342 lines
11 KiB
Idris
342 lines
11 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 Data.SnocVect
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%default total
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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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(//) : tm dfrom n -> Lazy (DSubst dfrom dto) -> tm dto 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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s // Shift SZ = s
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TYPE l // _ = TYPE l
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DCloT s ph // th = DCloT s $ ph . th
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s // th = DCloT s th
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private
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subDArgs : Elim dfrom n -> DSubst dfrom dto -> Elim dto n
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subDArgs (f :% d) th = subDArgs f th :% (d // th)
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subDArgs e th = DCloE 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 // _ = F x
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B i // _ = B i
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f :% d // th = subDArgs (f :% d) th
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DCloE e ph // th = DCloE e $ ph . th
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e // th = DCloE e th
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namespace DSubst.ScopeTermN
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export %inline
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(//) : ScopeTermN s dfrom n -> Lazy (DSubst dfrom dto) ->
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ScopeTermN s dto 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 dfrom n -> Lazy (DSubst dfrom dto) ->
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DScopeTermN s dto 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 fromVar = B
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export %inline FromVar (Term d) where fromVar = 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 // _ = F x
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B i // th = th !! i
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CloE e ph // th = assert_total CloE 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 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 from -> Lazy (TSubst d from to) -> tm d to
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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 // _ = TYPE l
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E e // th = E $ e // th
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CloT s ph // th = CloT 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 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 from -> Lazy (TSubst d from to) ->
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ScopeTermN s d to
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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 from -> Lazy (TSubst d from to) ->
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DScopeTermN s d to
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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 dfrom dto -> TSubst dfrom from mid -> TSubst dto mid to ->
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TSubst dto from to
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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 -> Term d n
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body.zero = dsub1 body $ K Zero
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public export %inline
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(.one) : DScopeTerm d n -> Term d n
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body.one = dsub1 body $ K One
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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 dfrom dto -> TSubst dto from to ->
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tm dfrom from -> Subset (tm dto to) (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 dfrom dto -> TSubst dto from to ->
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tm dfrom from -> tm dto to
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pushSubstsWith' th ph x = fst $ pushSubstsWith th ph x
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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) =
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nclo $ TYPE l
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pushSubstsWith th ph (Pi qty a body) =
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nclo $ Pi qty (a // th // ph) (body // th // ph)
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pushSubstsWith th ph (Lam body) =
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nclo $ Lam (body // th // ph)
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pushSubstsWith th ph (Sig a b) =
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nclo $ Sig (a // th // ph) (b // th // ph)
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pushSubstsWith th ph (Pair s t) =
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nclo $ Pair (s // th // ph) (t // th // ph)
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pushSubstsWith th ph (Enum tags) =
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nclo $ Enum tags
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pushSubstsWith th ph (Tag tag) =
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nclo $ Tag tag
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pushSubstsWith th ph (Eq ty l r) =
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nclo $ Eq (ty // th // ph) (l // th // ph) (r // th // ph)
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pushSubstsWith th ph (DLam body) =
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nclo $ DLam (body // th // ph)
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pushSubstsWith _ _ Nat = nclo Nat
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pushSubstsWith _ _ Zero = nclo Zero
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pushSubstsWith th ph (Succ n) = nclo $ Succ $ n // th // ph
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pushSubstsWith th ph (BOX pi ty) = nclo $ BOX pi $ ty // th // ph
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pushSubstsWith th ph (Box val) = nclo $ Box $ val // th // ph
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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 s ps) =
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pushSubstsWith th (comp th ps ph) s
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pushSubstsWith th ph (DCloT 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) =
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nclo $ F x
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pushSubstsWith th ph (B i) =
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let res = ph !! i 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 (f :@ s) =
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nclo $ (f // th // ph) :@ (s // th // ph)
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pushSubstsWith th ph (CasePair pi p r b) =
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nclo $ CasePair pi (p // th // ph) (r // th // ph) (b // th // ph)
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pushSubstsWith th ph (CaseEnum pi t r arms) =
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nclo $ CaseEnum pi (t // th // ph) (r // th // ph)
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(map (\b => b // th // ph) arms)
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pushSubstsWith th ph (CaseNat pi pi' n r z s) =
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nclo $ CaseNat pi pi' (n // th // ph) (r // th // ph)
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(z // th // ph) (s // th // ph)
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pushSubstsWith th ph (CaseBox pi x r b) =
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nclo $ CaseBox pi (x // th // ph) (r // th // ph) (b // th // ph)
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pushSubstsWith th ph (f :% d) =
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nclo $ (f // th // ph) :% (d // th)
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pushSubstsWith th ph (s :# a) =
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nclo $ (s // th // ph) :# (a // th // ph)
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pushSubstsWith th ph (Coe ty p q val) =
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nclo $ Coe (ty // th // ph) (p // th) (q // th) (val // th // ph)
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pushSubstsWith th ph (Comp ty p q val r zero one) =
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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)
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pushSubstsWith th ph (TypeCase ty ret arms def) =
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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)
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pushSubstsWith th ph (CloE e ps) =
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pushSubstsWith th (comp th ps ph) e
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pushSubstsWith th ph (DCloE e ps) =
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pushSubstsWith (ps . th) ph e
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||| heterogeneous composition, using Comp and Coe (and subst)
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||| comp [i ⇒ A] @p @q s { (r=0) j ⇒ t₀; (r=1) j ⇒ t₁ }
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||| ≔
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||| comp [A‹q/i›] @p @q (coe [i ⇒ A] @p @q s) {
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||| (r=0) j ⇒ coe [i ⇒ A] @j @q t₀;
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||| (r=1) j ⇒ coe [i ⇒ A] @j @q t₁
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||| }
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public export %inline
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CompH : (ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) ->
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(r : Dim d) -> (zero, one : DScopeTerm d n) -> Elim d n
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CompH {ty, p, q, val, r, zero, one} =
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let ty' = SY ty.names $ ty.term // (B VZ ::: shift 2) in
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Comp {
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ty = dsub1 ty q, p, q,
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val = E $ Coe ty p q val, r,
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zero = SY zero.names $ E $ Coe ty' (B VZ) (weakD 1 q) zero.term,
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one = SY one.names $ E $ Coe ty' (B VZ) (weakD 1 q) one.term
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}
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