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37
lib/Quox/Context.idr
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@ -6,12 +6,16 @@ import Quox.Name
import Data.DPair import Data.DPair
import Data.Nat import Data.Nat
import Data.Fin
import Data.Singleton
import Data.SnocList import Data.SnocList
import Data.SnocVect import Data.SnocVect
import Data.Vect import Data.Vect
import Control.Monad.Identity import Control.Monad.Identity
import Derive.Prelude
%default total %default total
%language ElabReflection
||| a sequence of bindings under an existing context. each successive element ||| a sequence of bindings under an existing context. each successive element
@ -83,6 +87,13 @@ export %inline
toSnocList' : Telescope' a _ _ -> SnocList a toSnocList' : Telescope' a _ _ -> SnocList a
toSnocList' = toSnocListWith id 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 export %inline
toList : Telescope tm _ _ -> List (Exists tm) toList : Telescope tm _ _ -> List (Exists tm)
toList = toListWith (Evidence _) toList = toListWith (Evidence _)
@ -136,34 +147,34 @@ tel ++ (sx :< x) = (tel ++ sx) :< x
public export public export
getShiftWith : (forall from, to. tm from -> Shift from to -> tm to) -> getShiftWith : (forall from, to. tm from -> Shift from to -> tm to) ->
Shift len out -> Context tm len -> Var len -> tm out Shift len out -> Context tm len -> Fin len -> tm out
getShiftWith shft by (ctx :< t) VZ = t `shft` ssDown by getShiftWith shft by (ctx :< t) FZ = t `shft` ssDown by
getShiftWith shft by (ctx :< t) (VS i) = getShiftWith shft (ssDown by) ctx i getShiftWith shft by (ctx :< t) (FS i) = getShiftWith shft (ssDown by) ctx i
public export %inline 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 (//) getShift = getShiftWith (//)
public export %inline public export %inline
getWith : (forall from, to. tm from -> Shift from to -> tm to) -> 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 getWith shft = getShiftWith shft SZ
infixl 8 !! infixl 8 !!
public export %inline public export %inline
(!!) : CanShift tm => Context tm len -> Var len -> tm len (!!) : CanShift tm => Context tm len -> Fin len -> tm len
(!!) = getWith (//) (!!) = getWith (//)
infixl 8 !!! infixl 8 !!!
public export %inline public export %inline
(!!!) : Context' tm len -> Var len -> tm (!!!) : Context' tm len -> Fin len -> tm
(!!!) = getWith const (!!!) = getWith const
public export public export
find : Alternative f => 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 [<] = 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 export
@ -320,6 +331,14 @@ export %inline
where Show (Exists tm) where showPrec d t = showPrec d t.snd 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} parameters {opts : LayoutOpts} {0 tm : Nat -> Type}
(nameHL : HL) (nameHL : HL)
(pterm : forall n. BContext n -> tm n -> Eff Pretty (Doc opts)) (pterm : forall n. BContext n -> tm n -> Eff Pretty (Doc opts))

44
lib/Quox/FinExtra.idr Normal file
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@ -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

110
lib/Quox/Syntax/Dim.idr
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@ -1,15 +1,18 @@
module Quox.Syntax.Dim module Quox.Syntax.Dim
import Quox.Loc import Quox.Thin
import Quox.Name
import Quox.Syntax.Var import Quox.Syntax.Var
import Quox.Syntax.Subst import Quox.Syntax.Subst
import Quox.Pretty import Quox.Pretty
import Quox.Name
import Quox.Loc
import Quox.Context import Quox.Context
import Decidable.Equality import Decidable.Equality
import Control.Function import Control.Function
import Derive.Prelude import Derive.Prelude
import Data.DPair
import Data.SnocVect
%default total %default total
%language ElabReflection %language ElabReflection
@ -39,38 +42,48 @@ DecEq DimConst where
public export public export
data Dim : Nat -> Type where data Dim : Nat -> Type where
K : DimConst -> Loc -> Dim d K : DimConst -> Loc -> Dim 0
B : Var d -> Loc -> Dim d B : Loc -> Dim 1
%name Dim.Dim p, q %name Dim.Dim p, q
%runElab deriveIndexed "Dim" [Eq, Ord, Show] %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 ||| `endsOr l r x p` returns `ends l r ε` if `p` is a constant ε, and
||| `x` otherwise. ||| `x` otherwise.
public export public export
endsOr : Lazy a -> Lazy a -> Lazy a -> Dim n -> a endsOr : Lazy a -> Lazy a -> Lazy a -> Dim n -> a
endsOr l r x (K e _) = ends l r e endsOr l r x (K e _) = ends l r e
endsOr l r x (B _ _) = x endsOr l r x (B _) = x
export export
Located (Dim d) where Located (Dim d) where
(K _ loc).loc = loc (K _ loc).loc = loc
(B _ loc).loc = loc (B loc).loc = loc
export export
Relocatable (Dim d) where Relocatable (Dim d) where
setLoc loc (K e _) = K e loc setLoc loc (K e _) = K e loc
setLoc loc (B i _) = B i loc setLoc loc (B _) = B loc
parameters {opts : LayoutOpts}
export export
prettyDimConst : {opts : _} -> DimConst -> Eff Pretty (Doc opts) prettyDimConst : DimConst -> Eff Pretty (Doc opts)
prettyDimConst = hl Dim . text . ends "0" "1" prettyDimConst = hl Dim . text . ends "0" "1"
export export
prettyDim : {opts : _} -> BContext d -> Dim d -> Eff Pretty (Doc opts) prettyDim : {d : Nat} -> BContext d -> DimT d -> Eff Pretty (Doc opts)
prettyDim names (K e _) = prettyDimConst e prettyDim names (Th _ (K e _)) = prettyDimConst e
prettyDim names (B i _) = prettyDBind $ names !!! i prettyDim names (Th i (B _)) = prettyDBind $ names !!! i.fin
public export %inline public export %inline
@ -83,57 +96,54 @@ DSubst : Nat -> Nat -> Type
DSubst = Subst Dim DSubst = Subst Dim
public export FromVar Dim where fromVarLoc = B -- public export FromVar Dim where fromVarLoc = B
export -- export
CanShift Dim where -- CanShift Dim where
K e loc // _ = K e loc -- K e loc // _ = K e loc
B i loc // by = B (i // by) loc -- B i loc // by = B (i // by) loc
export export %inline FromVar Dim where var = B
export %inline
CanSubstSelf Dim where CanSubstSelf Dim where
K e loc // _ = K e loc Th _ (K e loc) // _ = KT e loc
B i loc // th = getLoc th i loc Th i (B loc) // th = get th i.fin
export Uninhabited (B i loc1 = K e loc2) where uninhabited _ impossible export Uninhabited (B loc1 = K e loc2) where uninhabited _ impossible
export Uninhabited (K e loc1 = B i loc2) where uninhabited _ impossible export Uninhabited (K e loc1 = B loc2) where uninhabited _ impossible
public export -- public export
data Eqv : Dim d1 -> Dim d2 -> Type where -- data Eqv : Dim d1 -> Dim d2 -> Type where
EK : K e _ `Eqv` K e _ -- EK : K e _ `Eqv` K e _
EB : i `Eqv` j -> B i _ `Eqv` B j _ -- EB : i `Eqv` j -> B i _ `Eqv` B j _
export Uninhabited (K e l1 `Eqv` B i 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 Uninhabited (B i l1 `Eqv` K e l2) where uninhabited _ impossible
export -- export
injectiveB : B i loc1 `Eqv` B j loc2 -> i `Eqv` j -- injectiveB : B i loc1 `Eqv` B j loc2 -> i `Eqv` j
injectiveB (EB e) = e -- injectiveB (EB e) = e
export -- export
injectiveK : K e loc1 `Eqv` K f loc2 -> e = f -- injectiveK : K e loc1 `Eqv` K f loc2 -> e = f
injectiveK EK = Refl -- injectiveK EK = Refl
public export -- public export
decEqv : Dec2 Dim.Eqv -- decEqv : Dec2 Dim.Eqv
decEqv (K e _) (K f _) = case decEq e f of -- decEqv (K e _) (K f _) = case decEq e f of
Yes Refl => Yes EK -- Yes Refl => Yes EK
No n => No $ n . injectiveK -- No n => No $ n . injectiveK
decEqv (B i _) (B j _) = case decEqv i j of -- decEqv (B i _) (B j _) = case decEqv i j of
Yes y => Yes $ EB y -- Yes y => Yes $ EB y
No n => No $ \(EB y) => n y -- No n => No $ \(EB y) => n y
decEqv (B _ _) (K _ _) = No absurd -- decEqv (B _ _) (K _ _) = No absurd
decEqv (K _ _) (B _ _) = No absurd -- decEqv (K _ _) (B _ _) = No absurd
||| abbreviation for a bound variable like `BV 4` instead of ||| abbreviation for a bound variable like `BV 4` instead of
||| `B (VS (VS (VS (VS VZ))))` ||| `B (VS (VS (VS (VS VZ))))`
public export %inline public export %inline
BV : (i : Nat) -> (0 _ : LT i d) => (loc : Loc) -> Dim d BV : (i : Fin d) -> (loc : Loc) -> DimT d
BV i loc = B (V i) loc BV i loc = Th (one' i) $ B loc
export
weakD : (by : Nat) -> Dim d -> Dim (by + d)
weakD by p = p // shift by

191
lib/Quox/Syntax/DimEq.idr
View file

@ -6,11 +6,14 @@ import public Quox.Syntax.Subst
import public Quox.Context import public Quox.Context
import Quox.Pretty import Quox.Pretty
import Quox.Name import Quox.Name
import Quox.Thin
import Quox.FinExtra
import Data.Maybe import Data.Maybe
import Data.Nat import Data.Nat
import Data.DPair import Data.DPair
import Data.Fun.Graph import Data.Fun.Graph
import Data.SnocVect
import Decidable.Decidable import Decidable.Decidable
import Decidable.Equality import Decidable.Equality
import Derive.Prelude import Derive.Prelude
@ -21,7 +24,7 @@ import Derive.Prelude
public export public export
DimEq' : Nat -> Type DimEq' : Nat -> Type
DimEq' = Context (Maybe . Dim) DimEq' = Context (Maybe . DimT)
public export public export
@ -29,7 +32,12 @@ data DimEq : Nat -> Type where
ZeroIsOne : DimEq d ZeroIsOne : DimEq d
C : (eqs : DimEq' d) -> DimEq d C : (eqs : DimEq' d) -> DimEq d
%name DimEq eqs %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 public export
@ -72,7 +80,7 @@ toMaybe (Just x) = Just x
export export
fromGround' : Context' DimConst d -> DimEq' d fromGround' : Context' DimConst d -> DimEq' d
fromGround' [<] = [<] fromGround' [<] = [<]
fromGround' (ctx :< e) = fromGround' ctx :< Just (K e noLoc) fromGround' (ctx :< e) = fromGround' ctx :< Just (KT e noLoc)
export export
fromGround : Context' DimConst d -> DimEq d fromGround : Context' DimConst d -> DimEq d
@ -94,39 +102,40 @@ new = C new'
public export %inline 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 get' = getWith $ \p, by => map (// by) p
public export %inline public export %inline
getVar : DimEq' d -> Var d -> Loc -> Dim d getShift' : Shift len out -> DimEq' len -> Fin len -> Maybe (DimT out)
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' = getShiftWith $ \p, by => map (// by) p getShift' = getShiftWith $ \p, by => map (// by) p
public export %inline public export %inline
get : DimEq' d -> Dim d -> Dim d get : {d : Nat} -> DimEq' d -> DimT d -> DimT d
get _ (K e loc) = K e loc get eqs p@(Th _ (K {})) = p
get eqs (B i loc) = getVar eqs i loc get eqs p@(Th i (B _)) = fromMaybe p $ get' eqs i.fin
public export %inline 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 ZeroIsOne p q = True
equal (C eqs) p q = get eqs p == get eqs q equal (C eqs) p q = get eqs p == get eqs q
infixl 7 :<? infixl 7 :<?
export %inline export %inline
(:<?) : DimEq d -> Maybe (Dim d) -> DimEq (S d) (:<?) : {d : Nat} -> DimEq d -> Maybe (DimT d) -> DimEq (S d)
ZeroIsOne :<? d = ZeroIsOne ZeroIsOne :<? d = ZeroIsOne
C eqs :<? d = C $ eqs :< map (get eqs) d C eqs :<? d = C $ eqs :< map (get eqs) d
private %inline private %inline
ifVar : Var d -> Dim d -> Maybe (Dim d) -> Maybe (Dim d) isVar : {d : Nat} -> Fin d -> DimT d -> Bool
ifVar i p = map $ \q => if q == B i noLoc then p else q 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) -- (using decEq instead of (==) because of the proofs below)
private %inline private %inline
@ -135,43 +144,45 @@ checkConst e f eqs = if isYes $ e `decEq` f then C eqs else ZeroIsOne
export export
setConst : Var d -> DimConst -> Loc -> DimEq' d -> DimEq d setConst : {d : Nat} -> Fin d -> DimConst -> Loc -> DimEq' d -> DimEq d
setConst VZ e loc (eqs :< Nothing) = setConst FZ e loc (eqs :< Nothing) =
C $ eqs :< Just (K e loc) C $ eqs :< Just (KT e loc)
setConst VZ e _ (eqs :< Just (K f loc)) = setConst FZ e _ (eqs :< Just (Th _ (K f loc))) =
checkConst e f $ eqs :< Just (K f loc) checkConst e f $ eqs :< Just (KT f loc)
setConst VZ e loc (eqs :< Just (B i _)) = setConst FZ e loc (eqs :< Just (Th j (B _))) =
setConst i e loc eqs :<? Just (K e loc) setConst j.fin e loc eqs :<? Just (KT e loc)
setConst (VS i) e loc (eqs :< p) = setConst (FS i) e loc (eqs :< p) =
setConst i e loc eqs :<? ifVar i (K e loc) p setConst i e loc eqs :<? ifVar i (KT e loc) p
mutual mutual
private private
setVar' : (i, j : Var d) -> (0 _ : i `LT` j) -> Loc -> DimEq' d -> DimEq d setVar' : {d : Nat} ->
setVar' VZ (VS i) LTZ loc (eqs :< Nothing) = (i, j : Fin d) -> (0 _ : i `LT` j) -> Loc -> DimEq' d -> DimEq d
C eqs :<? Just (B i loc) setVar' FZ (FS i) LTZ loc (eqs :< Nothing) =
setVar' VZ (VS i) LTZ loc (eqs :< Just (K e eloc)) = C eqs :<? Just (BV i loc)
setConst i e loc eqs :<? Just (K e eloc) setVar' FZ (FS i) LTZ loc (eqs :< Just (Th _ (K e eloc))) =
setVar' VZ (VS i) LTZ loc (eqs :< Just (B j jloc)) = setConst i e loc eqs :<? Just (KT e eloc)
setVar i j loc jloc eqs :<? Just (if j > i then B j jloc else B i loc) setVar' FZ (FS i) LTZ loc (eqs :< Just (Th j (B jloc))) =
setVar' (VS i) (VS j) (LTS lt) loc (eqs :< p) = let j = j.fin in
setVar' i j lt loc eqs :<? ifVar i (B j loc) p 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 export %inline
setVar : (i, j : Var d) -> Loc -> Loc -> DimEq' d -> DimEq d setVar : {d : Nat} -> (i, j : Fin 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 with (compareP i j)
setVar i j li lj eqs | IsLT lt | LT = setVar' i j lt lj eqs setVar i j li lj eqs | IsLT lt = setVar' i j lt lj eqs
setVar i i li lj eqs | IsEQ | EQ = C eqs setVar i i li lj eqs | IsEQ = C eqs
setVar i j li lj eqs | IsGT gt | GT = setVar' j i gt li eqs setVar i j li lj eqs | IsGT gt = setVar' j i gt li eqs
export %inline 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 _ _ ZeroIsOne = ZeroIsOne
set (K e eloc) (K f floc) (C eqs) = checkConst e f eqs set (Th _ (K e _)) (Th _ (K f _)) (C eqs) = checkConst e f eqs
set (K e eloc) (B i iloc) (C eqs) = setConst i e eloc eqs set (Th _ (K e el)) (Th j (B _)) (C eqs) = setConst j.fin e el eqs
set (B i iloc) (K e eloc) (C eqs) = setConst i e eloc eqs set (Th i (B _)) (Th _ (K e el)) (C eqs) = setConst i.fin e el eqs
set (B i iloc) (B j jloc) (C eqs) = setVar i j iloc jloc eqs set (Th i (B il)) (Th j (B jl)) (C eqs) = setVar i.fin j.fin il jl eqs
public export %inline public export %inline
@ -179,74 +190,76 @@ Split : Nat -> Type
Split d = (DimEq' d, DSubst (S d) d) Split d = (DimEq' d, DSubst (S d) d)
export %inline export %inline
split1 : DimConst -> Loc -> DimEq' (S d) -> Maybe (Split d) split1 : {d : Nat} -> DimConst -> Loc -> DimEq' (S d) -> Maybe (Split d)
split1 e loc eqs = case setConst VZ e loc eqs of split1 e loc eqs = case setConst 0 e loc eqs of
ZeroIsOne => Nothing ZeroIsOne => Nothing
C (eqs :< _) => Just (eqs, K e loc ::: id) C (eqs :< _) => Just (eqs, id (B loc) :< KT e loc)
export %inline 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) split loc eqs = toList (split1 Zero loc eqs) <+> toList (split1 One loc eqs)
export export
splits' : Loc -> DimEq' d -> List (DSubst d 0) splits' : {d : Nat} -> Loc -> DimEq' d -> List (DSubst d 0)
splits' _ [<] = [id] splits' _ [<] = [[<]]
splits' loc eqs@(_ :< _) = splits' loc eqs@(_ :< _) =
[th . ph | (eqs', th) <- split loc eqs, ph <- splits' loc eqs'] [th . ph | (eqs', th) <- split loc eqs, ph <- splits' loc eqs']
||| the Loc is put into each of the DimConsts ||| the Loc is put into each of the DimConsts
export %inline export %inline
splits : Loc -> DimEq d -> List (DSubst d 0) splits : {d : Nat} -> Loc -> DimEq d -> List (DSubst d 0)
splits _ ZeroIsOne = [] splits _ ZeroIsOne = []
splits loc (C eqs) = splits' loc eqs splits loc (C eqs) = splits' loc eqs
-- 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 : 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 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
parameters {opts : LayoutOpts}
private private
0 newGetShift : (d : Nat) -> (i : Var d) -> (by : Shift d d') -> prettyDVars : {d : Nat} -> BContext d -> Eff Pretty (SnocList (Doc opts))
getShift' by (new' {d}) i = Nothing
newGetShift (S d) VZ by = Refl
newGetShift (S d) (VS 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) -> (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
private
prettyDVars : {opts : _} -> BContext d -> Eff Pretty (SnocList (Doc opts))
prettyDVars = traverse prettyDBind . toSnocList' prettyDVars = traverse prettyDBind . toSnocList'
private private
prettyCst : {opts : _} -> BContext d -> Dim d -> Dim d -> Eff Pretty (Doc opts) prettyCst : {d : Nat} -> BContext d -> DimT d -> DimT d -> Eff Pretty (Doc opts)
prettyCst dnames p q = prettyCst dnames p q =
hsep <$> sequence [prettyDim dnames p, cstD, prettyDim dnames q] hsep <$> sequence [prettyDim dnames p, cstD, prettyDim dnames q]
private private
prettyCsts : {opts : _} -> BContext d -> DimEq' d -> prettyCsts : {d : Nat} -> BContext d -> DimEq' d ->
Eff Pretty (SnocList (Doc opts)) Eff Pretty (SnocList (Doc opts))
prettyCsts [<] [<] = pure [<] prettyCsts [<] [<] = pure [<]
prettyCsts dnames (eqs :< Nothing) = prettyCsts (tail dnames) eqs prettyCsts dnames (eqs :< Nothing) = prettyCsts (tail dnames) eqs
prettyCsts dnames (eqs :< Just q) = prettyCsts dnames (eqs :< Just q) =
[|prettyCsts (tail dnames) eqs :< prettyCst dnames (BV 0 noLoc) (weakD 1 q)|] [|prettyCsts (tail dnames) eqs :<
prettyCst dnames (BV 0 noLoc) (weak 1 q)|]
export export
prettyDimEq' : {opts : _} -> BContext d -> DimEq' d -> Eff Pretty (Doc opts) prettyDimEq' : {d : Nat} -> BContext d -> DimEq' d -> Eff Pretty (Doc opts)
prettyDimEq' dnames eqs = do prettyDimEq' dnames eqs = do
vars <- prettyDVars dnames vars <- prettyDVars dnames
eqs <- prettyCsts dnames eqs eqs <- prettyCsts dnames eqs
@ -254,22 +267,22 @@ prettyDimEq' dnames eqs = do
parensIfM prec $ fillSeparateTight !commaD $ toList vars ++ toList eqs parensIfM prec $ fillSeparateTight !commaD $ toList vars ++ toList eqs
export export
prettyDimEq : {opts : _} -> BContext d -> DimEq d -> Eff Pretty (Doc opts) prettyDimEq : {d : Nat} -> BContext d -> DimEq d -> Eff Pretty (Doc opts)
prettyDimEq dnames ZeroIsOne = do prettyDimEq dnames ZeroIsOne = do
vars <- prettyDVars dnames vars <- prettyDVars dnames
cst <- prettyCst [<] (K Zero noLoc) (K One noLoc) cst <- prettyCst [<] (KT Zero noLoc) (KT One noLoc)
pure $ separateTight !commaD $ vars :< cst pure $ separateTight !commaD $ vars :< cst
prettyDimEq dnames (C eqs) = prettyDimEq' dnames eqs prettyDimEq dnames (C eqs) = prettyDimEq' dnames eqs
public export public export
wf' : DimEq' d -> Bool wf' : {d : Nat} -> DimEq' d -> Bool
wf' [<] = True wf' [<] = True
wf' (eqs :< Nothing) = wf' eqs wf' (eqs :< Nothing) = wf' eqs
wf' (eqs :< Just (K e _)) = wf' eqs wf' (eqs :< Just (Th _ (K {}))) = wf' eqs
wf' (eqs :< Just (B i _)) = isNothing (get' eqs i) && wf' eqs wf' (eqs :< Just (Th i (B _))) = isNothing (get' eqs i.fin) && wf' eqs
public export public export
wf : DimEq d -> Bool wf : {d : Nat} -> DimEq d -> Bool
wf ZeroIsOne = True wf ZeroIsOne = True
wf (C eqs) = wf' eqs wf (C eqs) = wf' eqs

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

@ -1,9 +1,11 @@
module Quox.Syntax.Shift module Quox.Syntax.Shift
import public Quox.Syntax.Var import public Quox.Syntax.Var
import public Quox.Thin
import Data.Nat import Data.Nat
import Data.So import Data.So
import Data.DPair
%default total %default total
@ -220,3 +222,15 @@ namespace CanShift
public export %inline public export %inline
[Const] CanShift (\_ => a) where x // _ = x [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

231
lib/Quox/Syntax/Subst.idr
View file

@ -1,10 +1,9 @@
module Quox.Syntax.Subst module Quox.Syntax.Subst
import public Quox.Syntax.Shift import Quox.Thin
import Quox.Syntax.Var import Quox.Loc
import Quox.Name
import Data.Nat import Data.DPair
import Data.List import Data.List
import Data.SnocVect import Data.SnocVect
import Derive.Prelude import Derive.Prelude
@ -14,149 +13,159 @@ import Derive.Prelude
public export public export
data Subst : (Nat -> Type) -> Nat -> Nat -> Type where Subst : (Nat -> Type) -> Nat -> Nat -> Type
Shift : Shift from to -> Subst env from to Subst env from to = SnocVect from (Lazy (Thinned env to))
(:::) : (t : Lazy (env to)) -> Subst env from to -> Subst env (S from) to
%name Subst th, ph, ps
infixr 7 !:::
||| in case the automatic laziness insertion gets confused
public export public export
(!:::) : env to -> Subst env from to -> Subst env (S from) to Subst2 : (Nat -> Nat -> Type) -> Nat -> Nat -> Nat -> Type
t !::: ts = t ::: ts Subst2 env d from to = SnocVect from (Lazy (Thinned2 env d to))
private public export
Repr : (Nat -> Type) -> Nat -> Type get : Subst env f t -> Fin f -> Thinned env t
Repr f to = (List (f to), Nat) get (sx :< x) FZ = x
get (sx :< x) (FS i) = get sx i
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)
export Eq (f to) => Eq (Subst f from to) where (==) = (==) `on` repr public export
export Ord (f to) => Ord (Subst f from to) where compare = compare `on` repr interface FromVar (0 term : Nat -> Type) where
export Show (f to) => Show (Subst f from to) where show = show . repr 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 // infixl 8 //
namespace CanSubstSelf
public export public export
interface FromVar term => CanSubstSelf term where interface FromVar term => CanSubstSelf term where
(//) : term from -> Lazy (Subst term from to) -> term to (//) : {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
(.) : {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 public export
getLoc : FromVar term => Subst term from to -> Var from -> Loc -> term to tabulate : (n : Nat) -> SnocVect n (Fin n)
getLoc (Shift by) i loc = fromVarLoc (shift by i) loc tabulate n = go n id where
getLoc (t ::: th) VZ _ = t go : (n : Nat) -> (Fin n -> Fin n') -> SnocVect n (Fin n')
getLoc (t ::: th) (VS i) loc = getLoc th i loc go 0 f = [<]
go (S n) f = go n (f . FS) :< f FZ
public export public export
CanSubstSelf Var where id : FromVar term => {n : Nat} -> (under : Nat) -> Loc ->
i // Shift by = shift by i Subst term n (n + under)
VZ // (t ::: th) = t id under loc =
VS i // (t ::: th) = i // th map (\i => delay $ varT (weakenN under i) loc) (tabulate n)
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
public export public export
(.) : CanSubstSelf f => Subst f from mid -> Subst f mid to -> Subst f from to id2 : FromVar2 term => {n : Nat} -> Loc -> Subst2 term d n n
Shift by . Shift bz = Shift $ by . bz id2 loc = map (\i => delay $ varT2 i loc) $ tabulate n
Shift SZ . ph = ph
Shift (SS by) . (t ::: th) = Shift by . th
(t ::: th) . ph = (t // ph) ::: (th . ph)
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 export
cmpShape : Subst env from1 to -> Subst env from2 to -> select : {n, mask : Nat} -> (0 ope : OPE m n mask) ->
Either Ordering (from1 = from2) SnocVect n a -> SnocVect m a
cmpShape (Shift by) (Shift bz) = cmpLen by bz select ope sx with %syntactic (view ope)
cmpShape (Shift _) (_ ::: _) = Left LT select _ [<] | StopV = [<]
cmpShape (_ ::: _) (Shift _) = Left GT select _ (sx :< x) | DropV _ ope = select ope sx
cmpShape (_ ::: th) (_ ::: ph) = cong S <$> cmpShape th ph 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 public export
record WithSubst tm env n where record WithSubst tm env n where
constructor Sub constructor Sub
term : tm from term : tm from
subst : Lazy (Subst env from n) subst : Subst env from n
{-
export 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 = Sub t1 s1 == Sub t2 s2 =
case cmpShape s1 s2 of case cmpShape s1 s2 of
Left _ => False Left _ => False
Right Refl => t1 == t2 && s1 == s2 Right Refl =>
t1 == t2 && concat @{All} (zipWith ((==) `on` force) s1 s2)
export 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 = Sub t1 s1 `compare` Sub t2 s2 =
case cmpShape s1 s2 of case cmpShape s1 s2 of
Left o => o Left o => o
Right Refl => compare (t1, s1) (t2, s2) Right Refl =>
compare t1 t2 <+> concat (zipWith (compare `on` force) s1 s2)
export %hint 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) 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 E : Elim d n -> Term d n
||| term closure/suspended substitution ||| 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 ||| dimension closure/suspended substitution
DCloT : WithSubst (\d => Term d n) Dim d -> Term d n DCloT : WithSubst (\d => Term d n) Dim d -> Term d n
@ -194,7 +194,7 @@ data Elim where
] d n -> Loc -> Elim d n ] d n -> Loc -> Elim d n
||| term closure/suspended substitution ||| 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 ||| dimension closure/suspended substitution
DCloE : WithSubst (\d => Elim d n) Dim d -> Elim d n DCloE : WithSubst (\d => Elim d n) Dim d -> Elim d n
@ -325,7 +325,7 @@ Located (Elim d n) where
(Coe _ loc).loc = loc (Coe _ loc).loc = loc
(Comp _ loc).loc = loc (Comp _ loc).loc = loc
(TypeCase _ 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 (DCloE (Sub e _)).loc = e.loc
export export
@ -345,7 +345,7 @@ Located (Term d n) where
(BOX _ _ loc).loc = loc (BOX _ _ loc).loc = loc
(Box _ loc).loc = loc (Box _ loc).loc = loc
(E e).loc = e.loc (E e).loc = e.loc
(CloT (Sub t _)).loc = t.loc (CloT (Sub2 t _)).loc = t.loc
(DCloT (Sub 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 (Coe ts _) = Coe ts loc
setLoc loc (Comp ts _) = Comp ts loc setLoc loc (Comp ts _) = Comp ts loc
setLoc loc (TypeCase ts _) = TypeCase 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 setLoc loc (DCloE (Sub term subst)) = DCloE $ Sub (setLoc loc term) subst
export export
@ -383,5 +383,5 @@ Relocatable (Term d n) where
setLoc loc (BOX qty ty _) = BOX qty ty loc setLoc loc (BOX qty ty _) = BOX qty ty loc
setLoc loc (Box val _) = Box val loc setLoc loc (Box val _) = Box val loc
setLoc loc (E e) = E $ setLoc loc e 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 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 export
prettyTerm : {opts : _} -> BContext d -> BContext n -> Term d n -> prettyTerm : {opts : _} -> BContext d -> BContext n -> TermT d n ->
Eff Pretty (Doc opts) Eff Pretty (Doc opts)
export export
prettyElim : {opts : _} -> BContext d -> BContext n -> Elim d n -> prettyElim : {opts : _} -> BContext d -> BContext n -> ElimT d n ->
Eff Pretty (Doc opts) Eff Pretty (Doc opts)
private private

788
lib/Quox/Syntax/Term/Subst.idr
View file

@ -2,374 +2,462 @@ module Quox.Syntax.Term.Subst
import Quox.No import Quox.No
import Quox.Syntax.Term.Base import Quox.Syntax.Term.Base
import Quox.Syntax.Term.Tighten import Quox.Syntax.Subst
import Data.SnocVect import Data.SnocVect
import Data.Singleton
%default total %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: infixl 8 ///
||| - deletes the closure around an atomic constant like `TYPE`
||| - deletes an identity substitution parameters {0 f : Nat -> Nat -> Type}
||| - composes (lazily) with an existing top-level dim-closure private
||| - otherwise, wraps in a new closure th0 : f 0 0 -> Thinned2 f d n
export th0 = Th2 zero zero
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
private private
subDArgs : Elim d1 n -> DSubst d1 d2 -> Elim d2 n th1 : {d, n : Nat} -> f d n -> Thinned2 f d n
subDArgs (DApp f d loc) th = DApp (subDArgs f th) (d // th) loc th1 = Th2 id' id'
subDArgs e th = DCloE $ Sub e th
||| does the minimal reasonable work: private dsubTerm : {d1, d2, n : Nat} -> Term d1 n -> DSubst d1 d2 -> TermT d2 n
||| - deletes the closure around a term variable private dsubElim : {d1, d2, n : Nat} -> Elim d1 n -> DSubst d1 d2 -> ElimT d2 n
||| - 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 dsubTerm (TYPE l loc) th = th0 $ TYPE l loc
export %inline dsubTerm (Enum strs loc) th = th0 $ Enum strs loc
(//) : ScopeTermN s d1 n -> Lazy (DSubst d1 d2) -> dsubTerm (Tag str loc) th = th0 $ Tag str loc
ScopeTermN s d2 n dsubTerm (Nat loc) th = th0 $ Nat loc
S ns (Y body) // th = S ns $ Y $ body // th dsubTerm (Zero loc) th = th0 $ Zero loc
S ns (N body) // th = S ns $ N $ body // th 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
namespace DSubst.DScopeTermN dsubElim (F x l loc) th = th0 $ F x l loc
export %inline dsubElim (B loc) th = Th2 zero id' $ B loc
(//) : {s : Nat} -> dsubElim (DCloE (Sub e ph)) th = th1 $ DCloE $ Sub e $ ph . th
DScopeTermN s d1 n -> Lazy (DSubst d1 d2) -> dsubElim e th = th1 $ DCloE $ Sub e th
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 mutual
public export namespace Term
isCloT : CloTest Term export
isCloT (CloT {}) = True (///) : {d1, d2, n : Nat} -> TermT d1 n -> DSubst d1 d2 -> TermT d2 n
isCloT (DCloT {}) = True Th2 dope tope term /// th =
isCloT (E e) = isCloE e let Val tscope = appOpe n tope; Val dscope = appOpe d1 dope
isCloT _ = False Th2 dope' tope' term' = dsubTerm term (select dope th)
in
Th2 dope' (tope . tope') term'
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'
public export public export
isCloE : CloTest Elim TSubst : Nat -> Nat -> Nat -> Type
isCloE (CloE {}) = True TSubst = Subst2 Elim
isCloE (DCloE {}) = True
isCloE _ = False
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
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 export
PushSubsts Elim Subst.isCloE where CanSubstSelf2 Elim where
pushSubstsWith th ph (F x u loc) = Th2 dope tope elim // th =
nclo $ F x u loc let
pushSubstsWith th ph (B i loc) = th' = select tope th
let res = getLoc ph i loc in in
case nchoose $ isCloE res of ?sube2
Left yes => assert_total pushSubsts res
Right no => Element res no -- namespace CanDSubst
pushSubstsWith th ph (App f s loc) = -- public export
nclo $ App (f // th // ph) (s // th // ph) loc -- interface CanDSubst (0 tm : TermLike) where
pushSubstsWith th ph (CasePair pi p r b loc) = -- (//) : {d1 : Nat} -> Thinned2 tm d1 n -> Lazy (DSubst d1 d2) ->
nclo $ CasePair pi (p // th // ph) (r // th // ph) (b // th // ph) loc -- Thinned2 tm d2 n
pushSubstsWith th ph (CaseEnum pi t r arms loc) =
nclo $ CaseEnum pi (t // th // ph) (r // th // ph) -- ||| does the minimal reasonable work:
(map (\b => b // th // ph) arms) loc -- ||| - deletes the closure around an atomic constant like `TYPE`
pushSubstsWith th ph (CaseNat pi pi' n r z s loc) = -- ||| - deletes an identity substitution
nclo $ CaseNat pi pi' (n // th // ph) (r // th // ph) -- ||| - composes (lazily) with an existing top-level dim-closure
(z // th // ph) (s // th // ph) loc -- ||| - otherwise, wraps in a new closure
pushSubstsWith th ph (CaseBox pi x r b loc) = -- export
nclo $ CaseBox pi (x // th // ph) (r // th // ph) (b // th // ph) loc -- CanDSubst Term where
pushSubstsWith th ph (DApp f d loc) = -- Th2 _ _ (TYPE l loc) // _ = Th2 zero zero $ TYPE l loc
nclo $ DApp (f // th // ph) (d // th) loc -- Th2 i j (DCloT (Sub s ph)) // th =
pushSubstsWith th ph (Ann s a loc) = -- Th2 ?i' j $ DCloT $ Sub s $ ph . ?th'
nclo $ Ann (s // th // ph) (a // th // ph) loc -- Th2 i j s // th = ?sdf -- DCloT $ Sub s th
pushSubstsWith th ph (Coe ty p q val loc) =
nclo $ Coe (ty // th // ph) (p // th) (q // th) (val // th // ph) loc -- -- private
pushSubstsWith th ph (Comp ty p q val r zero one loc) = -- -- subDArgs : Elim d1 n -> DSubst d1 d2 -> Elim d2 n
nclo $ Comp (ty // th // ph) (p // th) (q // th) -- -- subDArgs (DApp f d loc) th = DApp (subDArgs f th) (d // th) loc
(val // th // ph) (r // th) -- -- subDArgs e th = DCloE $ Sub e th
(zero // th // ph) (one // th // ph) loc
pushSubstsWith th ph (TypeCase ty ret arms def loc) = -- -- ||| does the minimal reasonable work:
nclo $ TypeCase (ty // th // ph) (ret // th // ph) -- -- ||| - deletes the closure around a term variable
(map (\t => t // th // ph) arms) (def // th // ph) loc -- -- ||| - deletes an identity substitution
pushSubstsWith th ph (CloE (Sub e ps)) = -- -- ||| - composes (lazily) with an existing top-level dim-closure
pushSubstsWith th (comp th ps ph) e -- -- ||| - immediately looks up bound variables in a
pushSubstsWith th ph (DCloE (Sub e ps)) = -- -- ||| top-level sequence of dimension applications
pushSubstsWith (ps . th) ph e -- -- ||| - 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
private %inline -- -- export %inline FromVar (Elim d) where fromVarLoc = B
CompHY : (ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) -> -- -- export %inline FromVar (Term d) where fromVarLoc = E .: fromVar
(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) -- -- ||| does the minimal reasonable work:
||| -- -- ||| - deletes the closure around a *free* name
||| comp [i ⇒ A] @p @q s @r { 0 j ⇒ t₀; 1 j ⇒ t₁ } -- -- ||| - deletes an identity substitution
||| ≔ -- -- ||| - composes (lazily) with an existing top-level closure
||| comp [A‹q/i›] @p @q (coe [i ⇒ A] @p @q s) @r { -- -- ||| - immediately looks up a bound variable
||| 0 j ⇒ coe [i ⇒ A] @j @q t₀; -- -- ||| - otherwise, wraps in a new closure
||| 1 j ⇒ coe [i ⇒ A] @j @q t₁ -- -- export
||| } -- -- CanSubstSelf (Elim d) where
public export %inline -- -- F x u loc // _ = F x u loc
CompH : (i : BindName) -> (ty : Term (S d) n) -> -- -- B i loc // th = getLoc th i loc
(p, q : Dim d) -> (val : Term d n) -> (r : Dim d) -> -- -- CloE (Sub e ph) // th = assert_total CloE $ Sub e $ ph . th
(j0 : BindName) -> (zero : Term (S d) n) -> -- -- e // th = case force th of
(j1 : BindName) -> (one : Term (S d) n) -> -- -- Shift SZ => e
(loc : Loc) -> -- -- th => CloE $ Sub e th
Elim d n
CompH {i, ty, p, q, val, r, j0, zero, j1, one, loc} = -- -- namespace CanTSubst
CompH' {ty = SY [< i] ty, p, q, val, r, -- -- public export
zero = SY [< j0] zero, one = SY [< j0] one, loc} -- -- 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) 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 export
tabulateV : {0 tm : Nat -> Type} -> (forall n. Var n -> tm n) -> tabulateV : {0 tm : Nat -> Type} -> (forall n. Var n -> tm n) ->
(n : Nat) -> Vect 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 id {m = S m} = Element _ $ Keep id.snd Refl
public export %inline 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 id' = id.snd
||| nothing selected ||| 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.Base
import public Quox.Thin.View import public Quox.Thin.View
import Quox.NatExtra
import Data.Singleton import Data.Singleton
%default total %default total
@ -52,8 +53,3 @@ export
0 (.) : (ope1 : OPE n p mask1) -> (ope2 : OPE m n mask2) -> 0 (.) : (ope1 : OPE n p mask1) -> (ope2 : OPE m n mask2) ->
OPE m p (comp ope1 ope2).mask OPE m p (comp ope1 ope2).mask
ope1 . ope2 = (comp ope1 ope2).ope 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 public Quox.Thin.List
import Quox.Thin.Eqv import Quox.Thin.Eqv
import public Quox.Thin.Cover import public Quox.Thin.Cover
import Quox.Thin.Append
import Quox.Name import Quox.Name
import Quox.Loc import Quox.Loc
import Data.DPair import Data.DPair
@ -15,6 +16,13 @@ import Decidable.Equality
%default total %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 public export
record Thinned f n where record Thinned f n where
constructor Th constructor Th
@ -26,9 +34,20 @@ record Thinned f n where
export export
(forall n. Eq (f n)) => Eq (Thinned f n) where (forall n. Eq (f n)) => Eq (Thinned f n) where
s == t = case decEq s.scopeMask t.scopeMask of s == t = case cmpMask s.scopeMask t.scopeMask of
Yes eq => s.term == (rewrite maskEqInner s.ope t.ope eq in t.term) Left _ => False
No _ => 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 export
(forall n. Located (f n)) => Located (Thinned f n) where (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 : {n : Nat} -> Thinned (Thinned f) n -> Thinned f n
join (Th ope1 (Th ope2 term)) = Th (ope1 . ope2) term 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 public export
record ScopedN (s : Nat) (f : Nat -> Type) (n : Nat) where 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) rewrite maskEqInner s.tope t.tope teq in t.term)
_ => False _ => 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 export
(forall d, n. Located (f d n)) => Located (Thinned2 f d n) where (forall d, n. Located (f d n)) => Located (Thinned2 f d n) where
term.loc = term.term.loc term.loc = term.term.loc
@ -122,6 +153,12 @@ namespace Thinned2
join (Th2 dope1 tope1 (Th2 dope2 tope2 term)) = join (Th2 dope1 tope1 (Th2 dope2 tope2 term)) =
Th2 (dope1 . dope2) (tope1 . 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 namespace TermList
public export public export

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

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