226 lines
7.0 KiB
Idris
226 lines
7.0 KiB
Idris
module Quox.Syntax.Term.Subst
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import Quox.Syntax.Term.Base
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import Data.Vect
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%default total
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infixl 8 ///
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mutual
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namespace Term
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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 dim-closure
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||| - otherwise, wraps in a new closure
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export
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(///) : Term q dfrom n -> DSubst dfrom dto -> Term q dto n
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s /// Shift SZ = s
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TYPE l /// _ = TYPE l
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DCloT s ph /// th = DCloT s $ ph . th
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s /// th = DCloT s th
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namespace Elim
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private
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subDArgs : Elim q dfrom n -> DSubst dfrom dto -> Elim q dto n
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subDArgs (f :% d) th = subDArgs f th :% (d // th)
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subDArgs e th = DCloE e th
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||| does the minimal reasonable work:
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||| - deletes the closure around a term variable
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||| - deletes an identity substitution
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||| - composes (lazily) with an existing top-level dim-closure
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||| - immediately looks up bound variables in a
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||| top-level sequence of dimension applications
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||| - otherwise, wraps in a new closure
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export
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(///) : Elim q dfrom n -> DSubst dfrom dto -> Elim q dto n
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e /// Shift SZ = e
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F x /// _ = F x
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B i /// _ = B i
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f :% d /// th = subDArgs (f :% d) th
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DCloE e ph /// th = DCloE e $ ph . th
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e /// th = DCloE e th
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namespace ScopeTermN
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export
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(///) : ScopeTermN s q dfrom n -> DSubst dfrom dto -> ScopeTermN s 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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namespace DScopeTermN
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export
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(///) : {s : Nat} ->
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DScopeTermN s q dfrom n -> DSubst dfrom dto ->
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DScopeTermN s q dto n
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DUsed body /// th = DUsed $ body /// pushN s th
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DUnused body /// th = DUnused $ body /// th
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export %inline FromVar (Elim q d) where fromVar = B
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export %inline 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
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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 %inline
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{s : Nat} -> CanSubst (Elim q d) (ScopeTermN s q d) where
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TUsed body // th = TUsed $ body // pushN s th
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TUnused body // th = TUnused $ body // th
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export %inline
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{s : Nat} -> CanSubst (Elim q d) (DScopeTermN s q d) where
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DUsed body // th = DUsed $ body // map (/// shift s) th
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DUnused body // th = DUnused $ body // th
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export %inline CanSubst Var (Term q d) where s // th = s // map (B {q, d}) th
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export %inline CanSubst Var (Elim q d) where e // th = e // map (B {q, d}) th
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export %inline
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{s : Nat} -> CanSubst Var (ScopeTermN s q d) where
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b // th = b // map (B {q, d}) th
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export %inline
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{s : Nat} -> CanSubst Var (DScopeTermN s q d) where
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b // th = b // 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 %inline
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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 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 %inline
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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 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 ScopeTermN
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||| applies a term substitution with a less ambiguous type
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export %inline
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(//.) : {s : Nat} ->
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ScopeTermN s q d from -> TSubst q d from to ->
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ScopeTermN s q d to
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body //. th = body // th
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||| applies a term and dimension substitution
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public export %inline
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subs : {s : Nat} ->
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ScopeTermN s q dfrom from ->
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DSubst dfrom dto -> TSubst q dto from to ->
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ScopeTermN s q dto to
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subs body th ph = body /// th // ph
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namespace DScopeTermN
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||| applies a term substitution with a less ambiguous type
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export %inline
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(//.) : {s : Nat} -> DScopeTermN s q d from -> TSubst q d from to ->
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DScopeTermN s q d to
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body //. th = body // th
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||| applies a term and dimension substitution
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public export %inline
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subs : {s : Nat} ->
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DScopeTermN s q dfrom from ->
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DSubst dfrom dto -> TSubst q dto from to ->
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DScopeTermN s q dto to
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subs body th ph = body /// th // ph
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export %inline CanShift (Term q d) where s // by = s //. Shift by
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export %inline CanShift (Elim q d) where e // by = e //. Shift by
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export %inline
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{s : Nat} -> CanShift (ScopeTermN s q d) where
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b // by = b //. 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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namespace ScopeTermN
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export %inline
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(.term) : {s : Nat} -> ScopeTermN s q d n -> Term q d (s + n)
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(TUsed body).term = body
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(TUnused body).term = body //. shift s
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namespace DScopeTermN
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export %inline
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(.term) : {s : Nat} -> DScopeTermN s q d n -> Term q (s + d) n
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(DUsed body).term = body
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(DUnused body).term = body /// shift s
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export %inline
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subN : ScopeTermN s q d n -> Vect s (Elim q d n) -> Term q d n
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subN (TUsed body) es = body // fromVect es
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subN (TUnused body) _ = body
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export %inline
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sub1 : ScopeTerm q d n -> Elim q d n -> Term q d n
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sub1 t e = subN t [e]
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export %inline
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dsubN : DScopeTermN s q d n -> Vect s (Dim d) -> Term q d n
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dsubN (DUsed body) ps = body /// fromVect ps
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dsubN (DUnused body) _ = body
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export %inline
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dsub1 : DScopeTerm q d n -> Dim d -> Term q d n
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dsub1 t p = dsubN t [p]
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public export %inline
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(.zero) : DScopeTerm q d n -> Term q d n
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body.zero = dsub1 body $ K Zero
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public export %inline
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(.one) : DScopeTerm q d n -> Term q d n
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body.one = dsub1 body $ K One
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