quox/lib/Quox/Syntax/Term/Subst.idr

135 lines
4.3 KiB
Idris

module Quox.Syntax.Term.Subst
import Quox.Syntax.Term.Base
%default total
export FromVar (Elim d) where fromVar = B
export FromVar (Term d) where fromVar = E . fromVar
||| does the minimal reasonable work:
||| - deletes the closure around a free name since it doesn't do anything
||| - deletes an identity substitution
||| - composes (lazily) with an existing top-level closure
||| - immediately looks up a bound variable
||| - otherwise, wraps in a new closure
export
CanSubst (Elim d) (Elim d) where
F x // _ = F x
B i // th = th !! i
CloE e ph // th = assert_total CloE e $ ph . th
e // th = case force th of
Shift SZ => e
th => CloE e th
||| does the minimal reasonable work:
||| - deletes the closure around an atomic constant like `TYPE`
||| - deletes an identity substitution
||| - composes (lazily) with an existing top-level closure
||| - goes inside `E` in case it is a simple variable or something
||| - otherwise, wraps in a new closure
export
CanSubst (Elim d) (Term d) where
TYPE l // _ = TYPE l
E e // th = E $ e // th
CloT s ph // th = CloT s $ ph . th
s // th = case force th of
Shift SZ => s
th => CloT s th
export
CanSubst (Elim d) (ScopeTerm d) where
TUsed body // th = TUsed $ body // push th
TUnused body // th = TUnused $ body // th
export CanSubst Var (Term d) where s // th = s // map (B {d}) th
export CanSubst Var (Elim d) where e // th = e // map (B {d}) th
export CanSubst Var (ScopeTerm d) where s // th = s // map (B {d}) th
infixl 8 //., ///
mutual
namespace Term
||| applies a term substitution with a less ambiguous type
export
(//.) : Term d from -> TSubst d from to -> Term d to
t //. th = t // th
||| applies a dimension substitution with the same behaviour as `(//)`
||| above
export
(///) : Term dfrom n -> DSubst dfrom dto -> Term dto n
TYPE l /// _ = TYPE l
E e /// th = E $ e /// th
DCloT s ph /// th = DCloT s $ ph . th
s /// Shift SZ = s
s /// th = DCloT s th
||| applies a term and dimension substitution
public export %inline
subs : Term dfrom from -> DSubst dfrom dto -> TSubst dto from to ->
Term dto to
subs s th ph = s /// th // ph
namespace Elim
||| applies a term substitution with a less ambiguous type
export
(//.) : Elim d from -> TSubst d from to -> Elim d to
e //. th = e // th
||| applies a dimension substitution with the same behaviour as `(//)`
||| above
export
(///) : Elim dfrom n -> DSubst dfrom dto -> Elim dto n
F x /// _ = F x
B i /// _ = B i
DCloE e ph /// th = DCloE e $ ph . th
e /// Shift SZ = e
e /// th = DCloE e th
||| applies a term and dimension substitution
public export %inline
subs : Elim dfrom from -> DSubst dfrom dto -> TSubst dto from to ->
Elim dto to
subs e th ph = e /// th // ph
namespace ScopeTerm
||| applies a term substitution with a less ambiguous type
export
(//.) : ScopeTerm d from -> TSubst d from to -> ScopeTerm d to
body //. th = body // th
||| applies a dimension substitution with the same behaviour as `(//)`
||| above
export
(///) : ScopeTerm dfrom n -> DSubst dfrom dto -> ScopeTerm dto n
TUsed body /// th = TUsed $ body /// th
TUnused body /// th = TUnused $ body /// th
||| applies a term and dimension substitution
public export %inline
subs : ScopeTerm dfrom from -> DSubst dfrom dto -> TSubst dto from to ->
ScopeTerm dto to
subs body th ph = body /// th // ph
export CanShift (Term d) where s // by = s //. Shift by
export CanShift (Elim d) where e // by = e //. Shift by
export CanShift (ScopeTerm d) where s // by = s //. Shift by
export %inline
comp' : DSubst dfrom dto -> TSubst dfrom from mid -> TSubst dto mid to ->
TSubst dto from to
comp' th ps ph = map (/// th) ps . ph
export
fromDScopeTerm : DScopeTerm d n -> Term (S d) n
fromDScopeTerm (DUsed body) = body
fromDScopeTerm (DUnused body) = body /// shift 1
export
fromScopeTerm : ScopeTerm d n -> Term d (S n)
fromScopeTerm (TUsed body) = body
fromScopeTerm (TUnused body) = body //. shift 1