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

198 lines
5.7 KiB
Idris

module Quox.Syntax.Term.Subst
import Quox.Syntax.Term.Base
import Data.Vect
%default total
namespace CanDSubst
public export
interface CanDSubst (0 tm : Nat -> Nat -> Type) where
(//) : tm dfrom n -> Lazy (DSubst dfrom dto) -> tm dto n
||| 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 dim-closure
||| - otherwise, wraps in a new closure
export
CanDSubst (Term q) where
s // Shift SZ = s
TYPE l // _ = TYPE l
DCloT s ph // th = DCloT s $ ph . th
s // th = DCloT s th
private
subDArgs : Elim q dfrom n -> DSubst dfrom dto -> Elim q dto n
subDArgs (f :% d) th = subDArgs f th :% (d // th)
subDArgs e th = DCloE e th
||| does the minimal reasonable work:
||| - deletes the closure around a term variable
||| - deletes an identity substitution
||| - composes (lazily) with an existing top-level dim-closure
||| - immediately looks up bound variables in a
||| top-level sequence of dimension applications
||| - otherwise, wraps in a new closure
export
CanDSubst (Elim q) where
e // Shift SZ = e
F x // _ = F x
B i // _ = B i
f :% d // th = subDArgs (f :% d) th
DCloE e ph // th = DCloE e $ ph . th
e // th = DCloE e th
namespace DSubst.ScopeTermN
export %inline
(//) : ScopeTermN s q dfrom n -> Lazy (DSubst dfrom dto) ->
ScopeTermN s q dto n
S ns (Y body) // th = S ns $ Y $ body // th
S ns (N body) // th = S ns $ N $ body // th
namespace DSubst.DScopeTermN
export %inline
(//) : {s : Nat} ->
DScopeTermN s q dfrom n -> Lazy (DSubst dfrom dto) ->
DScopeTermN s q dto n
S ns (Y body) // th = S ns $ Y $ body // pushN s th
S ns (N body) // th = S ns $ N $ body // th
export %inline FromVar (Elim q d) where fromVar = B
export %inline FromVar (Term q d) where fromVar = E . fromVar
||| does the minimal reasonable work:
||| - deletes the closure around a *free* name
||| - 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
CanSubstSelf (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
namespace CanTSubst
public export
interface CanTSubst (0 tm : TermLike) where
(//) : tm q d from -> Lazy (TSubst q d from to) -> tm q d to
||| 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
CanTSubst Term 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
namespace ScopeTermN
export %inline
(//) : {s : Nat} ->
ScopeTermN s q d from -> Lazy (TSubst q d from to) ->
ScopeTermN s q d to
S ns (Y body) // th = S ns $ Y $ body // pushN s th
S ns (N body) // th = S ns $ N $ body // th
namespace DScopeTermN
export %inline
(//) : {s : Nat} ->
DScopeTermN s q d from -> Lazy (TSubst q d from to) ->
DScopeTermN s q d to
S ns (Y body) // th = S ns $ Y $ body // map (// shift s) th
S ns (N body) // th = S ns $ N $ body // th
export %inline CanShift (Term q d) where s // by = s // Shift by
export %inline CanShift (Elim q d) where e // by = e // Shift by
export %inline
{s : Nat} -> CanShift (ScopeTermN s q d) where
b // by = b // 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
public export %inline
dweakT : {by : Nat} -> Term q d n -> Term q (by + d) n
dweakT t = t // shift by
public export %inline
dweakE : {by : Nat} -> Elim q d n -> Elim q (by + d) n
dweakE t = t // shift by
public export %inline
weakT : {default 1 by : Nat} -> Term q d n -> Term q d (by + n)
weakT t = t // shift by
public export %inline
weakE : {default 1 by : Nat} -> Elim q d n -> Elim q d (by + n)
weakE t = t // shift by
parameters {s : Nat}
namespace ScopeTermBody
export %inline
(.term) : ScopedBody s (Term q d) n -> Term q d (s + n)
(Y b).term = b
(N b).term = weakT b {by = s}
namespace ScopeTermN
export %inline
(.term) : ScopeTermN s q d n -> Term q d (s + n)
t.term = t.body.term
namespace DScopeTermBody
export %inline
(.term) : ScopedBody s (\d => Term q d n) d -> Term q (s + d) n
(Y b).term = b
(N b).term = dweakT b {by = s}
namespace DScopeTermN
export %inline
(.term) : DScopeTermN s q d n -> Term q (s + d) n
t.term = t.body.term
export %inline
subN : ScopeTermN s q d n -> Vect s (Elim q d n) -> Term q d n
subN (S _ (Y body)) es = body // fromVect es
subN (S _ (N body)) _ = body
export %inline
sub1 : ScopeTerm q d n -> Elim q d n -> Term q d n
sub1 t e = subN t [e]
export %inline
dsubN : DScopeTermN s q d n -> Vect s (Dim d) -> Term q d n
dsubN (S _ (Y body)) ps = body // fromVect ps
dsubN (S _ (N body)) _ = body
export %inline
dsub1 : DScopeTerm q d n -> Dim d -> Term q d n
dsub1 t p = dsubN t [p]
public export %inline
(.zero) : DScopeTerm q d n -> Term q d n
body.zero = dsub1 body $ K Zero
public export %inline
(.one) : DScopeTerm q d n -> Term q d n
body.one = dsub1 body $ K One