136 lines
4.4 KiB
Idris
136 lines
4.4 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 q d) where fromVar = B
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export 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 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 q d) (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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||| 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 q d) (Term q 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 q d) (ScopeTerm q 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 q d) where s // th = s // map (B {q, d}) th
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export CanSubst Var (Elim q d) where e // th = e // map (B {q, d}) th
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export CanSubst Var (ScopeTerm q d) where s // th = s // map (B {q, 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 q d from -> TSubst q d from to -> Term q 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 q dfrom n -> DSubst dfrom dto -> Term q 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 q dfrom from -> DSubst dfrom dto -> TSubst q dto from to ->
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Term q 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 q d from -> TSubst q d from to -> Elim q 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 q dfrom n -> DSubst dfrom dto -> Elim q 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 q dfrom from -> DSubst dfrom dto -> TSubst q dto from to ->
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Elim q 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 q d from -> TSubst q d from to -> ScopeTerm q 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 q dfrom n -> DSubst dfrom dto -> ScopeTerm q 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 q dfrom from -> DSubst dfrom dto -> TSubst q dto from to ->
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ScopeTerm q dto to
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subs body th ph = body /// th // ph
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export CanShift (Term q d) where s // by = s //. Shift by
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export CanShift (Elim q d) where e // by = e //. Shift by
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export CanShift (ScopeTerm q d) where s // by = s //. 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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export
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fromDScopeTerm : DScopeTerm q d n -> Term q (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 q d n -> Term q 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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