177 lines
5.2 KiB
Idris
177 lines
5.2 KiB
Idris
module Quox.Syntax.Term.Subst
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import Quox.Syntax.Term.Base
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import Data.Vect
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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 : Nat -> Nat -> Type) where
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(//) : tm dfrom n -> Lazy (DSubst dfrom dto) -> tm dto n
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mutual
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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 q) 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 q dfrom n -> DSubst dfrom dto -> Elim q 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 q) 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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export
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CanDSubst (ScopeTermN s q) where
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TUsed body // th = TUsed $ body // th
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TUnused body // th = TUnused $ body // th
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export
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{s : Nat} -> CanDSubst (DScopeTermN s q) where
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DUsed body // th = DUsed $ body // pushN s th
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DUnused body // th = DUnused $ body // th
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export %inline FromVar (Elim q d) where fromVar = B
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export %inline FromVar (Term q 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 q 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 q d from -> Lazy (TSubst q d from to) -> tm q 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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export %inline
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{s : Nat} -> CanTSubst (ScopeTermN s) where
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TUsed body // th = TUsed $ body // pushN s th
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TUnused body // th = TUnused $ body // th
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export %inline
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{s : Nat} -> CanTSubst (DScopeTermN s) where
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DUsed body // th = DUsed $ body // map (// shift s) th
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DUnused body // th = DUnused $ body // th
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export %inline CanShift (Term q d) where s // by = s // Shift by
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export %inline CanShift (Elim q d) where e // by = e // Shift by
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export %inline
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{s : Nat} -> CanShift (ScopeTermN s q 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 q dfrom from mid -> TSubst q dto mid to ->
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TSubst q 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 q d n -> Term q (by + d) n
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dweakT t = t // shift by
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public export %inline
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dweakE : {by : Nat} -> Elim q d n -> Elim q (by + d) n
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dweakE t = t // shift by
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public export %inline
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weakT : {default 1 by : Nat} -> Term q d n -> Term q d (by + n)
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weakT t = t // shift by
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public export %inline
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weakE : {default 1 by : Nat} -> Elim q d n -> Elim q d (by + n)
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weakE t = t // shift by
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namespace ScopeTermN
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export %inline
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(.term) : {s : Nat} -> ScopeTermN s q d n -> Term q d (s + n)
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(TUsed body).term = body
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(TUnused body).term = weakT body {by = s}
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namespace DScopeTermN
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export %inline
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(.term) : {s : Nat} -> DScopeTermN s q d n -> Term q (s + d) n
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(DUsed body).term = body
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(DUnused body).term = dweakT body {by = s}
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export %inline
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subN : ScopeTermN s q d n -> Vect s (Elim q d n) -> Term q d n
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subN (TUsed body) es = body // fromVect es
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subN (TUnused body) _ = body
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export %inline
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sub1 : ScopeTerm q d n -> Elim q d n -> Term q 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 q d n -> Vect s (Dim d) -> Term q d n
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dsubN (DUsed body) ps = body // fromVect ps
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dsubN (DUnused body) _ = body
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export %inline
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dsub1 : DScopeTerm q d n -> Dim d -> Term q 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 q d n -> Term q 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 q d n -> Term q d n
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body.one = dsub1 body $ K One
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