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

135 lines
4.4 KiB
Idris

module Quox.Syntax.Term.Subst
import Quox.Syntax.Term.Base
%default total
export FromVar (Elim q d) where fromVar = B
export FromVar (Term q 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 q d) (Elim q 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 q d) (Term q 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 q d) (ScopeTerm q d) where
TUsed body // th = TUsed $ body // push th
TUnused body // th = TUnused $ body // th
export CanSubst Var (Term q d) where s // th = s // map (B {q, d}) th
export CanSubst Var (Elim q d) where e // th = e // map (B {q, d}) th
export CanSubst Var (ScopeTerm q d) where s // th = s // map (B {q, d}) th
infixl 8 //., ///
mutual
namespace Term
||| applies a term substitution with a less ambiguous type
export
(//.) : Term q d from -> TSubst q d from to -> Term q d to
t //. th = t // th
||| applies a dimension substitution with the same behaviour as `(//)`
||| above
export
(///) : Term q dfrom n -> DSubst dfrom dto -> Term q 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 q dfrom from -> DSubst dfrom dto -> TSubst q dto from to ->
Term q dto to
subs s th ph = s /// th // ph
namespace Elim
||| applies a term substitution with a less ambiguous type
export
(//.) : Elim q d from -> TSubst q d from to -> Elim q d to
e //. th = e // th
||| applies a dimension substitution with the same behaviour as `(//)`
||| above
export
(///) : Elim q dfrom n -> DSubst dfrom dto -> Elim q 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 q dfrom from -> DSubst dfrom dto -> TSubst q dto from to ->
Elim q dto to
subs e th ph = e /// th // ph
namespace ScopeTerm
||| applies a term substitution with a less ambiguous type
export
(//.) : ScopeTerm q d from -> TSubst q d from to -> ScopeTerm q d to
body //. th = body // th
||| applies a dimension substitution with the same behaviour as `(//)`
||| above
export
(///) : ScopeTerm q dfrom n -> DSubst dfrom dto -> ScopeTerm q 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 q dfrom from -> DSubst dfrom dto -> TSubst q dto from to ->
ScopeTerm q dto to
subs body th ph = body /// th // ph
export CanShift (Term q d) where s // by = s //. Shift by
export CanShift (Elim q d) where e // by = e //. Shift by
export CanShift (ScopeTerm q d) where s // by = s //. Shift by
export %inline
comp' : DSubst dfrom dto -> TSubst q dfrom from mid -> TSubst q dto mid to ->
TSubst q dto from to
comp' th ps ph = map (/// th) ps . ph
export
fromDScopeTerm : DScopeTerm q d n -> Term q (S d) n
fromDScopeTerm (DUsed body) = body
fromDScopeTerm (DUnused body) = body /// shift 1
export
fromScopeTerm : ScopeTerm q d n -> Term q d (S n)
fromScopeTerm (TUsed body) = body
fromScopeTerm (TUnused body) = body //. shift 1