quox/lib/Quox/Reduce.idr

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module Quox.Reduce
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import Quox.No
import Quox.Syntax
import Quox.Definition
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import Data.Vect
import Data.Maybe
import Data.List
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%default total
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public export
0 CloTest : TermLike -> Type
CloTest tm = forall q, d, n. tm q d n -> Bool
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interface PushSubsts (0 tm : TermLike) (0 isClo : CloTest tm) | tm where
pushSubstsWith : DSubst dfrom dto -> TSubst q dto from to ->
tm q dfrom from -> Subset (tm q dto to) (No . isClo)
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public export
0 NotClo : {isClo : CloTest tm} -> PushSubsts tm isClo => Pred (tm q d n)
NotClo = No . isClo
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public export
0 NonClo : (tm : TermLike) -> {isClo : CloTest tm} ->
PushSubsts tm isClo => TermLike
NonClo tm q d n = Subset (tm q d n) NotClo
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public export %inline
nclo : {isClo : CloTest tm} -> (0 _ : PushSubsts tm isClo) =>
(t : tm q d n) -> (0 nc : NotClo t) => NonClo tm q d n
nclo t = Element t nc
parameters {0 isClo : CloTest tm} {auto _ : PushSubsts tm isClo}
||| if the input term has any top-level closures, push them under one layer of
||| syntax
export %inline
pushSubsts : tm q d n -> NonClo tm q d n
pushSubsts s = pushSubstsWith id id s
export %inline
pushSubstsWith' : DSubst dfrom dto -> TSubst q dto from to ->
tm q dfrom from -> tm q dto to
pushSubstsWith' th ph x = fst $ pushSubstsWith th ph x
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mutual
public export
isCloT : CloTest Term
isCloT (CloT {}) = True
isCloT (DCloT {}) = True
isCloT (E e) = isCloE e
isCloT _ = False
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public export
isCloE : CloTest Elim
isCloE (CloE {}) = True
isCloE (DCloE {}) = True
isCloE _ = False
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mutual
export
PushSubsts Term Reduce.isCloT where
pushSubstsWith th ph (TYPE l) =
nclo $ TYPE l
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pushSubstsWith th ph (Pi qty a body) =
nclo $ Pi qty (a // th // ph) (body // th // ph)
pushSubstsWith th ph (Lam body) =
nclo $ Lam (body // th // ph)
pushSubstsWith th ph (Sig a b) =
nclo $ Sig (a // th // ph) (b // th // ph)
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pushSubstsWith th ph (Pair s t) =
nclo $ Pair (s // th // ph) (t // th // ph)
pushSubstsWith th ph (Enum tags) =
nclo $ Enum tags
pushSubstsWith th ph (Tag tag) =
nclo $ Tag tag
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pushSubstsWith th ph (Eq ty l r) =
nclo $ Eq (ty // th // ph) (l // th // ph) (r // th // ph)
pushSubstsWith th ph (DLam body) =
nclo $ DLam (body // th // ph)
pushSubstsWith th ph (E e) =
let Element e nc = pushSubstsWith th ph e in nclo $ E e
pushSubstsWith th ph (CloT s ps) =
pushSubstsWith th (comp th ps ph) s
pushSubstsWith th ph (DCloT s ps) =
pushSubstsWith (ps . th) ph s
export
PushSubsts Elim Reduce.isCloE where
pushSubstsWith th ph (F x) =
nclo $ F x
pushSubstsWith th ph (B i) =
let res = ph !! i in
case nchoose $ isCloE res of
Left yes => assert_total pushSubsts res
Right no => Element res no
pushSubstsWith th ph (f :@ s) =
nclo $ (f // th // ph) :@ (s // th // ph)
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pushSubstsWith th ph (CasePair pi p r b) =
nclo $ CasePair pi (p // th // ph) (r // th // ph) (b // th // ph)
pushSubstsWith th ph (CaseEnum pi t r arms) =
nclo $ CaseEnum pi (t // th // ph) (r // th // ph)
(map (\b => b // th // ph) arms)
pushSubstsWith th ph (f :% d) =
nclo $ (f // th // ph) :% (d // th)
pushSubstsWith th ph (s :# a) =
nclo $ (s // th // ph) :# (a // th // ph)
pushSubstsWith th ph (CloE e ps) =
pushSubstsWith th (comp th ps ph) e
pushSubstsWith th ph (DCloE e ps) =
pushSubstsWith (ps . th) ph e
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||| errors that might happen if you pass an ill typed expression into
||| whnf. don't do that please
public export
data WhnfErr = MissingEnumArm TagVal (List TagVal)
public export
0 RedexTest : TermLike -> Type
RedexTest tm = forall q, d, n, g. Definitions' q g -> tm q d n -> Bool
public export
interface Whnf (0 tm : TermLike)
(0 isRedex : RedexTest tm)
(0 err : Type) | tm
where
whnf : (defs : Definitions' q g) ->
tm q d n -> Either err (Subset (tm q d n) (No . isRedex defs))
public export
0 IsRedex, NotRedex : {isRedex : RedexTest tm} -> Whnf tm isRedex err =>
Definitions' q g -> Pred (tm q d n)
IsRedex defs = So . isRedex defs
NotRedex defs = No . isRedex defs
public export
0 NonRedex : (tm : TermLike) -> {isRedex : RedexTest tm} ->
Whnf tm isRedex err =>
(q : Type) -> (d, n : Nat) -> {g : _} ->
(defs : Definitions' q g) -> Type
NonRedex tm q d n defs = Subset (tm q d n) (NotRedex defs)
public export %inline
nred : {0 isRedex : RedexTest tm} -> (0 _ : Whnf tm isRedex err) =>
(t : tm q d n) -> (0 nr : NotRedex defs t) =>
NonRedex tm q d n defs
nred t = Element t nr
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public export %inline
isLamHead : Elim {} -> Bool
isLamHead (Lam {} :# Pi {}) = True
isLamHead _ = False
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public export %inline
isDLamHead : Elim {} -> Bool
isDLamHead (DLam {} :# Eq {}) = True
isDLamHead _ = False
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public export %inline
isPairHead : Elim {} -> Bool
isPairHead (Pair {} :# Sig {}) = True
isPairHead _ = False
public export %inline
isTagHead : Elim {} -> Bool
isTagHead (Tag t :# Enum _) = True
isTagHead _ = False
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public export %inline
isE : Term {} -> Bool
isE (E _) = True
isE _ = False
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public export %inline
isAnn : Elim {} -> Bool
isAnn (_ :# _) = True
isAnn _ = False
mutual
public export
isRedexE : RedexTest Elim
isRedexE defs (F x) {d, n} =
isJust $ lookupElim x defs {d, n}
isRedexE _ (B _) = False
isRedexE defs (f :@ _) =
isRedexE defs f || isLamHead f
isRedexE defs (CasePair {pair, _}) =
isRedexE defs pair || isPairHead pair
isRedexE defs (CaseEnum {tag, _}) =
isRedexE defs tag || isTagHead tag
isRedexE defs (f :% _) =
isRedexE defs f || isDLamHead f
isRedexE defs (t :# a) =
isE t || isRedexT defs t || isRedexT defs a
isRedexE _ (CloE {}) = True
isRedexE _ (DCloE {}) = True
public export
isRedexT : RedexTest Term
isRedexT _ (CloT {}) = True
isRedexT _ (DCloT {}) = True
isRedexT defs (E e) = isAnn e || isRedexE defs e
isRedexT _ _ = False
mutual
export covering
Whnf Elim Reduce.isRedexE WhnfErr where
whnf defs (F x) with (lookupElim x defs) proof eq
_ | Just y = whnf defs y
_ | Nothing = pure $ Element (F x) $ rewrite eq in Ah
whnf _ (B i) = pure $ nred $ B i
whnf defs (f :@ s) = do
Element f fnf <- whnf defs f
case nchoose $ isLamHead f of
Left _ =>
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let Lam body :# Pi {arg, res, _} = f
s = s :# arg
in
whnf defs $ sub1 body s :# sub1 res s
Right nlh => pure $ Element (f :@ s) $ fnf `orNo` nlh
whnf defs (CasePair pi pair ret body) = do
Element pair pairnf <- whnf defs pair
case nchoose $ isPairHead pair of
Left _ =>
let Pair {fst, snd} :# Sig {fst = tfst, snd = tsnd, _} = pair
fst = fst :# tfst
snd = snd :# sub1 tsnd fst
in
whnf defs $ subN body [fst, snd] :# sub1 ret pair
Right np =>
pure $ Element (CasePair pi pair ret body)
(pairnf `orNo` np)
whnf defs (CaseEnum pi tag ret arms) = do
Element tag tagnf <- whnf defs tag
case nchoose $ isTagHead tag of
Left t =>
let Tag t :# Enum ts = tag
ty = sub1 ret tag
in
case lookup t arms of
Just arm => whnf defs $ arm :# ty
Nothing => Left $ MissingEnumArm t (keys arms)
Right nt =>
pure $ Element (CaseEnum pi tag ret arms) $ tagnf `orNo` nt
whnf defs (f :% p) = do
Element f fnf <- whnf defs f
case nchoose $ isDLamHead f of
Left _ =>
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let DLam body :# Eq {ty = ty, l, r, _} = f
body = endsOr l r (dsub1 body p) p
in
whnf defs $ body :# dsub1 ty p
Right ndlh =>
pure $ Element (f :% p) $ fnf `orNo` ndlh
whnf defs (s :# a) = do
Element s snf <- whnf defs s
case nchoose $ isE s of
Left _ => let E e = s in pure $ Element e $ noOr2 snf
Right ne => do
Element a anf <- whnf defs a
pure $ Element (s :# a) $ ne `orNo` snf `orNo` anf
whnf defs (CloE el th) = whnf defs $ pushSubstsWith' id th el
whnf defs (DCloE el th) = whnf defs $ pushSubstsWith' th id el
export covering
Whnf Term Reduce.isRedexT WhnfErr where
whnf _ t@(TYPE {}) = pure $ nred t
whnf _ t@(Pi {}) = pure $ nred t
whnf _ t@(Lam {}) = pure $ nred t
whnf _ t@(Sig {}) = pure $ nred t
whnf _ t@(Pair {}) = pure $ nred t
whnf _ t@(Enum {}) = pure $ nred t
whnf _ t@(Tag {}) = pure $ nred t
whnf _ t@(Eq {}) = pure $ nred t
whnf _ t@(DLam {}) = pure $ nred t
whnf defs (E e) = do
Element e enf <- whnf defs e
case nchoose $ isAnn e of
Left _ => let tm :# _ = e in pure $ Element tm $ noOr1 $ noOr2 enf
Right na => pure $ Element (E e) $ na `orNo` enf
whnf defs (CloT tm th) = whnf defs $ pushSubstsWith' id th tm
whnf defs (DCloT tm th) = whnf defs $ pushSubstsWith' th id tm