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37
lib/Quox/Context.idr
View file

@ -6,12 +6,16 @@ import Quox.Name
import Data.DPair
import Data.Nat
import Data.Fin
import Data.Singleton
import Data.SnocList
import Data.SnocVect
import Data.Vect
import Control.Monad.Identity
import Derive.Prelude
%default total
%language ElabReflection
||| a sequence of bindings under an existing context. each successive element
@ -83,6 +87,13 @@ export %inline
toSnocList' : Telescope' a _ _ -> SnocList a
toSnocList' = toSnocListWith id
export %inline
toSnocListRelevant : {n1 : Nat} -> Telescope tm n1 n2 -> SnocList (n ** tm n)
toSnocListRelevant tel = toSnocList' $ snd $ go tel where
go : Telescope tm n1 n2' -> (Singleton n2', Telescope' (n ** tm n) n1 n2')
go [<] = (Val n1, [<])
go (tel :< x) = let (Val n, tel) = go tel in (Val (S n), tel :< (n ** x))
export %inline
toList : Telescope tm _ _ -> List (Exists tm)
toList = toListWith (Evidence _)
@ -136,34 +147,34 @@ tel ++ (sx :< x) = (tel ++ sx) :< x
public export
getShiftWith : (forall from, to. tm from -> Shift from to -> tm to) ->
Shift len out -> Context tm len -> Var len -> tm out
getShiftWith shft by (ctx :< t) VZ = t `shft` ssDown by
getShiftWith shft by (ctx :< t) (VS i) = getShiftWith shft (ssDown by) ctx i
Shift len out -> Context tm len -> Fin len -> tm out
getShiftWith shft by (ctx :< t) FZ = t `shft` ssDown by
getShiftWith shft by (ctx :< t) (FS i) = getShiftWith shft (ssDown by) ctx i
public export %inline
getShift : CanShift tm => Shift len out -> Context tm len -> Var len -> tm out
getShift : CanShift tm => Shift len out -> Context tm len -> Fin len -> tm out
getShift = getShiftWith (//)
public export %inline
getWith : (forall from, to. tm from -> Shift from to -> tm to) ->
Context tm len -> Var len -> tm len
Context tm len -> Fin len -> tm len
getWith shft = getShiftWith shft SZ
infixl 8 !!
public export %inline
(!!) : CanShift tm => Context tm len -> Var len -> tm len
(!!) : CanShift tm => Context tm len -> Fin len -> tm len
(!!) = getWith (//)
infixl 8 !!!
public export %inline
(!!!) : Context' tm len -> Var len -> tm
(!!!) : Context' tm len -> Fin len -> tm
(!!!) = getWith const
public export
find : Alternative f =>
(forall n. tm n -> Bool) -> Context tm len -> f (Var len)
(forall n. tm n -> Bool) -> Context tm len -> f (Fin len)
find p [<] = empty
find p (ctx :< x) = (guard (p x) $> VZ) <|> (VS <$> find p ctx)
find p (ctx :< x) = (guard (p x) $> FZ) <|> (FS <$> find p ctx)
export
@ -320,6 +331,14 @@ export %inline
where Show (Exists tm) where showPrec d t = showPrec d t.snd
export
implementation [ShowTelRelevant]
{n1 : Nat} -> ({n : Nat} -> Show (f n)) => Show (Telescope f n1 n2)
where
showPrec d = showPrec d . toSnocListRelevant
where Show (n : Nat ** f n) where showPrec d (_ ** t) = showPrec d t
parameters {opts : LayoutOpts} {0 tm : Nat -> Type}
(nameHL : HL)
(pterm : forall n. BContext n -> tm n -> Eff Pretty (Doc opts))

44
lib/Quox/FinExtra.idr Normal file
View file

@ -0,0 +1,44 @@
module Quox.FinExtra
import public Data.Fin
import Quox.Decidable
public export
data LT : Rel (Fin n) where
LTZ : FZ `LT` FS i
LTS : i `LT` j -> FS i `LT` FS j
%builtin Natural FinExtra.LT
%name FinExtra.LT lt
public export %inline
GT : Rel (Fin n)
GT = flip LT
export
Transitive (Fin n) LT where
transitive LTZ (LTS _) = LTZ
transitive (LTS p) (LTS q) = LTS $ transitive p q
export Uninhabited (i `FinExtra.LT` i) where uninhabited (LTS p) = uninhabited p
export Uninhabited (FS i `LT` FZ) where uninhabited _ impossible
public export
data Compare : Rel (Fin n) where
IsLT : (lt : i `LT` j) -> Compare i j
IsEQ : Compare i i
IsGT : (gt : i `GT` j) -> Compare i j
%name Compare cmp
export
compareS : Compare i j -> Compare (FS i) (FS j)
compareS (IsLT lt) = IsLT (LTS lt)
compareS IsEQ = IsEQ
compareS (IsGT gt) = IsGT (LTS gt)
export
compareP : (i, j : Fin n) -> Compare i j
compareP FZ FZ = IsEQ
compareP FZ (FS j) = IsLT LTZ
compareP (FS i) FZ = IsGT LTZ
compareP (FS i) (FS j) = compareS $ compareP i j

116
lib/Quox/Syntax/Dim.idr
View file

@ -1,15 +1,18 @@
module Quox.Syntax.Dim
import Quox.Loc
import Quox.Name
import Quox.Thin
import Quox.Syntax.Var
import Quox.Syntax.Subst
import Quox.Pretty
import Quox.Name
import Quox.Loc
import Quox.Context
import Decidable.Equality
import Control.Function
import Derive.Prelude
import Data.DPair
import Data.SnocVect
%default total
%language ElabReflection
@ -39,38 +42,48 @@ DecEq DimConst where
public export
data Dim : Nat -> Type where
K : DimConst -> Loc -> Dim d
B : Var d -> Loc -> Dim d
K : DimConst -> Loc -> Dim 0
B : Loc -> Dim 1
%name Dim.Dim p, q
%runElab deriveIndexed "Dim" [Eq, Ord, Show]
public export
DimT : Nat -> Type
DimT = Thinned Dim
public export %inline
KT : DimConst -> Loc -> DimT d
KT e loc = Th zero $ K e loc
||| `endsOr l r x p` returns `ends l r ε` if `p` is a constant ε, and
||| `x` otherwise.
public export
endsOr : Lazy a -> Lazy a -> Lazy a -> Dim n -> a
endsOr l r x (K e _) = ends l r e
endsOr l r x (B _ _) = x
endsOr l r x (B _) = x
export
Located (Dim d) where
(K _ loc).loc = loc
(B _ loc).loc = loc
(B loc).loc = loc
export
Relocatable (Dim d) where
setLoc loc (K e _) = K e loc
setLoc loc (B i _) = B i loc
setLoc loc (B _) = B loc
export
prettyDimConst : {opts : _} -> DimConst -> Eff Pretty (Doc opts)
prettyDimConst = hl Dim . text . ends "0" "1"
parameters {opts : LayoutOpts}
export
prettyDimConst : DimConst -> Eff Pretty (Doc opts)
prettyDimConst = hl Dim . text . ends "0" "1"
export
prettyDim : {opts : _} -> BContext d -> Dim d -> Eff Pretty (Doc opts)
prettyDim names (K e _) = prettyDimConst e
prettyDim names (B i _) = prettyDBind $ names !!! i
export
prettyDim : {d : Nat} -> BContext d -> DimT d -> Eff Pretty (Doc opts)
prettyDim names (Th _ (K e _)) = prettyDimConst e
prettyDim names (Th i (B _)) = prettyDBind $ names !!! i.fin
public export %inline
@ -83,57 +96,54 @@ DSubst : Nat -> Nat -> Type
DSubst = Subst Dim
public export FromVar Dim where fromVarLoc = B
-- public export FromVar Dim where fromVarLoc = B
export
CanShift Dim where
K e loc // _ = K e loc
B i loc // by = B (i // by) loc
-- export
-- CanShift Dim where
-- K e loc // _ = K e loc
-- B i loc // by = B (i // by) loc
export
export %inline FromVar Dim where var = B
export %inline
CanSubstSelf Dim where
K e loc // _ = K e loc
B i loc // th = getLoc th i loc
Th _ (K e loc) // _ = KT e loc
Th i (B loc) // th = get th i.fin
export Uninhabited (B i loc1 = K e loc2) where uninhabited _ impossible
export Uninhabited (K e loc1 = B i loc2) where uninhabited _ impossible
export Uninhabited (B loc1 = K e loc2) where uninhabited _ impossible
export Uninhabited (K e loc1 = B loc2) where uninhabited _ impossible
public export
data Eqv : Dim d1 -> Dim d2 -> Type where
EK : K e _ `Eqv` K e _
EB : i `Eqv` j -> B i _ `Eqv` B j _
-- public export
-- data Eqv : Dim d1 -> Dim d2 -> Type where
-- EK : K e _ `Eqv` K e _
-- EB : i `Eqv` j -> B i _ `Eqv` B j _
export Uninhabited (K e l1 `Eqv` B i l2) where uninhabited _ impossible
export Uninhabited (B i l1 `Eqv` K e l2) where uninhabited _ impossible
-- export Uninhabited (K e l1 `Eqv` B i l2) where uninhabited _ impossible
-- export Uninhabited (B i l1 `Eqv` K e l2) where uninhabited _ impossible
export
injectiveB : B i loc1 `Eqv` B j loc2 -> i `Eqv` j
injectiveB (EB e) = e
-- export
-- injectiveB : B i loc1 `Eqv` B j loc2 -> i `Eqv` j
-- injectiveB (EB e) = e
export
injectiveK : K e loc1 `Eqv` K f loc2 -> e = f
injectiveK EK = Refl
-- export
-- injectiveK : K e loc1 `Eqv` K f loc2 -> e = f
-- injectiveK EK = Refl
public export
decEqv : Dec2 Dim.Eqv
decEqv (K e _) (K f _) = case decEq e f of
Yes Refl => Yes EK
No n => No $ n . injectiveK
decEqv (B i _) (B j _) = case decEqv i j of
Yes y => Yes $ EB y
No n => No $ \(EB y) => n y
decEqv (B _ _) (K _ _) = No absurd
decEqv (K _ _) (B _ _) = No absurd
-- public export
-- decEqv : Dec2 Dim.Eqv
-- decEqv (K e _) (K f _) = case decEq e f of
-- Yes Refl => Yes EK
-- No n => No $ n . injectiveK
-- decEqv (B i _) (B j _) = case decEqv i j of
-- Yes y => Yes $ EB y
-- No n => No $ \(EB y) => n y
-- decEqv (B _ _) (K _ _) = No absurd
-- decEqv (K _ _) (B _ _) = No absurd
||| abbreviation for a bound variable like `BV 4` instead of
||| `B (VS (VS (VS (VS VZ))))`
public export %inline
BV : (i : Nat) -> (0 _ : LT i d) => (loc : Loc) -> Dim d
BV i loc = B (V i) loc
export
weakD : (by : Nat) -> Dim d -> Dim (by + d)
weakD by p = p // shift by
BV : (i : Fin d) -> (loc : Loc) -> DimT d
BV i loc = Th (one' i) $ B loc

225
lib/Quox/Syntax/DimEq.idr
View file

@ -6,11 +6,14 @@ import public Quox.Syntax.Subst
import public Quox.Context
import Quox.Pretty
import Quox.Name
import Quox.Thin
import Quox.FinExtra
import Data.Maybe
import Data.Nat
import Data.DPair
import Data.Fun.Graph
import Data.SnocVect
import Decidable.Decidable
import Decidable.Equality
import Derive.Prelude
@ -21,7 +24,7 @@ import Derive.Prelude
public export
DimEq' : Nat -> Type
DimEq' = Context (Maybe . Dim)
DimEq' = Context (Maybe . DimT)
public export
@ -29,7 +32,12 @@ data DimEq : Nat -> Type where
ZeroIsOne : DimEq d
C : (eqs : DimEq' d) -> DimEq d
%name DimEq eqs
%runElab deriveIndexed "DimEq" [Eq, Ord, Show]
%runElab deriveIndexed "DimEq" [Eq]
export
Show (DimEq d) where
showPrec d ZeroIsOne = "ZeroIsOne"
showPrec d (C eq') = showCon d "C" $ showArg eq' @{ShowTelRelevant}
public export
@ -72,7 +80,7 @@ toMaybe (Just x) = Just x
export
fromGround' : Context' DimConst d -> DimEq' d
fromGround' [<] = [<]
fromGround' (ctx :< e) = fromGround' ctx :< Just (K e noLoc)
fromGround' (ctx :< e) = fromGround' ctx :< Just (KT e noLoc)
export
fromGround : Context' DimConst d -> DimEq d
@ -94,39 +102,40 @@ new = C new'
public export %inline
get' : DimEq' d -> Var d -> Maybe (Dim d)
get' : DimEq' d -> Fin d -> Maybe (DimT d)
get' = getWith $ \p, by => map (// by) p
public export %inline
getVar : DimEq' d -> Var d -> Loc -> Dim d
getVar eqs i loc = fromMaybe (B i loc) $ get' eqs i
public export %inline
getShift' : Shift len out -> DimEq' len -> Var len -> Maybe (Dim out)
getShift' : Shift len out -> DimEq' len -> Fin len -> Maybe (DimT out)
getShift' = getShiftWith $ \p, by => map (// by) p
public export %inline
get : DimEq' d -> Dim d -> Dim d
get _ (K e loc) = K e loc
get eqs (B i loc) = getVar eqs i loc
get : {d : Nat} -> DimEq' d -> DimT d -> DimT d
get eqs p@(Th _ (K {})) = p
get eqs p@(Th i (B _)) = fromMaybe p $ get' eqs i.fin
public export %inline
equal : DimEq d -> (p, q : Dim d) -> Bool
equal : {d : Nat} -> DimEq d -> (p, q : DimT d) -> Bool
equal ZeroIsOne p q = True
equal (C eqs) p q = get eqs p == get eqs q
infixl 7 :<?
export %inline
(:<?) : DimEq d -> Maybe (Dim d) -> DimEq (S d)
(:<?) : {d : Nat} -> DimEq d -> Maybe (DimT d) -> DimEq (S d)
ZeroIsOne :<? d = ZeroIsOne
C eqs :<? d = C $ eqs :< map (get eqs) d
private %inline
ifVar : Var d -> Dim d -> Maybe (Dim d) -> Maybe (Dim d)
ifVar i p = map $ \q => if q == B i noLoc then p else q
isVar : {d : Nat} -> Fin d -> DimT d -> Bool
isVar i (Th j (B _)) = i == j.fin
isVar i (Th _ (K {})) = False
private %inline
ifVar : {d : Nat} -> Fin d -> DimT d -> Maybe (DimT d) -> Maybe (DimT d)
ifVar i p = map $ \q => if isVar i q then p else q
-- (using decEq instead of (==) because of the proofs below)
private %inline
@ -135,43 +144,45 @@ checkConst e f eqs = if isYes $ e `decEq` f then C eqs else ZeroIsOne
export
setConst : Var d -> DimConst -> Loc -> DimEq' d -> DimEq d
setConst VZ e loc (eqs :< Nothing) =
C $ eqs :< Just (K e loc)
setConst VZ e _ (eqs :< Just (K f loc)) =
checkConst e f $ eqs :< Just (K f loc)
setConst VZ e loc (eqs :< Just (B i _)) =
setConst i e loc eqs :<? Just (K e loc)
setConst (VS i) e loc (eqs :< p) =
setConst i e loc eqs :<? ifVar i (K e loc) p
setConst : {d : Nat} -> Fin d -> DimConst -> Loc -> DimEq' d -> DimEq d
setConst FZ e loc (eqs :< Nothing) =
C $ eqs :< Just (KT e loc)
setConst FZ e _ (eqs :< Just (Th _ (K f loc))) =
checkConst e f $ eqs :< Just (KT f loc)
setConst FZ e loc (eqs :< Just (Th j (B _))) =
setConst j.fin e loc eqs :<? Just (KT e loc)
setConst (FS i) e loc (eqs :< p) =
setConst i e loc eqs :<? ifVar i (KT e loc) p
mutual
private
setVar' : (i, j : Var d) -> (0 _ : i `LT` j) -> Loc -> DimEq' d -> DimEq d
setVar' VZ (VS i) LTZ loc (eqs :< Nothing) =
C eqs :<? Just (B i loc)
setVar' VZ (VS i) LTZ loc (eqs :< Just (K e eloc)) =
setConst i e loc eqs :<? Just (K e eloc)
setVar' VZ (VS i) LTZ loc (eqs :< Just (B j jloc)) =
setVar i j loc jloc eqs :<? Just (if j > i then B j jloc else B i loc)
setVar' (VS i) (VS j) (LTS lt) loc (eqs :< p) =
setVar' i j lt loc eqs :<? ifVar i (B j loc) p
setVar' : {d : Nat} ->
(i, j : Fin d) -> (0 _ : i `LT` j) -> Loc -> DimEq' d -> DimEq d
setVar' FZ (FS i) LTZ loc (eqs :< Nothing) =
C eqs :<? Just (BV i loc)
setVar' FZ (FS i) LTZ loc (eqs :< Just (Th _ (K e eloc))) =
setConst i e loc eqs :<? Just (KT e eloc)
setVar' FZ (FS i) LTZ loc (eqs :< Just (Th j (B jloc))) =
let j = j.fin in
setVar i j loc jloc eqs :<? Just (if j > i then BV j jloc else BV i loc)
setVar' (FS i) (FS j) (LTS lt) loc (eqs :< p) =
setVar' i j lt loc eqs :<? ifVar i (BV j loc) p
export %inline
setVar : (i, j : Var d) -> Loc -> Loc -> DimEq' d -> DimEq d
setVar i j li lj eqs with (compareP i j) | (compare i.nat j.nat)
setVar i j li lj eqs | IsLT lt | LT = setVar' i j lt lj eqs
setVar i i li lj eqs | IsEQ | EQ = C eqs
setVar i j li lj eqs | IsGT gt | GT = setVar' j i gt li eqs
setVar : {d : Nat} -> (i, j : Fin d) -> Loc -> Loc -> DimEq' d -> DimEq d
setVar i j li lj eqs with (compareP i j)
setVar i j li lj eqs | IsLT lt = setVar' i j lt lj eqs
setVar i i li lj eqs | IsEQ = C eqs
setVar i j li lj eqs | IsGT gt = setVar' j i gt li eqs
export %inline
set : (p, q : Dim d) -> DimEq d -> DimEq d
set : {d : Nat} -> (p, q : DimT d) -> DimEq d -> DimEq d
set _ _ ZeroIsOne = ZeroIsOne
set (K e eloc) (K f floc) (C eqs) = checkConst e f eqs
set (K e eloc) (B i iloc) (C eqs) = setConst i e eloc eqs
set (B i iloc) (K e eloc) (C eqs) = setConst i e eloc eqs
set (B i iloc) (B j jloc) (C eqs) = setVar i j iloc jloc eqs
set (Th _ (K e _)) (Th _ (K f _)) (C eqs) = checkConst e f eqs
set (Th _ (K e el)) (Th j (B _)) (C eqs) = setConst j.fin e el eqs
set (Th i (B _)) (Th _ (K e el)) (C eqs) = setConst i.fin e el eqs
set (Th i (B il)) (Th j (B jl)) (C eqs) = setVar i.fin j.fin il jl eqs
public export %inline
@ -179,97 +190,99 @@ Split : Nat -> Type
Split d = (DimEq' d, DSubst (S d) d)
export %inline
split1 : DimConst -> Loc -> DimEq' (S d) -> Maybe (Split d)
split1 e loc eqs = case setConst VZ e loc eqs of
split1 : {d : Nat} -> DimConst -> Loc -> DimEq' (S d) -> Maybe (Split d)
split1 e loc eqs = case setConst 0 e loc eqs of
ZeroIsOne => Nothing
C (eqs :< _) => Just (eqs, K e loc ::: id)
C (eqs :< _) => Just (eqs, id (B loc) :< KT e loc)
export %inline
split : Loc -> DimEq' (S d) -> List (Split d)
split : {d : Nat} -> Loc -> DimEq' (S d) -> List (Split d)
split loc eqs = toList (split1 Zero loc eqs) <+> toList (split1 One loc eqs)
export
splits' : Loc -> DimEq' d -> List (DSubst d 0)
splits' _ [<] = [id]
splits' : {d : Nat} -> Loc -> DimEq' d -> List (DSubst d 0)
splits' _ [<] = [[<]]
splits' loc eqs@(_ :< _) =
[th . ph | (eqs', th) <- split loc eqs, ph <- splits' loc eqs']
||| the Loc is put into each of the DimConsts
export %inline
splits : Loc -> DimEq d -> List (DSubst d 0)
splits : {d : Nat} -> Loc -> DimEq d -> List (DSubst d 0)
splits _ ZeroIsOne = []
splits loc (C eqs) = splits' loc eqs
private
0 newGetShift : (d : Nat) -> (i : Var d) -> (by : Shift d d') ->
getShift' by (new' {d}) i = Nothing
newGetShift (S d) VZ by = Refl
newGetShift (S d) (VS i) by = newGetShift d i (ssDown by)
-- private
-- 0 newGetShift : (d : Nat) -> (i : Fin d) -> (by : Shift d d') ->
-- getShift' by (new' {d}) i = Nothing
-- newGetShift (S d) FZ by = Refl
-- newGetShift (S d) (FS i) by = newGetShift d i (ssDown by)
export
0 newGet' : (d : Nat) -> (i : Var d) -> get' (new' {d}) i = Nothing
newGet' d i = newGetShift d i SZ
-- export
-- 0 newGet' : (d : Nat) -> (i : Fin d) -> get' (new' {d}) i = Nothing
-- newGet' d i = newGetShift d i SZ
export
0 newGet : (d : Nat) -> (p : Dim d) -> get (new' {d}) p = p
newGet d (K e _) = Refl
newGet d (B i _) = rewrite newGet' d i in Refl
-- export
-- 0 newGet : (d : Nat) -> (p : Dim d) -> get (new' {d}) p = p
-- newGet d (K e _) = Refl
-- newGet d (B i _) = rewrite newGet' d i in Refl
export
0 setSelf : (p : Dim d) -> (eqs : DimEq d) -> set p p eqs = eqs
setSelf p ZeroIsOne = Refl
setSelf (K Zero _) (C eqs) = Refl
setSelf (K One _) (C eqs) = Refl
setSelf (B i _) (C eqs) with (compareP i i) | (compare i.nat i.nat)
_ | IsLT lt | LT = absurd lt
_ | IsEQ | EQ = Refl
_ | IsGT gt | GT = absurd gt
-- export
-- 0 setSelf : (p : Dim d) -> (eqs : DimEq d) -> set p p eqs = eqs
-- setSelf p ZeroIsOne = Refl
-- setSelf (K Zero _) (C eqs) = Refl
-- setSelf (K One _) (C eqs) = Refl
-- setSelf (B i _) (C eqs) with (compareP i i) | (compare i.nat i.nat)
-- _ | IsLT lt | LT = absurd lt
-- _ | IsEQ | EQ = Refl
-- _ | IsGT gt | GT = absurd gt
private
prettyDVars : {opts : _} -> BContext d -> Eff Pretty (SnocList (Doc opts))
prettyDVars = traverse prettyDBind . toSnocList'
parameters {opts : LayoutOpts}
private
prettyDVars : {d : Nat} -> BContext d -> Eff Pretty (SnocList (Doc opts))
prettyDVars = traverse prettyDBind . toSnocList'
private
prettyCst : {opts : _} -> BContext d -> Dim d -> Dim d -> Eff Pretty (Doc opts)
prettyCst dnames p q =
hsep <$> sequence [prettyDim dnames p, cstD, prettyDim dnames q]
private
prettyCst : {d : Nat} -> BContext d -> DimT d -> DimT d -> Eff Pretty (Doc opts)
prettyCst dnames p q =
hsep <$> sequence [prettyDim dnames p, cstD, prettyDim dnames q]
private
prettyCsts : {opts : _} -> BContext d -> DimEq' d ->
Eff Pretty (SnocList (Doc opts))
prettyCsts [<] [<] = pure [<]
prettyCsts dnames (eqs :< Nothing) = prettyCsts (tail dnames) eqs
prettyCsts dnames (eqs :< Just q) =
[|prettyCsts (tail dnames) eqs :< prettyCst dnames (BV 0 noLoc) (weakD 1 q)|]
private
prettyCsts : {d : Nat} -> BContext d -> DimEq' d ->
Eff Pretty (SnocList (Doc opts))
prettyCsts [<] [<] = pure [<]
prettyCsts dnames (eqs :< Nothing) = prettyCsts (tail dnames) eqs
prettyCsts dnames (eqs :< Just q) =
[|prettyCsts (tail dnames) eqs :<
prettyCst dnames (BV 0 noLoc) (weak 1 q)|]
export
prettyDimEq' : {opts : _} -> BContext d -> DimEq' d -> Eff Pretty (Doc opts)
prettyDimEq' dnames eqs = do
vars <- prettyDVars dnames
eqs <- prettyCsts dnames eqs
let prec = if length vars <= 1 && null eqs then Arg else Outer
parensIfM prec $ fillSeparateTight !commaD $ toList vars ++ toList eqs
export
prettyDimEq' : {d : Nat} -> BContext d -> DimEq' d -> Eff Pretty (Doc opts)
prettyDimEq' dnames eqs = do
vars <- prettyDVars dnames
eqs <- prettyCsts dnames eqs
let prec = if length vars <= 1 && null eqs then Arg else Outer
parensIfM prec $ fillSeparateTight !commaD $ toList vars ++ toList eqs
export
prettyDimEq : {opts : _} -> BContext d -> DimEq d -> Eff Pretty (Doc opts)
prettyDimEq dnames ZeroIsOne = do
vars <- prettyDVars dnames
cst <- prettyCst [<] (K Zero noLoc) (K One noLoc)
pure $ separateTight !commaD $ vars :< cst
prettyDimEq dnames (C eqs) = prettyDimEq' dnames eqs
export
prettyDimEq : {d : Nat} -> BContext d -> DimEq d -> Eff Pretty (Doc opts)
prettyDimEq dnames ZeroIsOne = do
vars <- prettyDVars dnames
cst <- prettyCst [<] (KT Zero noLoc) (KT One noLoc)
pure $ separateTight !commaD $ vars :< cst
prettyDimEq dnames (C eqs) = prettyDimEq' dnames eqs
public export
wf' : DimEq' d -> Bool
wf' [<] = True
wf' (eqs :< Nothing) = wf' eqs
wf' (eqs :< Just (K e _)) = wf' eqs
wf' (eqs :< Just (B i _)) = isNothing (get' eqs i) && wf' eqs
wf' : {d : Nat} -> DimEq' d -> Bool
wf' [<] = True
wf' (eqs :< Nothing) = wf' eqs
wf' (eqs :< Just (Th _ (K {}))) = wf' eqs
wf' (eqs :< Just (Th i (B _))) = isNothing (get' eqs i.fin) && wf' eqs
public export
wf : DimEq d -> Bool
wf : {d : Nat} -> DimEq d -> Bool
wf ZeroIsOne = True
wf (C eqs) = wf' eqs

14
lib/Quox/Syntax/Shift.idr
View file

@ -1,9 +1,11 @@
module Quox.Syntax.Shift
import public Quox.Syntax.Var
import public Quox.Thin
import Data.Nat
import Data.So
import Data.DPair
%default total
@ -220,3 +222,15 @@ namespace CanShift
public export %inline
[Const] CanShift (\_ => a) where x // _ = x
export
shiftOPE : {mask : Nat} -> (0 ope : OPE m n mask) ->
Shift n n' -> Subset Nat (OPE m n')
shiftOPE ope SZ = Element _ ope
shiftOPE ope (SS by) =
let Element _ ope = shiftOPE ope by in Element _ $ drop ope
export
CanShift (Thinned f) where
Th ope tm // by = Th (shiftOPE ope by).snd tm

233
lib/Quox/Syntax/Subst.idr
View file

@ -1,10 +1,9 @@
module Quox.Syntax.Subst
import public Quox.Syntax.Shift
import Quox.Syntax.Var
import Quox.Name
import Quox.Thin
import Quox.Loc
import Data.Nat
import Data.DPair
import Data.List
import Data.SnocVect
import Derive.Prelude
@ -14,149 +13,159 @@ import Derive.Prelude
public export
data Subst : (Nat -> Type) -> Nat -> Nat -> Type where
Shift : Shift from to -> Subst env from to
(:::) : (t : Lazy (env to)) -> Subst env from to -> Subst env (S from) to
%name Subst th, ph, ps
Subst : (Nat -> Type) -> Nat -> Nat -> Type
Subst env from to = SnocVect from (Lazy (Thinned env to))
infixr 7 !:::
||| in case the automatic laziness insertion gets confused
public export
(!:::) : env to -> Subst env from to -> Subst env (S from) to
t !::: ts = t ::: ts
Subst2 : (Nat -> Nat -> Type) -> Nat -> Nat -> Nat -> Type
Subst2 env d from to = SnocVect from (Lazy (Thinned2 env d to))
private
Repr : (Nat -> Type) -> Nat -> Type
Repr f to = (List (f to), Nat)
private
repr : Subst f from to -> Repr f to
repr (Shift by) = ([], by.nat)
repr (t ::: th) = let (ts, i) = repr th in (t::ts, i)
public export
get : Subst env f t -> Fin f -> Thinned env t
get (sx :< x) FZ = x
get (sx :< x) (FS i) = get sx i
export Eq (f to) => Eq (Subst f from to) where (==) = (==) `on` repr
export Ord (f to) => Ord (Subst f from to) where compare = compare `on` repr
export Show (f to) => Show (Subst f from to) where show = show . repr
public export
interface FromVar (0 term : Nat -> Type) where
var : Loc -> term 1
public export
0 FromVar2 : (Nat -> Nat -> Type) -> Type
FromVar2 t = FromVar (t 0)
public export
varT : FromVar term => Fin n -> Loc -> Thinned term n
varT i loc = Th (one' i) (var loc)
public export
varT2 : FromVar2 term => Fin n -> Loc -> Thinned2 term d n
varT2 i loc = Th2 zero (one' i) (var loc)
infixl 8 //
namespace CanSubstSelf
public export
interface FromVar term => CanSubstSelf term where
(//) : {f : Nat} -> Thinned term f -> Subst term f t -> Thinned term t
namespace CanSubstSelf2
public export
interface FromVar2 term => CanSubstSelf2 term where
(//) : {f : Nat} -> Thinned2 term d f ->
Subst2 term d f t -> Thinned2 term d t
public export
interface FromVar term => CanSubstSelf term where
(//) : term from -> Lazy (Subst term from to) -> term to
(.) : {mid : Nat} -> CanSubstSelf f =>
Subst f from mid -> Subst f mid to -> Subst f from to
th . ph = map (\(Delay x) => x // ph) th
infixr 9 .%
public export
(.%) : {mid : Nat} -> CanSubstSelf2 f =>
Subst2 f d from mid -> Subst2 f d mid to -> Subst2 f d from to
th .% ph = map (\(Delay x) => x // ph) th
public export
getLoc : FromVar term => Subst term from to -> Var from -> Loc -> term to
getLoc (Shift by) i loc = fromVarLoc (shift by i) loc
getLoc (t ::: th) VZ _ = t
getLoc (t ::: th) (VS i) loc = getLoc th i loc
tabulate : (n : Nat) -> SnocVect n (Fin n)
tabulate n = go n id where
go : (n : Nat) -> (Fin n -> Fin n') -> SnocVect n (Fin n')
go 0 f = [<]
go (S n) f = go n (f . FS) :< f FZ
public export
CanSubstSelf Var where
i // Shift by = shift by i
VZ // (t ::: th) = t
VS i // (t ::: th) = i // th
public export %inline
shift : (by : Nat) -> Subst env from (by + from)
shift by = Shift $ fromNat by
public export %inline
shift0 : (by : Nat) -> Subst env 0 by
shift0 by = rewrite sym $ plusZeroRightNeutral by in Shift $ fromNat by
id : FromVar term => {n : Nat} -> (under : Nat) -> Loc ->
Subst term n (n + under)
id under loc =
map (\i => delay $ varT (weakenN under i) loc) (tabulate n)
public export
(.) : CanSubstSelf f => Subst f from mid -> Subst f mid to -> Subst f from to
Shift by . Shift bz = Shift $ by . bz
Shift SZ . ph = ph
Shift (SS by) . (t ::: th) = Shift by . th
(t ::: th) . ph = (t // ph) ::: (th . ph)
id2 : FromVar2 term => {n : Nat} -> Loc -> Subst2 term d n n
id2 loc = map (\i => delay $ varT2 i loc) $ tabulate n
public export %inline
id : Subst f n n
id = shift 0
public export
traverse : Applicative m =>
(f to -> m (g to)) -> Subst f from to -> m (Subst g from to)
traverse f (Shift by) = pure $ Shift by
traverse f (t ::: th) = [|f t !::: traverse f th|]
-- not in terms of traverse because this map can maintain laziness better
public export
map : (f to -> g to) -> Subst f from to -> Subst g from to
map f (Shift by) = Shift by
map f (t ::: th) = f t ::: map f th
public export %inline
push : CanSubstSelf f => Subst f from to -> Subst f (S from) (S to)
push th = fromVar VZ ::: (th . shift 1)
-- [fixme] a better way to do this?
public export
pushN : CanSubstSelf f => (s : Nat) ->
Subst f from to -> Subst f (s + from) (s + to)
pushN 0 th = th
pushN (S s) th =
rewrite plusSuccRightSucc s from in
rewrite plusSuccRightSucc s to in
pushN s $ fromVar VZ ::: (th . shift 1)
public export
drop1 : Subst f (S from) to -> Subst f from to
drop1 (Shift by) = Shift $ ssDown by
drop1 (t ::: th) = th
public export
fromSnocVect : SnocVect s (f n) -> Subst f (s + n) n
fromSnocVect [<] = id
fromSnocVect (xs :< x) = x ::: fromSnocVect xs
public export %inline
one : f n -> Subst f (S n) n
one x = fromSnocVect [< x]
||| whether two substitutions with the same codomain have the same shape
||| (the same number of terms and the same shift at the end). if so, they
||| also have the same domain
export
cmpShape : Subst env from1 to -> Subst env from2 to ->
Either Ordering (from1 = from2)
cmpShape (Shift by) (Shift bz) = cmpLen by bz
cmpShape (Shift _) (_ ::: _) = Left LT
cmpShape (_ ::: _) (Shift _) = Left GT
cmpShape (_ ::: th) (_ ::: ph) = cong S <$> cmpShape th ph
select : {n, mask : Nat} -> (0 ope : OPE m n mask) ->
SnocVect n a -> SnocVect m a
select ope sx with %syntactic (view ope)
select _ [<] | StopV = [<]
select _ (sx :< x) | DropV _ ope = select ope sx
select _ (sx :< x) | KeepV _ ope = select ope sx :< x
export
opeToFins : {n, mask : Nat} ->
(0 ope : OPE m n mask) -> SnocVect m (Fin n)
opeToFins ope = select ope $ tabulate n
export
shift : FromVar term => {from : Nat} ->
(n : Nat) -> Loc -> Subst term from (n + from)
shift n loc = map (\i => delay $ varT (shift n i) loc) $ tabulate from
public export
pushN : CanSubstSelf term => {to : Nat} -> (by : Nat) ->
Subst term from to -> Loc -> Subst term (by + from) (by + to)
pushN by th loc =
rewrite plusCommutative by from in
(th . shift by loc) ++ id to loc
public export %inline
push : CanSubstSelf f => {to : Nat} ->
Subst f from to -> Loc -> Subst f (S from) (S to)
push = pushN 1
public export %inline
one : Thinned f n -> Subst f 1 n
one x = [< x]
||| whether two substitutions with the same codomain have the same domain
export
cmpShape : SnocVect m a -> SnocVect n a -> Either Ordering (m = n)
cmpShape [<] [<] = Right Refl
cmpShape [<] (sx :< _) = Left LT
cmpShape (sx :< _) [<] = Left GT
cmpShape (sx :< _) (sy :< _) = cong S <$> cmpShape sx sy
public export
record WithSubst tm env n where
constructor Sub
term : tm from
subst : Lazy (Subst env from n)
subst : Subst env from n
{-
export
(Eq (env n), forall n. Eq (tm n)) => Eq (WithSubst tm env n) where
(forall n. Eq (env n), forall n. Eq (tm n)) =>
Eq (WithSubst tm env n) where
Sub t1 s1 == Sub t2 s2 =
case cmpShape s1 s2 of
Left _ => False
Right Refl => t1 == t2 && s1 == s2
Right Refl =>
t1 == t2 && concat @{All} (zipWith ((==) `on` force) s1 s2)
export
(Ord (env n), forall n. Ord (tm n)) => Ord (WithSubst tm env n) where
(forall n. Ord (env n), forall n. Ord (tm n)) =>
Ord (WithSubst tm env n) where
Sub t1 s1 `compare` Sub t2 s2 =
case cmpShape s1 s2 of
Left o => o
Right Refl => compare (t1, s1) (t2, s2)
Right Refl =>
compare t1 t2 <+> concat (zipWith (compare `on` force) s1 s2)
export %hint
ShowWithSubst : (Show (env n), forall n. Show (tm n)) =>
ShowWithSubst : {n : Nat} ->
(forall n. Show (env n), forall n. Show (tm n)) =>
Show (WithSubst tm env n)
ShowWithSubst = deriveShow
ShowWithSubst = deriveShow where
Show (Lazy (Thinned env n)) where showPrec d = showPrec d . force
-}
public export
record WithSubst2 tm env d n where
constructor Sub2
term : tm d from
subst : Subst2 env d from n

12
lib/Quox/Syntax/Term/Base.idr
View file

@ -129,7 +129,7 @@ data Term where
E : Elim d n -> Term d n
||| term closure/suspended substitution
CloT : WithSubst (Term d) (Elim d) n -> Term d n
CloT : WithSubst2 Term Elim d n -> Term d n
||| dimension closure/suspended substitution
DCloT : WithSubst (\d => Term d n) Dim d -> Term d n
@ -194,7 +194,7 @@ data Elim where
] d n -> Loc -> Elim d n
||| term closure/suspended substitution
CloE : WithSubst (Elim d) (Elim d) n -> Elim d n
CloE : WithSubst2 Elim Elim d n -> Elim d n
||| dimension closure/suspended substitution
DCloE : WithSubst (\d => Elim d n) Dim d -> Elim d n
@ -325,7 +325,7 @@ Located (Elim d n) where
(Coe _ loc).loc = loc
(Comp _ loc).loc = loc
(TypeCase _ loc).loc = loc
(CloE (Sub e _)).loc = e.loc
(CloE (Sub2 e _)).loc = e.loc
(DCloE (Sub e _)).loc = e.loc
export
@ -345,7 +345,7 @@ Located (Term d n) where
(BOX _ _ loc).loc = loc
(Box _ loc).loc = loc
(E e).loc = e.loc
(CloT (Sub t _)).loc = t.loc
(CloT (Sub2 t _)).loc = t.loc
(DCloT (Sub t _)).loc = t.loc
@ -363,7 +363,7 @@ Relocatable (Elim d n) where
setLoc loc (Coe ts _) = Coe ts loc
setLoc loc (Comp ts _) = Comp ts loc
setLoc loc (TypeCase ts _) = TypeCase ts loc
setLoc loc (CloE (Sub term subst)) = CloE $ Sub (setLoc loc term) subst
setLoc loc (CloE (Sub2 term subst)) = CloE $ Sub2 (setLoc loc term) subst
setLoc loc (DCloE (Sub term subst)) = DCloE $ Sub (setLoc loc term) subst
export
@ -383,5 +383,5 @@ Relocatable (Term d n) where
setLoc loc (BOX qty ty _) = BOX qty ty loc
setLoc loc (Box val _) = Box val loc
setLoc loc (E e) = E $ setLoc loc e
setLoc loc (CloT (Sub term subst)) = CloT $ Sub (setLoc loc term) subst
setLoc loc (CloT (Sub2 term subst)) = CloT $ Sub2 (setLoc loc term) subst
setLoc loc (DCloT (Sub term subst)) = DCloT $ Sub (setLoc loc term) subst

4
lib/Quox/Syntax/Term/Pretty.idr
View file

@ -18,11 +18,11 @@ prettyUniverse = hl Universe . text . show
export
prettyTerm : {opts : _} -> BContext d -> BContext n -> Term d n ->
prettyTerm : {opts : _} -> BContext d -> BContext n -> TermT d n ->
Eff Pretty (Doc opts)
export
prettyElim : {opts : _} -> BContext d -> BContext n -> Elim d n ->
prettyElim : {opts : _} -> BContext d -> BContext n -> ElimT d n ->
Eff Pretty (Doc opts)
private

796
lib/Quox/Syntax/Term/Subst.idr
View file

@ -2,374 +2,462 @@ module Quox.Syntax.Term.Subst
import Quox.No
import Quox.Syntax.Term.Base
import Quox.Syntax.Term.Tighten
import Quox.Syntax.Subst
import Data.SnocVect
import Data.Singleton
%default total
namespace CanDSubst
public export
interface CanDSubst (0 tm : TermLike) where
(//) : tm d1 n -> Lazy (DSubst d1 d2) -> tm d2 n
||| does the minimal reasonable work:
||| - deletes the closure around an atomic constant like `TYPE`
||| - deletes an identity substitution
||| - composes (lazily) with an existing top-level dim-closure
||| - otherwise, wraps in a new closure
export
CanDSubst Term where
s // Shift SZ = s
TYPE l loc // _ = TYPE l loc
DCloT (Sub s ph) // th = DCloT $ Sub s $ ph . th
s // th = DCloT $ Sub s th
infixl 8 ///
private
subDArgs : Elim d1 n -> DSubst d1 d2 -> Elim d2 n
subDArgs (DApp f d loc) th = DApp (subDArgs f th) (d // th) loc
subDArgs e th = DCloE $ Sub e th
parameters {0 f : Nat -> Nat -> Type}
private
th0 : f 0 0 -> Thinned2 f d n
th0 = Th2 zero zero
||| does the minimal reasonable work:
||| - deletes the closure around a term variable
||| - deletes an identity substitution
||| - composes (lazily) with an existing top-level dim-closure
||| - immediately looks up bound variables in a
||| top-level sequence of dimension applications
||| - otherwise, wraps in a new closure
export
CanDSubst Elim where
e // Shift SZ = e
F x u loc // _ = F x u loc
B i loc // _ = B i loc
e@(DApp {}) // th = subDArgs e th
DCloE (Sub e ph) // th = DCloE $ Sub e $ ph . th
e // th = DCloE $ Sub e th
private
th1 : {d, n : Nat} -> f d n -> Thinned2 f d n
th1 = Th2 id' id'
namespace DSubst.ScopeTermN
export %inline
(//) : ScopeTermN s d1 n -> Lazy (DSubst d1 d2) ->
ScopeTermN s d2 n
S ns (Y body) // th = S ns $ Y $ body // th
S ns (N body) // th = S ns $ N $ body // th
private dsubTerm : {d1, d2, n : Nat} -> Term d1 n -> DSubst d1 d2 -> TermT d2 n
private dsubElim : {d1, d2, n : Nat} -> Elim d1 n -> DSubst d1 d2 -> ElimT d2 n
namespace DSubst.DScopeTermN
export %inline
(//) : {s : Nat} ->
DScopeTermN s d1 n -> Lazy (DSubst d1 d2) ->
DScopeTermN s d2 n
S ns (Y body) // th = S ns $ Y $ body // pushN s th
S ns (N body) // th = S ns $ N $ body // th
dsubTerm (TYPE l loc) th = th0 $ TYPE l loc
dsubTerm (Enum strs loc) th = th0 $ Enum strs loc
dsubTerm (Tag str loc) th = th0 $ Tag str loc
dsubTerm (Nat loc) th = th0 $ Nat loc
dsubTerm (Zero loc) th = th0 $ Zero loc
dsubTerm (E e) th =
let Th2 dope tope e' = dsubElim e th in
Th2 dope tope $ E e'
dsubTerm (DCloT (Sub t ph)) th = th1 $ DCloT $ Sub t $ ph . th
dsubTerm t th = th1 $ DCloT $ Sub t th
export %inline FromVar (Elim d) where fromVarLoc = B
export %inline FromVar (Term d) where fromVarLoc = E .: fromVar
||| does the minimal reasonable work:
||| - deletes the closure around a *free* name
||| - deletes an identity substitution
||| - composes (lazily) with an existing top-level closure
||| - immediately looks up a bound variable
||| - otherwise, wraps in a new closure
export
CanSubstSelf (Elim d) where
F x u loc // _ = F x u loc
B i loc // th = getLoc th i loc
CloE (Sub e ph) // th = assert_total CloE $ Sub e $ ph . th
e // th = case force th of
Shift SZ => e
th => CloE $ Sub e th
namespace CanTSubst
public export
interface CanTSubst (0 tm : TermLike) where
(//) : tm d n1 -> Lazy (TSubst d n1 n2) -> tm d n2
||| does the minimal reasonable work:
||| - deletes the closure around an atomic constant like `TYPE`
||| - deletes an identity substitution
||| - composes (lazily) with an existing top-level closure
||| - goes inside `E` in case it is a simple variable or something
||| - otherwise, wraps in a new closure
export
CanTSubst Term where
TYPE l loc // _ = TYPE l loc
E e // th = E $ e // th
CloT (Sub s ph) // th = CloT $ Sub s $ ph . th
s // th = case force th of
Shift SZ => s
th => CloT $ Sub s th
namespace ScopeTermN
export %inline
(//) : {s : Nat} ->
ScopeTermN s d n1 -> Lazy (TSubst d n1 n2) ->
ScopeTermN s d n2
S ns (Y body) // th = S ns $ Y $ body // pushN s th
S ns (N body) // th = S ns $ N $ body // th
namespace DScopeTermN
export %inline
(//) : {s : Nat} ->
DScopeTermN s d n1 -> Lazy (TSubst d n1 n2) -> DScopeTermN s d n2
S ns (Y body) // th = S ns $ Y $ body // map (// shift s) th
S ns (N body) // th = S ns $ N $ body // th
export %inline CanShift (Term d) where s // by = s // Shift by
export %inline CanShift (Elim d) where e // by = e // Shift by
export %inline
{s : Nat} -> CanShift (ScopeTermN s d) where
b // by = b // Shift by
export %inline
comp : DSubst d1 d2 -> TSubst d1 n1 mid -> TSubst d2 mid n2 -> TSubst d2 n1 n2
comp th ps ph = map (// th) ps . ph
public export %inline
dweakT : (by : Nat) -> Term d n -> Term (by + d) n
dweakT by t = t // shift by
public export %inline
dweakE : (by : Nat) -> Elim d n -> Elim (by + d) n
dweakE by t = t // shift by
public export %inline
weakT : (by : Nat) -> Term d n -> Term d (by + n)
weakT by t = t // shift by
public export %inline
weakE : (by : Nat) -> Elim d n -> Elim d (by + n)
weakE by t = t // shift by
parameters {s : Nat}
namespace ScopeTermBody
export %inline
(.term) : ScopedBody s (Term d) n -> Term d (s + n)
(Y b).term = b
(N b).term = weakT s b
namespace ScopeTermN
export %inline
(.term) : ScopeTermN s d n -> Term d (s + n)
t.term = t.body.term
namespace DScopeTermBody
export %inline
(.term) : ScopedBody s (\d => Term d n) d -> Term (s + d) n
(Y b).term = b
(N b).term = dweakT s b
namespace DScopeTermN
export %inline
(.term) : DScopeTermN s d n -> Term (s + d) n
t.term = t.body.term
export %inline
subN : ScopeTermN s d n -> SnocVect s (Elim d n) -> Term d n
subN (S _ (Y body)) es = body // fromSnocVect es
subN (S _ (N body)) _ = body
export %inline
sub1 : ScopeTerm d n -> Elim d n -> Term d n
sub1 t e = subN t [< e]
export %inline
dsubN : DScopeTermN s d n -> SnocVect s (Dim d) -> Term d n
dsubN (S _ (Y body)) ps = body // fromSnocVect ps
dsubN (S _ (N body)) _ = body
export %inline
dsub1 : DScopeTerm d n -> Dim d -> Term d n
dsub1 t p = dsubN t [< p]
public export %inline
(.zero) : DScopeTerm d n -> {default noLoc loc : Loc} -> Term d n
body.zero = dsub1 body $ K Zero loc
public export %inline
(.one) : DScopeTerm d n -> {default noLoc loc : Loc} -> Term d n
body.one = dsub1 body $ K One loc
public export
0 CloTest : TermLike -> Type
CloTest tm = forall d, n. tm d n -> Bool
interface PushSubsts (0 tm : TermLike) (0 isClo : CloTest tm) | tm where
pushSubstsWith : DSubst d1 d2 -> TSubst d2 n1 n2 ->
tm d1 n1 -> Subset (tm d2 n2) (No . isClo)
public export
0 NotClo : {isClo : CloTest tm} -> PushSubsts tm isClo => Pred (tm d n)
NotClo = No . isClo
public export
0 NonClo : (tm : TermLike) -> {isClo : CloTest tm} ->
PushSubsts tm isClo => TermLike
NonClo tm d n = Subset (tm d n) NotClo
public export %inline
nclo : {isClo : CloTest tm} -> (0 _ : PushSubsts tm isClo) =>
(t : tm d n) -> (0 nc : NotClo t) => NonClo tm 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 d n -> NonClo tm d n
pushSubsts s = pushSubstsWith id id s
export %inline
pushSubstsWith' : DSubst d1 d2 -> TSubst d2 n1 n2 -> tm d1 n1 -> tm d2 n2
pushSubstsWith' th ph x = fst $ pushSubstsWith th ph x
export %inline
pushSubsts' : tm d n -> tm d n
pushSubsts' s = fst $ pushSubsts s
dsubElim (F x l loc) th = th0 $ F x l loc
dsubElim (B loc) th = Th2 zero id' $ B loc
dsubElim (DCloE (Sub e ph)) th = th1 $ DCloE $ Sub e $ ph . th
dsubElim e th = th1 $ DCloE $ Sub e th
mutual
public export
isCloT : CloTest Term
isCloT (CloT {}) = True
isCloT (DCloT {}) = True
isCloT (E e) = isCloE e
isCloT _ = False
namespace Term
export
(///) : {d1, d2, n : Nat} -> TermT d1 n -> DSubst d1 d2 -> TermT d2 n
Th2 dope tope term /// th =
let Val tscope = appOpe n tope; Val dscope = appOpe d1 dope
Th2 dope' tope' term' = dsubTerm term (select dope th)
in
Th2 dope' (tope . tope') term'
public export
isCloE : CloTest Elim
isCloE (CloE {}) = True
isCloE (DCloE {}) = True
isCloE _ = False
mutual
export
PushSubsts Term Subst.isCloT where
pushSubstsWith th ph (TYPE l loc) =
nclo $ TYPE l loc
pushSubstsWith th ph (Pi qty a body loc) =
nclo $ Pi qty (a // th // ph) (body // th // ph) loc
pushSubstsWith th ph (Lam body loc) =
nclo $ Lam (body // th // ph) loc
pushSubstsWith th ph (Sig a b loc) =
nclo $ Sig (a // th // ph) (b // th // ph) loc
pushSubstsWith th ph (Pair s t loc) =
nclo $ Pair (s // th // ph) (t // th // ph) loc
pushSubstsWith th ph (Enum tags loc) =
nclo $ Enum tags loc
pushSubstsWith th ph (Tag tag loc) =
nclo $ Tag tag loc
pushSubstsWith th ph (Eq ty l r loc) =
nclo $ Eq (ty // th // ph) (l // th // ph) (r // th // ph) loc
pushSubstsWith th ph (DLam body loc) =
nclo $ DLam (body // th // ph) loc
pushSubstsWith _ _ (Nat loc) =
nclo $ Nat loc
pushSubstsWith _ _ (Zero loc) =
nclo $ Zero loc
pushSubstsWith th ph (Succ n loc) =
nclo $ Succ (n // th // ph) loc
pushSubstsWith th ph (BOX pi ty loc) =
nclo $ BOX pi (ty // th // ph) loc
pushSubstsWith th ph (Box val loc) =
nclo $ Box (val // th // ph) loc
pushSubstsWith th ph (E e) =
let Element e nc = pushSubstsWith th ph e in nclo $ E e
pushSubstsWith th ph (CloT (Sub s ps)) =
pushSubstsWith th (comp th ps ph) s
pushSubstsWith th ph (DCloT (Sub s ps)) =
pushSubstsWith (ps . th) ph s
export
PushSubsts Elim Subst.isCloE where
pushSubstsWith th ph (F x u loc) =
nclo $ F x u loc
pushSubstsWith th ph (B i loc) =
let res = getLoc ph i loc in
case nchoose $ isCloE res of
Left yes => assert_total pushSubsts res
Right no => Element res no
pushSubstsWith th ph (App f s loc) =
nclo $ App (f // th // ph) (s // th // ph) loc
pushSubstsWith th ph (CasePair pi p r b loc) =
nclo $ CasePair pi (p // th // ph) (r // th // ph) (b // th // ph) loc
pushSubstsWith th ph (CaseEnum pi t r arms loc) =
nclo $ CaseEnum pi (t // th // ph) (r // th // ph)
(map (\b => b // th // ph) arms) loc
pushSubstsWith th ph (CaseNat pi pi' n r z s loc) =
nclo $ CaseNat pi pi' (n // th // ph) (r // th // ph)
(z // th // ph) (s // th // ph) loc
pushSubstsWith th ph (CaseBox pi x r b loc) =
nclo $ CaseBox pi (x // th // ph) (r // th // ph) (b // th // ph) loc
pushSubstsWith th ph (DApp f d loc) =
nclo $ DApp (f // th // ph) (d // th) loc
pushSubstsWith th ph (Ann s a loc) =
nclo $ Ann (s // th // ph) (a // th // ph) loc
pushSubstsWith th ph (Coe ty p q val loc) =
nclo $ Coe (ty // th // ph) (p // th) (q // th) (val // th // ph) loc
pushSubstsWith th ph (Comp ty p q val r zero one loc) =
nclo $ Comp (ty // th // ph) (p // th) (q // th)
(val // th // ph) (r // th)
(zero // th // ph) (one // th // ph) loc
pushSubstsWith th ph (TypeCase ty ret arms def loc) =
nclo $ TypeCase (ty // th // ph) (ret // th // ph)
(map (\t => t // th // ph) arms) (def // th // ph) loc
pushSubstsWith th ph (CloE (Sub e ps)) =
pushSubstsWith th (comp th ps ph) e
pushSubstsWith th ph (DCloE (Sub e ps)) =
pushSubstsWith (ps . th) ph e
namespace Elim
export
(///) : {d1, d2, n : Nat} -> ElimT d1 n -> DSubst d1 d2 -> ElimT d2 n
Th2 dope tope elim /// th =
let Val tscope = appOpe n tope; Val dscope = appOpe d1 dope
Th2 dope' tope' elim' = dsubElim elim (select dope th)
in
Th2 dope' (tope . tope') elim'
private %inline
CompHY : (ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) ->
(r : Dim d) -> (zero, one : DScopeTerm d n) -> (loc : Loc) -> Elim d n
CompHY {ty, p, q, val, r, zero, one, loc} =
let ty' = SY ty.names $ ty.term // (B VZ ty.loc ::: shift 2) in
Comp {
ty = dsub1 ty q, p, q,
val = E $ Coe ty p q val val.loc, r,
-- [fixme] better locations for these vars?
zero = SY zero.names $ E $
Coe ty' (B VZ zero.loc) (weakD 1 q) zero.term zero.loc,
one = SY one.names $ E $
Coe ty' (B VZ one.loc) (weakD 1 q) one.term one.loc,
loc
}
public export
TSubst : Nat -> Nat -> Nat -> Type
TSubst = Subst2 Elim
public export %inline
CompH' : (ty : DScopeTerm d n) ->
(p, q : Dim d) -> (val : Term d n) -> (r : Dim d) ->
(zero : DScopeTerm d n) ->
(one : DScopeTerm d n) ->
(loc : Loc) ->
Elim d n
CompH' {ty, p, q, val, r, zero, one, loc} =
case dsqueeze ty of
S _ (N ty) => Comp {ty, p, q, val, r, zero, one, loc}
S _ (Y _) => CompHY {ty, p, q, val, r, zero, one, loc}
||| heterogeneous composition, using Comp and Coe (and subst)
|||
||| comp [i ⇒ A] @p @q s @r { 0 j ⇒ t₀; 1 j ⇒ t₁ }
||| ≔
||| comp [A‹q/i›] @p @q (coe [i ⇒ A] @p @q s) @r {
||| 0 j ⇒ coe [i ⇒ A] @j @q t₀;
||| 1 j ⇒ coe [i ⇒ A] @j @q t₁
||| }
public export %inline
CompH : (i : BindName) -> (ty : Term (S d) n) ->
(p, q : Dim d) -> (val : Term d n) -> (r : Dim d) ->
(j0 : BindName) -> (zero : Term (S d) n) ->
(j1 : BindName) -> (one : Term (S d) n) ->
(loc : Loc) ->
Elim d n
CompH {i, ty, p, q, val, r, j0, zero, j1, one, loc} =
CompH' {ty = SY [< i] ty, p, q, val, r,
zero = SY [< j0] zero, one = SY [< j0] one, loc}
public export %inline FromVar (Elim 0) where var = B
export CanSubstSelf2 Elim
private subTerm : {d, n1, n2 : Nat} -> Term d n1 -> TSubst d n1 n2 -> TermT d n2
private subElim : {d, n1, n2 : Nat} -> Elim d n1 -> TSubst d n1 n2 -> ElimT d n2
subTerm (TYPE l loc) th = th0 $ TYPE l loc
subTerm (Nat loc) th = th0 $ Nat loc
subTerm (Zero loc) th = th0 $ Zero loc
subTerm (E e) th = let Th2 dope tope e' = subElim e th in Th2 dope tope $ E e'
subTerm (CloT (Sub2 s ph)) th = th1 $ CloT $ Sub2 s $ ph .% th
subTerm s th = th1 $ CloT $ Sub2 s th
subElim (F x k loc) th = th0 $ F x k loc
subElim (B loc) [< e] = e
subElim (CloE (Sub2 e ph)) th = th1 $ CloE $ Sub2 e $ ph .% th
subElim e th = th1 $ CloE $ Sub2 e th
export
CanSubstSelf2 Elim where
Th2 dope tope elim // th =
let
th' = select tope th
in
?sube2
-- namespace CanDSubst
-- public export
-- interface CanDSubst (0 tm : TermLike) where
-- (//) : {d1 : Nat} -> Thinned2 tm d1 n -> Lazy (DSubst d1 d2) ->
-- Thinned2 tm d2 n
-- ||| does the minimal reasonable work:
-- ||| - deletes the closure around an atomic constant like `TYPE`
-- ||| - deletes an identity substitution
-- ||| - composes (lazily) with an existing top-level dim-closure
-- ||| - otherwise, wraps in a new closure
-- export
-- CanDSubst Term where
-- Th2 _ _ (TYPE l loc) // _ = Th2 zero zero $ TYPE l loc
-- Th2 i j (DCloT (Sub s ph)) // th =
-- Th2 ?i' j $ DCloT $ Sub s $ ph . ?th'
-- Th2 i j s // th = ?sdf -- DCloT $ Sub s th
-- -- private
-- -- subDArgs : Elim d1 n -> DSubst d1 d2 -> Elim d2 n
-- -- subDArgs (DApp f d loc) th = DApp (subDArgs f th) (d // th) loc
-- -- subDArgs e th = DCloE $ Sub e th
-- -- ||| does the minimal reasonable work:
-- -- ||| - deletes the closure around a term variable
-- -- ||| - deletes an identity substitution
-- -- ||| - composes (lazily) with an existing top-level dim-closure
-- -- ||| - immediately looks up bound variables in a
-- -- ||| top-level sequence of dimension applications
-- -- ||| - otherwise, wraps in a new closure
-- -- export
-- -- CanDSubst Elim where
-- -- e // Shift SZ = e
-- -- F x u loc // _ = F x u loc
-- -- B i loc // _ = B i loc
-- -- e@(DApp {}) // th = subDArgs e th
-- -- DCloE (Sub e ph) // th = DCloE $ Sub e $ ph . th
-- -- e // th = DCloE $ Sub e th
-- -- namespace DSubst.ScopeTermN
-- -- export %inline
-- -- (//) : ScopeTermN s d1 n -> Lazy (DSubst d1 d2) ->
-- -- ScopeTermN s d2 n
-- -- S ns (Y body) // th = S ns $ Y $ body // th
-- -- S ns (N body) // th = S ns $ N $ body // th
-- -- namespace DSubst.DScopeTermN
-- -- export %inline
-- -- (//) : {s : Nat} ->
-- -- DScopeTermN s d1 n -> Lazy (DSubst d1 d2) ->
-- -- DScopeTermN s d2 n
-- -- S ns (Y body) // th = S ns $ Y $ body // pushN s th
-- -- S ns (N body) // th = S ns $ N $ body // th
-- -- export %inline FromVar (Elim d) where fromVarLoc = B
-- -- export %inline FromVar (Term d) where fromVarLoc = E .: fromVar
-- -- ||| does the minimal reasonable work:
-- -- ||| - deletes the closure around a *free* name
-- -- ||| - deletes an identity substitution
-- -- ||| - composes (lazily) with an existing top-level closure
-- -- ||| - immediately looks up a bound variable
-- -- ||| - otherwise, wraps in a new closure
-- -- export
-- -- CanSubstSelf (Elim d) where
-- -- F x u loc // _ = F x u loc
-- -- B i loc // th = getLoc th i loc
-- -- CloE (Sub e ph) // th = assert_total CloE $ Sub e $ ph . th
-- -- e // th = case force th of
-- -- Shift SZ => e
-- -- th => CloE $ Sub e th
-- -- namespace CanTSubst
-- -- public export
-- -- interface CanTSubst (0 tm : TermLike) where
-- -- (//) : tm d n1 -> Lazy (TSubst d n1 n2) -> tm d n2
-- -- ||| does the minimal reasonable work:
-- -- ||| - deletes the closure around an atomic constant like `TYPE`
-- -- ||| - deletes an identity substitution
-- -- ||| - composes (lazily) with an existing top-level closure
-- -- ||| - goes inside `E` in case it is a simple variable or something
-- -- ||| - otherwise, wraps in a new closure
-- -- export
-- -- CanTSubst Term where
-- -- TYPE l loc // _ = TYPE l loc
-- -- E e // th = E $ e // th
-- -- CloT (Sub s ph) // th = CloT $ Sub s $ ph . th
-- -- s // th = case force th of
-- -- Shift SZ => s
-- -- th => CloT $ Sub s th
-- -- namespace ScopeTermN
-- -- export %inline
-- -- (//) : {s : Nat} ->
-- -- ScopeTermN s d n1 -> Lazy (TSubst d n1 n2) ->
-- -- ScopeTermN s d n2
-- -- S ns (Y body) // th = S ns $ Y $ body // pushN s th
-- -- S ns (N body) // th = S ns $ N $ body // th
-- -- namespace DScopeTermN
-- -- export %inline
-- -- (//) : {s : Nat} ->
-- -- DScopeTermN s d n1 -> Lazy (TSubst d n1 n2) -> DScopeTermN s d n2
-- -- S ns (Y body) // th = S ns $ Y $ body // map (// shift s) th
-- -- S ns (N body) // th = S ns $ N $ body // th
-- -- export %inline CanShift (Term d) where s // by = s // Shift by
-- -- export %inline CanShift (Elim d) where e // by = e // Shift by
-- -- export %inline
-- -- {s : Nat} -> CanShift (ScopeTermN s d) where
-- -- b // by = b // Shift by
-- -- export %inline
-- -- comp : DSubst d1 d2 -> TSubst d1 n1 mid -> TSubst d2 mid n2 -> TSubst d2 n1 n2
-- -- comp th ps ph = map (// th) ps . ph
-- -- public export %inline
-- -- dweakT : (by : Nat) -> Term d n -> Term (by + d) n
-- -- dweakT by t = t // shift by
-- -- public export %inline
-- -- dweakE : (by : Nat) -> Elim d n -> Elim (by + d) n
-- -- dweakE by t = t // shift by
-- -- public export %inline
-- -- weakT : (by : Nat) -> Term d n -> Term d (by + n)
-- -- weakT by t = t // shift by
-- -- public export %inline
-- -- weakE : (by : Nat) -> Elim d n -> Elim d (by + n)
-- -- weakE by t = t // shift by
-- -- parameters {s : Nat}
-- -- namespace ScopeTermBody
-- -- export %inline
-- -- (.term) : ScopedBody s (Term d) n -> Term d (s + n)
-- -- (Y b).term = b
-- -- (N b).term = weakT s b
-- -- namespace ScopeTermN
-- -- export %inline
-- -- (.term) : ScopeTermN s d n -> Term d (s + n)
-- -- t.term = t.body.term
-- -- namespace DScopeTermBody
-- -- export %inline
-- -- (.term) : ScopedBody s (\d => Term d n) d -> Term (s + d) n
-- -- (Y b).term = b
-- -- (N b).term = dweakT s b
-- -- namespace DScopeTermN
-- -- export %inline
-- -- (.term) : DScopeTermN s d n -> Term (s + d) n
-- -- t.term = t.body.term
-- -- export %inline
-- -- subN : ScopeTermN s d n -> SnocVect s (Elim d n) -> Term d n
-- -- subN (S _ (Y body)) es = body // fromSnocVect es
-- -- subN (S _ (N body)) _ = body
-- -- export %inline
-- -- sub1 : ScopeTerm d n -> Elim d n -> Term d n
-- -- sub1 t e = subN t [< e]
-- -- export %inline
-- -- dsubN : DScopeTermN s d n -> SnocVect s (Dim d) -> Term d n
-- -- dsubN (S _ (Y body)) ps = body // fromSnocVect ps
-- -- dsubN (S _ (N body)) _ = body
-- -- export %inline
-- -- dsub1 : DScopeTerm d n -> Dim d -> Term d n
-- -- dsub1 t p = dsubN t [< p]
-- -- public export %inline
-- -- (.zero) : DScopeTerm d n -> {default noLoc loc : Loc} -> Term d n
-- -- body.zero = dsub1 body $ K Zero loc
-- -- public export %inline
-- -- (.one) : DScopeTerm d n -> {default noLoc loc : Loc} -> Term d n
-- -- body.one = dsub1 body $ K One loc
-- -- public export
-- -- 0 CloTest : TermLike -> Type
-- -- CloTest tm = forall d, n. tm d n -> Bool
-- -- interface PushSubsts (0 tm : TermLike) (0 isClo : CloTest tm) | tm where
-- -- pushSubstsWith : DSubst d1 d2 -> TSubst d2 n1 n2 ->
-- -- tm d1 n1 -> Subset (tm d2 n2) (No . isClo)
-- -- public export
-- -- 0 NotClo : {isClo : CloTest tm} -> PushSubsts tm isClo => Pred (tm d n)
-- -- NotClo = No . isClo
-- -- public export
-- -- 0 NonClo : (tm : TermLike) -> {isClo : CloTest tm} ->
-- -- PushSubsts tm isClo => TermLike
-- -- NonClo tm d n = Subset (tm d n) NotClo
-- -- public export %inline
-- -- nclo : {isClo : CloTest tm} -> (0 _ : PushSubsts tm isClo) =>
-- -- (t : tm d n) -> (0 nc : NotClo t) => NonClo tm 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 d n -> NonClo tm d n
-- -- pushSubsts s = pushSubstsWith id id s
-- -- export %inline
-- -- pushSubstsWith' : DSubst d1 d2 -> TSubst d2 n1 n2 -> tm d1 n1 -> tm d2 n2
-- -- pushSubstsWith' th ph x = fst $ pushSubstsWith th ph x
-- -- export %inline
-- -- pushSubsts' : tm d n -> tm d n
-- -- pushSubsts' s = fst $ pushSubsts s
-- -- 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 Subst.isCloT where
-- -- pushSubstsWith th ph (TYPE l loc) =
-- -- nclo $ TYPE l loc
-- -- pushSubstsWith th ph (Pi qty a body loc) =
-- -- nclo $ Pi qty (a // th // ph) (body // th // ph) loc
-- -- pushSubstsWith th ph (Lam body loc) =
-- -- nclo $ Lam (body // th // ph) loc
-- -- pushSubstsWith th ph (Sig a b loc) =
-- -- nclo $ Sig (a // th // ph) (b // th // ph) loc
-- -- pushSubstsWith th ph (Pair s t loc) =
-- -- nclo $ Pair (s // th // ph) (t // th // ph) loc
-- -- pushSubstsWith th ph (Enum tags loc) =
-- -- nclo $ Enum tags loc
-- -- pushSubstsWith th ph (Tag tag loc) =
-- -- nclo $ Tag tag loc
-- -- pushSubstsWith th ph (Eq ty l r loc) =
-- -- nclo $ Eq (ty // th // ph) (l // th // ph) (r // th // ph) loc
-- -- pushSubstsWith th ph (DLam body loc) =
-- -- nclo $ DLam (body // th // ph) loc
-- -- pushSubstsWith _ _ (Nat loc) =
-- -- nclo $ Nat loc
-- -- pushSubstsWith _ _ (Zero loc) =
-- -- nclo $ Zero loc
-- -- pushSubstsWith th ph (Succ n loc) =
-- -- nclo $ Succ (n // th // ph) loc
-- -- pushSubstsWith th ph (BOX pi ty loc) =
-- -- nclo $ BOX pi (ty // th // ph) loc
-- -- pushSubstsWith th ph (Box val loc) =
-- -- nclo $ Box (val // th // ph) loc
-- -- pushSubstsWith th ph (E e) =
-- -- let Element e nc = pushSubstsWith th ph e in nclo $ E e
-- -- pushSubstsWith th ph (CloT (Sub s ps)) =
-- -- pushSubstsWith th (comp th ps ph) s
-- -- pushSubstsWith th ph (DCloT (Sub s ps)) =
-- -- pushSubstsWith (ps . th) ph s
-- -- export
-- -- PushSubsts Elim Subst.isCloE where
-- -- pushSubstsWith th ph (F x u loc) =
-- -- nclo $ F x u loc
-- -- pushSubstsWith th ph (B i loc) =
-- -- let res = getLoc ph i loc in
-- -- case nchoose $ isCloE res of
-- -- Left yes => assert_total pushSubsts res
-- -- Right no => Element res no
-- -- pushSubstsWith th ph (App f s loc) =
-- -- nclo $ App (f // th // ph) (s // th // ph) loc
-- -- pushSubstsWith th ph (CasePair pi p r b loc) =
-- -- nclo $ CasePair pi (p // th // ph) (r // th // ph) (b // th // ph) loc
-- -- pushSubstsWith th ph (CaseEnum pi t r arms loc) =
-- -- nclo $ CaseEnum pi (t // th // ph) (r // th // ph)
-- -- (map (\b => b // th // ph) arms) loc
-- -- pushSubstsWith th ph (CaseNat pi pi' n r z s loc) =
-- -- nclo $ CaseNat pi pi' (n // th // ph) (r // th // ph)
-- -- (z // th // ph) (s // th // ph) loc
-- -- pushSubstsWith th ph (CaseBox pi x r b loc) =
-- -- nclo $ CaseBox pi (x // th // ph) (r // th // ph) (b // th // ph) loc
-- -- pushSubstsWith th ph (DApp f d loc) =
-- -- nclo $ DApp (f // th // ph) (d // th) loc
-- -- pushSubstsWith th ph (Ann s a loc) =
-- -- nclo $ Ann (s // th // ph) (a // th // ph) loc
-- -- pushSubstsWith th ph (Coe ty p q val loc) =
-- -- nclo $ Coe (ty // th // ph) (p // th) (q // th) (val // th // ph) loc
-- -- pushSubstsWith th ph (Comp ty p q val r zero one loc) =
-- -- nclo $ Comp (ty // th // ph) (p // th) (q // th)
-- -- (val // th // ph) (r // th)
-- -- (zero // th // ph) (one // th // ph) loc
-- -- pushSubstsWith th ph (TypeCase ty ret arms def loc) =
-- -- nclo $ TypeCase (ty // th // ph) (ret // th // ph)
-- -- (map (\t => t // th // ph) arms) (def // th // ph) loc
-- -- pushSubstsWith th ph (CloE (Sub e ps)) =
-- -- pushSubstsWith th (comp th ps ph) e
-- -- pushSubstsWith th ph (DCloE (Sub e ps)) =
-- -- pushSubstsWith (ps . th) ph e
-- -- private %inline
-- -- CompHY : (ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) ->
-- -- (r : Dim d) -> (zero, one : DScopeTerm d n) -> (loc : Loc) -> Elim d n
-- -- CompHY {ty, p, q, val, r, zero, one, loc} =
-- -- let ty' = SY ty.names $ ty.term // (B VZ ty.loc ::: shift 2) in
-- -- Comp {
-- -- ty = dsub1 ty q, p, q,
-- -- val = E $ Coe ty p q val val.loc, r,
-- -- -- [fixme] better locations for these vars?
-- -- zero = SY zero.names $ E $
-- -- Coe ty' (B VZ zero.loc) (weakD 1 q) zero.term zero.loc,
-- -- one = SY one.names $ E $
-- -- Coe ty' (B VZ one.loc) (weakD 1 q) one.term one.loc,
-- -- loc
-- -- }
-- -- public export %inline
-- -- CompH' : (ty : DScopeTerm d n) ->
-- -- (p, q : Dim d) -> (val : Term d n) -> (r : Dim d) ->
-- -- (zero : DScopeTerm d n) ->
-- -- (one : DScopeTerm d n) ->
-- -- (loc : Loc) ->
-- -- Elim d n
-- -- CompH' {ty, p, q, val, r, zero, one, loc} =
-- -- case dsqueeze ty of
-- -- S _ (N ty) => Comp {ty, p, q, val, r, zero, one, loc}
-- -- S _ (Y _) => CompHY {ty, p, q, val, r, zero, one, loc}
-- -- ||| heterogeneous composition, using Comp and Coe (and subst)
-- -- |||
-- -- ||| comp [i ⇒ A] @p @q s @r { 0 j ⇒ t₀; 1 j ⇒ t₁ }
-- -- ||| ≔
-- -- ||| comp [A‹q/i›] @p @q (coe [i ⇒ A] @p @q s) @r {
-- -- ||| 0 j ⇒ coe [i ⇒ A] @j @q t₀;
-- -- ||| 1 j ⇒ coe [i ⇒ A] @j @q t₁
-- -- ||| }
-- -- public export %inline
-- -- CompH : (i : BindName) -> (ty : Term (S d) n) ->
-- -- (p, q : Dim d) -> (val : Term d n) -> (r : Dim d) ->
-- -- (j0 : BindName) -> (zero : Term (S d) n) ->
-- -- (j1 : BindName) -> (one : Term (S d) n) ->
-- -- (loc : Loc) ->
-- -- Elim d n
-- -- CompH {i, ty, p, q, val, r, j0, zero, j1, one, loc} =
-- -- CompH' {ty = SY [< i] ty, p, q, val, r,
-- -- zero = SY [< j0] zero, one = SY [< j0] one, loc}

9
lib/Quox/Syntax/Var.idr
View file

@ -138,15 +138,6 @@ export
weakIsSpec p i = toNatInj $ trans (weakCorrect p i) (sym $ weakSpecCorrect p i)
public export
interface FromVar f where %inline fromVarLoc : Var n -> Loc -> f n
public export %inline
fromVar : FromVar f => Var n -> {default noLoc loc : Loc} -> f n
fromVar x = fromVarLoc x loc
public export FromVar Var where fromVarLoc x _ = x
export
tabulateV : {0 tm : Nat -> Type} -> (forall n. Var n -> tm n) ->
(n : Nat) -> Vect n (tm n)

2
lib/Quox/Thin/Base.idr
View file

@ -53,7 +53,7 @@ id {m = 0} = Element _ Stop
id {m = S m} = Element _ $ Keep id.snd Refl
public export %inline
0 id' : OPE m m Base.id.fst
0 id' : {m : Nat} -> OPE m m (fst (Base.id {m}))
id' = id.snd
||| nothing selected

6
lib/Quox/Thin/Comp.idr
View file

@ -2,6 +2,7 @@ module Quox.Thin.Comp
import public Quox.Thin.Base
import public Quox.Thin.View
import Quox.NatExtra
import Data.Singleton
%default total
@ -52,8 +53,3 @@ export
0 (.) : (ope1 : OPE n p mask1) -> (ope2 : OPE m n mask2) ->
OPE m p (comp ope1 ope2).mask
ope1 . ope2 = (comp ope1 ope2).ope
-- export
-- 0 compMask : (ope1 : OPE n p mask1) -> (ope2 : OPE m n mask2) ->
-- (ope3 : OPE m p mask3) -> Comp ope1 ope2 ope3 ->
-- mask3 = ?aaa

43
lib/Quox/Thin/Term.idr
View file

@ -5,6 +5,7 @@ import public Quox.Thin.Comp
import public Quox.Thin.List
import Quox.Thin.Eqv
import public Quox.Thin.Cover
import Quox.Thin.Append
import Quox.Name
import Quox.Loc
import Data.DPair
@ -15,6 +16,13 @@ import Decidable.Equality
%default total
private
cmpMask : (m, n : Nat) -> Either Ordering (m = n)
cmpMask 0 0 = Right Refl
cmpMask 0 (S n) = Left LT
cmpMask (S m) 0 = Left GT
cmpMask (S m) (S n) = map (cong S) $ cmpMask m n
public export
record Thinned f n where
constructor Th
@ -26,9 +34,20 @@ record Thinned f n where
export
(forall n. Eq (f n)) => Eq (Thinned f n) where
s == t = case decEq s.scopeMask t.scopeMask of
Yes eq => s.term == (rewrite maskEqInner s.ope t.ope eq in t.term)
No _ => False
s == t = case cmpMask s.scopeMask t.scopeMask of
Left _ => False
Right eq => s.term == (rewrite maskEqInner s.ope t.ope eq in t.term)
export
(forall n. Ord (f n)) => Ord (Thinned f n) where
compare s t = case cmpMask s.scopeMask t.scopeMask of
Left o => o
Right eq => compare s.term (rewrite maskEqInner s.ope t.ope eq in t.term)
export
{n : Nat} -> (forall s. Show (f s)) => Show (Thinned f n) where
showPrec d (Th ope term) =
showCon d "Th" $ showArg (unVal $ maskToOpe ope) ++ showArg term
export
(forall n. Located (f n)) => Located (Thinned f n) where
@ -47,6 +66,10 @@ namespace Thinned
join : {n : Nat} -> Thinned (Thinned f) n -> Thinned f n
join (Th ope1 (Th ope2 term)) = Th (ope1 . ope2) term
export
weak : {n : Nat} -> (by : Nat) -> Thinned f n -> Thinned f (by + n)
weak by (Th ope term) = Th (zero ++ ope).snd term
public export
record ScopedN (s : Nat) (f : Nat -> Type) (n : Nat) where
@ -104,6 +127,14 @@ export
rewrite maskEqInner s.tope t.tope teq in t.term)
_ => False
export
{d, n : Nat} -> (forall sd, sn. Show (f sd sn)) => Show (Thinned2 f d n) where
showPrec d (Th2 dope tope term) =
showCon d "Th2" $
showArg (unVal $ maskToOpe dope) ++
showArg (unVal $ maskToOpe tope) ++
showArg term
export
(forall d, n. Located (f d n)) => Located (Thinned2 f d n) where
term.loc = term.term.loc
@ -122,6 +153,12 @@ namespace Thinned2
join (Th2 dope1 tope1 (Th2 dope2 tope2 term)) =
Th2 (dope1 . dope2) (tope1 . tope2) term
export
weak : {d, n : Nat} -> (dby, nby : Nat) ->
Thinned2 f d n -> Thinned2 f (dby + d) (nby + n)
weak dby nby (Th2 dope tope term) =
Th2 (zero ++ dope).snd (zero ++ tope).snd term
namespace TermList
public export

21
lib/Quox/Thin/View.idr
View file

@ -4,6 +4,7 @@ import public Quox.Thin.Base
import Quox.NatExtra
import Data.Singleton
import Data.SnocVect
import Data.Fin
%default total
@ -52,6 +53,12 @@ view {n = S n} ope with %syntactic (half mask)
_ | HalfEven mask' with %syntactic 0 (fromDrop ope)
_ | (ope' ** eq) = rewrite eq in DropV mask' ope'
export
(.fin) : {n, mask : Nat} -> (0 ope : OPE 1 n mask) -> Fin n
ope.fin with (view ope)
_.fin | DropV _ ope = FS ope.fin
_.fin | KeepV _ ope = FZ
export
appOpe : {0 m : Nat} -> (n : Nat) -> {mask : Nat} ->
@ -83,21 +90,11 @@ viewStop = Refl
export
0 viewDrop : (ope : OPE m n mask) -> (eq : mask2 = mask + mask) ->
view (Drop {mask} ope eq) = DropV mask ope
viewDrop ope eq with (view (Drop ope eq))
viewDrop ope eq with %syntactic (view (Drop ope eq))
viewDrop ope Refl | DropV _ ope = Refl
export
0 viewKeep : (ope : OPE m n mask) -> (eq : mask2 = S (mask + mask)) ->
view (Keep {mask} ope eq) = KeepV mask ope
viewKeep ope eq with (view (Keep ope eq))
viewKeep ope eq with %syntactic (view (Keep ope eq))
viewKeep ope Refl | KeepV _ ope = Refl
namespace SnocVect
export
select : {n, mask : Nat} -> (0 ope : OPE m n mask) ->
SnocVect n a -> SnocVect m a
select ope sx with (view ope)
select _ [<] | StopV = [<]
select _ (sx :< x) | DropV _ ope = select ope sx
select _ (sx :< x) | KeepV _ ope = select ope sx :< x