quox/lib/Quox/Reduce.idr

267 lines
7.9 KiB
Idris

module Quox.Reduce
import Quox.No
import Quox.Syntax
import Quox.Definition
import Data.Vect
import Data.Maybe
%default total
namespace Elim
public export %inline
isClo : Elim {} -> Bool
isClo (CloE {}) = True
isClo (DCloE {}) = True
isClo _ = False
public export
0 NotClo : Pred $ Elim {}
NotClo = No . isClo
namespace Term
public export %inline
isClo : Term {} -> Bool
isClo (CloT {}) = True
isClo (DCloT {}) = True
isClo (E e) = isClo e
isClo _ = False
public export
0 NotClo : Pred $ Term {}
NotClo = No . isClo
public export
0 NonCloElim : TermLike
NonCloElim q d n = Subset (Elim q d n) NotClo
public export
0 NonCloTerm : TermLike
NonCloTerm q d n = Subset (Term q d n) NotClo
public export %inline
ncloT : (t : Term q d n) -> (0 nc : NotClo t) => NonCloTerm q d n
ncloT t = Element t nc
public export %inline
ncloE : (e : Elim q d n) -> (0 nc : NotClo e) => NonCloElim q d n
ncloE e = Element e nc
mutual
namespace Term
||| if the input term has any top-level closures, push them under one layer of
||| syntax
export %inline
pushSubsts : Term q d n -> NonCloTerm q d n
pushSubsts s = pushSubstsWith id id s
export
pushSubstsWith : DSubst dfrom dto -> TSubst q dto from to ->
Term q dfrom from -> NonCloTerm q dto to
pushSubstsWith th ph (TYPE l) =
ncloT $ TYPE l
pushSubstsWith th ph (Pi qty x a body) =
ncloT $ Pi qty x (subs a th ph) (subs body th ph)
pushSubstsWith th ph (Lam x body) =
ncloT $ Lam x $ subs body th ph
pushSubstsWith th ph (Sig x a b) =
ncloT $ Sig x (subs a th ph) (subs b th ph)
pushSubstsWith th ph (Pair s t) =
ncloT $ Pair (subs s th ph) (subs t th ph)
pushSubstsWith th ph (Eq i ty l r) =
ncloT $ Eq i (subs ty th ph) (subs l th ph) (subs r th ph)
pushSubstsWith th ph (DLam i body) =
ncloT $ DLam i $ subs body th ph
pushSubstsWith th ph (E e) =
let Element e nc = pushSubstsWith th ph e in ncloT $ 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
namespace Elim
||| if the input elimination has any top-level closures, push them under one
||| layer of syntax
export %inline
pushSubsts : Elim q d n -> NonCloElim q d n
pushSubsts e = pushSubstsWith id id e
export
pushSubstsWith : DSubst dfrom dto -> TSubst q dto from to ->
Elim q dfrom from -> NonCloElim q dto to
pushSubstsWith th ph (F x) =
ncloE $ F x
pushSubstsWith th ph (B i) =
let res = ph !! i in
case nchoose $ isClo res of
Left yes => assert_total pushSubsts res
Right no => Element res no
pushSubstsWith th ph (f :@ s) =
ncloE $ subs f th ph :@ subs s th ph
pushSubstsWith th ph (CasePair pi p x r y z b) =
ncloE $ CasePair pi (subs p th ph) x (subs r th ph) y z (subs b th ph)
pushSubstsWith th ph (f :% d) =
ncloE $ subs f th ph :% (d // th)
pushSubstsWith th ph (s :# a) =
ncloE $ subs s th ph :# subs 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
parameters (th : DSubst dfrom dto) (ph : TSubst q dto from to)
namespace Term
public export %inline
pushSubstsWith' : Term q dfrom from -> Term q dto to
pushSubstsWith' s = (pushSubstsWith th ph s).fst
namespace Elim
public export %inline
pushSubstsWith' : Elim q dfrom from -> Elim q dto to
pushSubstsWith' e = (pushSubstsWith th ph e).fst
public export %inline
isLamHead : Elim {} -> Bool
isLamHead (Lam {} :# Pi {}) = True
isLamHead _ = False
public export %inline
isDLamHead : Elim {} -> Bool
isDLamHead (DLam {} :# Eq {}) = True
isDLamHead _ = False
public export %inline
isPairHead : Elim {} -> Bool
isPairHead (Pair {} :# Sig {}) = True
isPairHead _ = False
public export %inline
isE : Term {} -> Bool
isE (E _) = True
isE _ = False
public export %inline
isAnn : Elim {} -> Bool
isAnn (_ :# _) = True
isAnn _ = False
parameters (defs : Definitions' q g)
mutual
namespace Elim
public export
isRedex : Elim q d n -> Bool
isRedex (F x) {d, n} = isJust $ lookupElim x defs {d, n}
isRedex (B _) = False
isRedex (f :@ _) = isRedex f || isLamHead f
isRedex (CasePair {pair, _}) = isRedex pair || isPairHead pair
isRedex (f :% _) = isRedex f || isDLamHead f
isRedex (t :# a) = isE t || isRedex t || isRedex a
isRedex (CloE {}) = True
isRedex (DCloE {}) = True
namespace Term
public export
isRedex : Term q d n -> Bool
isRedex (CloT {}) = True
isRedex (DCloT {}) = True
isRedex (E e) = isAnn e || isRedex e
isRedex _ = False
namespace Elim
public export
0 IsRedex, NotRedex : Pred $ Elim q d n
IsRedex = So . isRedex
NotRedex = No . isRedex
namespace Term
public export
0 IsRedex, NotRedex : Pred $ Term q d n
IsRedex = So . isRedex
NotRedex = No . isRedex
parameters (q : Type) (d, n : Nat) {g : q -> Type} (defs : Definitions' q g)
public export
0 NonRedexElim, NonRedexTerm : Type
NonRedexElim = Subset (Elim q d n) (NotRedex defs)
NonRedexTerm = Subset (Term q d n) (NotRedex defs)
parameters (defs : Definitions' q g)
mutual
namespace Elim
export covering
whnf : Elim q d n -> NonRedexElim q d n defs
whnf (F x) with (lookupElim x defs) proof eq
_ | Just y = whnf y
_ | Nothing = Element (F x) $ rewrite eq in Ah
whnf (B i) = Element (B i) Ah
whnf (f :@ s) =
let Element f fnf = whnf f in
case nchoose $ isLamHead f of
Left _ =>
let Lam {body, _} :# Pi {arg, res, _} = f
s = s :# arg
in
whnf $ sub1 body s :# sub1 res s
Right nlh => Element (f :@ s) $ fnf `orNo` nlh
whnf (CasePair pi pair r ret x y body) =
let Element pair pairnf = whnf pair in
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 $ subN body [fst, snd] :# sub1 ret pair
Right np =>
Element (CasePair pi pair r ret x y body) $ pairnf `orNo` np
whnf (f :% p) =
let Element f fnf = whnf f in
case nchoose $ isDLamHead f of
Left _ =>
let DLam {body, _} :# Eq {ty, l, r, _} = f
body = endsOr l r (dsub1 body p) p
in
whnf $ body :# dsub1 ty p
Right ndlh =>
Element (f :% p) $ fnf `orNo` ndlh
whnf (s :# a) =
let Element s snf = whnf s in
case nchoose $ isE s of
Left _ => let E e = s in Element e $ noOr2 snf
Right ne =>
let Element a anf = whnf a in
Element (s :# a) $ ne `orNo` snf `orNo` anf
whnf (CloE el th) = whnf $ pushSubstsWith' id th el
whnf (DCloE el th) = whnf $ pushSubstsWith' th id el
namespace Term
export covering
whnf : Term q d n -> NonRedexTerm q d n defs
whnf t@(TYPE {}) = Element t Ah
whnf t@(Pi {}) = Element t Ah
whnf t@(Lam {}) = Element t Ah
whnf t@(Sig {}) = Element t Ah
whnf t@(Pair {}) = Element t Ah
whnf t@(Eq {}) = Element t Ah
whnf t@(DLam {}) = Element t Ah
whnf (E e) =
let Element e enf = whnf e in
case nchoose $ isAnn e of
Left _ => let tm :# _ = e in Element tm $ noOr1 $ noOr2 enf
Right na => Element (E e) $ na `orNo` enf
whnf (CloT tm th) = whnf $ pushSubstsWith' id th tm
whnf (DCloT tm th) = whnf $ pushSubstsWith' th id tm