135 lines
4.3 KiB
Idris
135 lines
4.3 KiB
Idris
module Quox.Syntax.Term.Subst
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import Quox.Syntax.Term.Base
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%default total
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export FromVar (Elim d) where fromVar = B
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export 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 since it doesn't do anything
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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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CanSubst (Elim d) (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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||| 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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CanSubst (Elim d) (Term d) 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
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CanSubst (Elim d) (ScopeTerm d) where
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TUsed body // th = TUsed $ body // push th
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TUnused body // th = TUnused $ body // th
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export CanSubst Var (Term d) where s // th = s // map (B {d}) th
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export CanSubst Var (Elim d) where e // th = e // map (B {d}) th
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export CanSubst Var (ScopeTerm d) where s // th = s // map (B {d}) th
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infixl 8 //., ///
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mutual
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namespace Term
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||| applies a term substitution with a less ambiguous type
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export
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(//.) : Term d from -> TSubst d from to -> Term d to
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t //. th = t // th
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||| applies a dimension substitution with the same behaviour as `(//)`
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||| above
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export
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(///) : Term dfrom n -> DSubst dfrom dto -> Term dto n
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TYPE l /// _ = TYPE l
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E e /// th = E $ e /// th
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DCloT s ph /// th = DCloT s $ ph . th
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s /// Shift SZ = s
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s /// th = DCloT s th
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||| applies a term and dimension substitution
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public export %inline
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subs : Term dfrom from -> DSubst dfrom dto -> TSubst dto from to ->
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Term dto to
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subs s th ph = s /// th // ph
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namespace Elim
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||| applies a term substitution with a less ambiguous type
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export
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(//.) : Elim d from -> TSubst d from to -> Elim d to
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e //. th = e // th
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||| applies a dimension substitution with the same behaviour as `(//)`
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||| above
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export
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(///) : Elim dfrom n -> DSubst dfrom dto -> Elim dto n
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F x /// _ = F x
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B i /// _ = B i
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DCloE e ph /// th = DCloE e $ ph . th
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e /// Shift SZ = e
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e /// th = DCloE e th
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||| applies a term and dimension substitution
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public export %inline
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subs : Elim dfrom from -> DSubst dfrom dto -> TSubst dto from to ->
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Elim dto to
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subs e th ph = e /// th // ph
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namespace ScopeTerm
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||| applies a term substitution with a less ambiguous type
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export
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(//.) : ScopeTerm d from -> TSubst d from to -> ScopeTerm d to
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body //. th = body // th
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||| applies a dimension substitution with the same behaviour as `(//)`
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||| above
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export
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(///) : ScopeTerm dfrom n -> DSubst dfrom dto -> ScopeTerm dto n
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TUsed body /// th = TUsed $ body /// th
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TUnused body /// th = TUnused $ body /// th
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||| applies a term and dimension substitution
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public export %inline
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subs : ScopeTerm dfrom from -> DSubst dfrom dto -> TSubst dto from to ->
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ScopeTerm dto to
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subs body th ph = body /// th // ph
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export CanShift (Term d) where s // by = s //. Shift by
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export CanShift (Elim d) where e // by = e //. Shift by
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export CanShift (ScopeTerm d) where s // by = s //. 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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export
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fromDScopeTerm : DScopeTerm d n -> Term (S d) n
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fromDScopeTerm (DUsed body) = body
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fromDScopeTerm (DUnused body) = body /// shift 1
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export
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fromScopeTerm : ScopeTerm d n -> Term d (S n)
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fromScopeTerm (TUsed body) = body
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fromScopeTerm (TUnused body) = body //. shift 1
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