quox/lib/Quox/Reduce.idr
rhiannon morris cb5bd6c98c make overloaded reduce stuff into interfaces
this is kinda a pain so i might change it back i guess
2023-02-20 21:42:31 +01:00

257 lines
7.7 KiB
Idris

module Quox.Reduce
import Quox.No
import Quox.Syntax
import Quox.Definition
import Data.Vect
import Data.Maybe
%default total
public export
0 CloTest : TermLike -> Type
CloTest tm = forall q, d, n. tm q d n -> Bool
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)
public export
0 NotClo : {isClo : CloTest tm} -> PushSubsts tm isClo => Pred (tm q d n)
NotClo = No . isClo
public export
0 NonClo : (tm : TermLike) -> {isClo : CloTest tm} ->
PushSubsts tm isClo => TermLike
NonClo tm q d n = Subset (tm q d n) NotClo
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
mutual
public export
isCloT : CloTest Term
isCloT (CloT {}) = True
isCloT (DCloT {}) = True
isCloT (E e) = isCloE e
isCloT _ = False
public export
isCloE : CloTest Elim
isCloE (CloE {}) = True
isCloE (DCloE {}) = True
isCloE _ = False
mutual
export
PushSubsts Term Reduce.isCloT where
pushSubstsWith th ph (TYPE l) =
nclo $ TYPE l
pushSubstsWith th ph (Pi qty x a body) =
nclo $ Pi qty x (subs a th ph) (subs body th ph)
pushSubstsWith th ph (Lam x body) =
nclo $ Lam x $ subs body th ph
pushSubstsWith th ph (Sig x a b) =
nclo $ Sig x (subs a th ph) (subs b th ph)
pushSubstsWith th ph (Pair s t) =
nclo $ Pair (subs s th ph) (subs t th ph)
pushSubstsWith th ph (Eq i ty l r) =
nclo $ Eq i (subs ty th ph) (subs l th ph) (subs r th ph)
pushSubstsWith th ph (DLam i body) =
nclo $ DLam i $ subs 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 $ subs f th ph :@ subs s th ph
pushSubstsWith th ph (CasePair pi p x r y z b) =
nclo $ CasePair pi (subs p th ph) x (subs r th ph) y z (subs b th ph)
pushSubstsWith th ph (f :% d) =
nclo $ subs f th ph :% (d // th)
pushSubstsWith th ph (s :# a) =
nclo $ 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
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) | tm where
whnf : (defs : Definitions' q g) ->
tm q d n -> Subset (tm q d n) (No . isRedex defs)
public export
0 IsRedex, NotRedex : {isRedex : RedexTest tm} -> Whnf tm isRedex =>
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 =>
(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) =>
(t : tm q d n) -> (0 nr : NotRedex defs t) =>
NonRedex tm q d n defs
nred t = Element t nr
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
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 (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 where
whnf defs (F x) with (lookupElim x defs) proof eq
_ | Just y = whnf defs y
_ | Nothing = Element (F x) $ rewrite eq in Ah
whnf _ (B i) = nred $ B i
whnf defs (f :@ s) =
let Element f fnf = whnf defs f in
case nchoose $ isLamHead f of
Left _ =>
let Lam {body, _} :# Pi {arg, res, _} = f
s = s :# arg
in
whnf defs $ sub1 body s :# sub1 res s
Right nlh => Element (f :@ s) $ fnf `orNo` nlh
whnf defs (CasePair pi pair r ret x y body) =
let Element pair pairnf = whnf defs 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 defs $ subN body [fst, snd] :# sub1 ret pair
Right np =>
Element (CasePair pi pair r ret x y body) $ pairnf `orNo` np
whnf defs (f :% p) =
let Element f fnf = whnf defs 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 defs $ body :# dsub1 ty p
Right ndlh =>
Element (f :% p) $ fnf `orNo` ndlh
whnf defs (s :# a) =
let Element s snf = whnf defs s in
case nchoose $ isE s of
Left _ => let E e = s in Element e $ noOr2 snf
Right ne =>
let Element a anf = whnf defs a in
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 where
whnf _ t@(TYPE {}) = nred t
whnf _ t@(Pi {}) = nred t
whnf _ t@(Lam {}) = nred t
whnf _ t@(Sig {}) = nred t
whnf _ t@(Pair {}) = nred t
whnf _ t@(Eq {}) = nred t
whnf _ t@(DLam {}) = nred t
whnf defs (E e) =
let Element e enf = whnf defs 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 defs (CloT tm th) = whnf defs $ pushSubstsWith' id th tm
whnf defs (DCloT tm th) = whnf defs $ pushSubstsWith' th id tm