||
parameters (mode : EqMode)
|
||
namespace Term
|
||
export covering
|
||
compare : (ty, s, t : Term q d n) -> m ()
|
||
compare ty s t = do
|
||
defs <- ask
|
||
runReaderT {m} (MkCmpContext {mode}) $
|
||
for_ (splits ctx.dctx) $ \th =>
|
||
compare0 defs (map (// th) ctx.tctx)
|
||
(ty // th) (s // th) (t // th)
|
||
|
||
export covering
|
||
compareType : (s, t : Term q d n) -> m ()
|
||
compareType s t = do
|
||
defs <- ask
|
||
runReaderT {m} (MkCmpContext {mode}) $
|
||
for_ (splits ctx.dctx) $ \th =>
|
||
compareType defs (map (// th) ctx.tctx) (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 %inline
|
||
compare : (e, f : Elim q d n) -> m ()
|
||
compare e f = do
|
||
defs <- ask
|
||
runReaderT {m} (MkCmpContext {mode}) $
|
||
for_ (splits ctx.dctx) $ \th =>
|
||
compare0 defs (map (// th) ctx.tctx) (e // th) (f // th)
|
||
|
||
namespace Term
|
||
export covering %inline
|
||
equal, sub, super : (ty, s, t : Term q d n) -> m ()
|
||
equal = compare Equal
|
||
sub = compare Sub
|
||
super = compare Super
|
||
|
||
export covering %inline
|
||
equalType, subtype, supertype : (s, t : Term q d n) -> m ()
|
||
equalType = compareType Equal
|
||
subtype = compareType Sub
|
||
supertype = compareType Super
|
||
|
||
namespace Elim
|
||
export covering %inline
|
||
equal, sub, super : (e, f : Elim q d n) -> m ()
|
||
equal = compare Equal
|
||
sub = compare Sub
|
||
super = compare Super
|