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