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

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Idris

module Quox.Syntax.Term.Pretty
import Quox.Syntax.Term.Base
import Quox.Syntax.Term.Subst
import Quox.Context
import Quox.Pretty
import Data.Vect
import Derive.Prelude
%default total
%language ElabReflection
export
prettyUniverse : {opts : _} -> Universe -> Eff Pretty (Doc opts)
prettyUniverse = hl Universe . text . show
export
prettyTerm : {opts : _} -> BContext d -> BContext n -> Term d n ->
Eff Pretty (Doc opts)
export
prettyElim : {opts : _} -> BContext d -> BContext n -> Elim d n ->
Eff Pretty (Doc opts)
private
BTelescope : Nat -> Nat -> Type
BTelescope = Telescope' BindName
private
superscript : String -> String
superscript = pack . map sup . unpack where
sup : Char -> Char
sup c = case c of
'0' => ''; '1' => '¹'; '2' => '²'; '3' => '³'; '4' => ''
'5' => ''; '6' => ''; '7' => ''; '8' => ''; '9' => ''; _ => c
private
PiBind : Nat -> Nat -> Type
PiBind d n = (Qty, BindName, Term d n)
private
pbname : PiBind d n -> BindName
pbname (_, x, _) = x
private
record SplitPi d n where
constructor MkSplitPi
{0 inner : Nat}
binds : Telescope (PiBind d) n inner
cod : Term d inner
private
splitPi : Telescope (PiBind d) n n' -> Term d n' -> SplitPi d n
splitPi binds (Pi qty arg res _) =
splitPi (binds :< (qty, res.name, arg)) $
assert_smaller res $ pushSubsts' res.term
splitPi binds cod = MkSplitPi {binds, cod}
private
prettyPiBind1 : {opts : _} ->
Qty -> BindName -> BContext d -> BContext n -> Term d n ->
Eff Pretty (Doc opts)
prettyPiBind1 pi (BN Unused _) dnames tnames s =
hcat <$> sequence
[prettyQty pi, dotD,
withPrec Arg $ assert_total prettyTerm dnames tnames s]
prettyPiBind1 pi x dnames tnames s = hcat <$> sequence
[prettyQty pi, dotD,
hl Delim $ text "(",
hsep <$> sequence
[prettyTBind x, hl Delim $ text ":",
withPrec Outer $ assert_total prettyTerm dnames tnames s],
hl Delim $ text ")"]
private
prettyPiBinds : {opts : _} ->
BContext d -> BContext n ->
Telescope (PiBind d) n n' ->
Eff Pretty (SnocList (Doc opts))
prettyPiBinds _ _ [<] = pure [<]
prettyPiBinds dnames tnames (binds :< (q, x, t)) =
let tnames' = tnames . map pbname binds in
[|prettyPiBinds dnames tnames binds :<
prettyPiBind1 q x dnames tnames' t|]
private
SigBind : Nat -> Nat -> Type
SigBind d n = (BindName, Term d n)
private
record SplitSig d n where
constructor MkSplitSig
{0 inner : Nat}
binds : Telescope (SigBind d) n inner
last : Term d inner
private
splitSig : Telescope (SigBind d) n n' -> Term d n' -> SplitSig d n
splitSig binds (Sig fst snd _) =
splitSig (binds :< (snd.name, fst)) $
assert_smaller snd $ pushSubsts' snd.term
splitSig binds last = MkSplitSig {binds, last}
private
prettySigBind1 : {opts : _} ->
BindName -> BContext d -> BContext n -> Term d n ->
Eff Pretty (Doc opts)
prettySigBind1 (BN Unused _) dnames tnames s =
withPrec InTimes $ assert_total prettyTerm dnames tnames s
prettySigBind1 x dnames tnames s = hcat <$> sequence
[hl Delim $ text "(",
hsep <$> sequence
[prettyTBind x, hl Delim $ text ":",
withPrec Outer $ assert_total prettyTerm dnames tnames s],
hl Delim $ text ")"]
private
prettySigBinds : {opts : _} ->
BContext d -> BContext n ->
Telescope (SigBind d) n n' ->
Eff Pretty (SnocList (Doc opts))
prettySigBinds _ _ [<] = pure [<]
prettySigBinds dnames tnames (binds :< (x, t)) =
let tnames' = tnames . map fst binds in
[|prettySigBinds dnames tnames binds :<
prettySigBind1 x dnames tnames' t|]
private
prettyTypeLine : {opts : _} ->
BContext d -> BContext n ->
DScopeTerm d n ->
Eff Pretty (Doc opts)
prettyTypeLine dnames tnames (S _ (N body)) =
withPrec Arg (prettyTerm dnames tnames body)
prettyTypeLine dnames tnames (S [< i] (Y body)) =
parens =<< do
i' <- prettyDBind i
ty' <- withPrec Outer $ prettyTerm (dnames :< i) tnames body
pure $ sep [hsep [i', !darrowD], ty']
private
data NameSort = T | D
%runElab derive "NameSort" [Eq]
private
NameChunks : Type
NameChunks = SnocList (NameSort, SnocList BindName)
private
record SplitLams d n where
constructor MkSplitLams
{0 dinner, ninner : Nat}
dnames : BTelescope d dinner
tnames : BTelescope n ninner
chunks : NameChunks
body : Term dinner ninner
private
splitLams : Term d n -> SplitLams d n
splitLams s = go [<] [<] [<] (pushSubsts' s)
where
push : NameSort -> BindName -> NameChunks -> NameChunks
push s y [<] = [< (s, [< y])]
push s y (xss :< (s', xs)) =
if s == s' then xss :< (s', xs :< y)
else xss :< (s', xs) :< (s, [< y])
go : BTelescope d d' -> BTelescope n n' ->
SnocList (NameSort, SnocList BindName) ->
Term d' n' -> SplitLams d n
go dnames tnames chunks (Lam b _) =
go dnames (tnames :< b.name) (push T b.name chunks) $
assert_smaller b $ pushSubsts' b.term
go dnames tnames chunks (DLam b _) =
go (dnames :< b.name) tnames (push D b.name chunks) $
assert_smaller b $ pushSubsts' b.term
go dnames tnames chunks s =
MkSplitLams dnames tnames chunks s
private
splitTuple : SnocList (Term d n) -> Term d n -> SnocList (Term d n)
splitTuple ss p@(Pair t1 t2 _) =
splitTuple (ss :< t1) $ assert_smaller p $ pushSubsts' t2
splitTuple ss t = ss :< t
private
prettyTArg : {opts : _} -> BContext d -> BContext n ->
Term d n -> Eff Pretty (Doc opts)
prettyTArg dnames tnames s =
withPrec Arg $ assert_total prettyTerm dnames tnames s
private
prettyDArg : {opts : _} -> BContext d -> Dim d -> Eff Pretty (Doc opts)
prettyDArg dnames p = [|atD <+> withPrec Arg (prettyDim dnames p)|]
private
splitApps : Elim d n -> (Elim d n, List (Either (Dim d) (Term d n)))
splitApps e = go [] (pushSubsts' e)
where
go : List (Either (Dim d) (Term d n)) -> Elim d n ->
(Elim d n, List (Either (Dim d) (Term d n)))
go xs e@(App f s _) =
go (Right s :: xs) $ assert_smaller e $ pushSubsts' f
go xs e@(DApp f p _) =
go (Left p :: xs) $ assert_smaller e $ pushSubsts' f
go xs s = (s, xs)
private
prettyDTApps : {opts : _} ->
BContext d -> BContext n ->
Elim d n -> List (Either (Dim d) (Term d n)) ->
Eff Pretty (Doc opts)
prettyDTApps dnames tnames f xs = do
f <- withPrec Arg $ assert_total prettyElim dnames tnames f
xs <- for xs $ either (prettyDArg dnames) (prettyTArg dnames tnames)
parensIfM App =<< prettyAppD f xs
private
record CaseArm opts d n where
constructor MkCaseArm
pat : Doc opts
dbinds : BTelescope d dinner -- 🍴
tbinds : BTelescope n ninner
body : Term dinner ninner
parameters {opts : LayoutOpts} (dnames : BContext d) (tnames : BContext n)
private
prettyCaseArm : CaseArm opts d n -> Eff Pretty (Doc opts)
prettyCaseArm (MkCaseArm pat dbinds tbinds body) = do
body <- withPrec Outer $ assert_total
prettyTerm (dnames . dbinds) (tnames . tbinds) body
header <- (pat <++>) <$> darrowD
pure $ ifMultiline (header <++> body) (vsep [header, !(indentD body)])
private
prettyCaseBody : List (CaseArm opts d n) -> Eff Pretty (List (Doc opts))
prettyCaseBody xs = traverse prettyCaseArm xs
private
prettyCompPat : {opts : _} -> DimConst -> BindName -> Eff Pretty (Doc opts)
prettyCompPat e x = [|prettyDimConst e <++> prettyDBind x|]
private
prettyCompArm : {opts : _} -> BContext d -> BContext n ->
DimConst -> DScopeTerm d n -> Eff Pretty (Doc opts)
prettyCompArm dnames tnames e s = prettyCaseArm dnames tnames $
MkCaseArm !(prettyCompPat e s.name) [< s.name] [<] s.term
private
layoutComp : {opts : _} ->
(typq : List (Doc opts)) -> (val, r : Doc opts) ->
(arms : List (Doc opts)) -> Eff Pretty (Doc opts)
layoutComp typq val r arms = do
comp <- compD; lb <- hl Delim "{"; rb <- hl Delim "}"
ind <- askAt INDENT
pure $ ifMultiline
(hsep $ concat {t = List} [[comp], typq, [val, r, lb], arms, [rb]]) $
(comp <++>
vsep [sep typq, val, r <++> lb, indent ind $ vsep arms, rb]) <|>
(vsep $ (comp ::) $ map (indent ind) $ concat {t = List}
[typq, [val, r <++> lb], map (indent ind) arms, [rb]])
export
prettyEnum : {opts : _} -> List String -> Eff Pretty (Doc opts)
prettyEnum cases =
tightBraces =<<
fillSeparateTight !commaD <$>
traverse (hl Constant . Doc.text . quoteTag) cases
private
prettyCaseRet : {opts : _} ->
BContext d -> BContext n ->
ScopeTerm d n -> Eff Pretty (Doc opts)
prettyCaseRet dnames tnames body = withPrec Outer $ case body of
S _ (N tm) => assert_total prettyTerm dnames tnames tm
S [< x] (Y tm) => do
header <- [|prettyTBind x <++> darrowD|]
body <- assert_total prettyTerm dnames (tnames :< x) tm
hangDSingle header body
private
prettyCase_ : {opts : _} ->
BContext d -> BContext n ->
Doc opts -> Elim d n -> ScopeTerm d n -> List (CaseArm opts d n) ->
Eff Pretty (Doc opts)
prettyCase_ dnames tnames intro head ret body = do
head <- withPrec Outer $ assert_total prettyElim dnames tnames head
ret <- prettyCaseRet dnames tnames ret
bodys <- prettyCaseBody dnames tnames body
return <- returnD; of_ <- ofD
lb <- hl Delim "{"; rb <- hl Delim "}"; semi <- semiD
ind <- askAt INDENT
parensIfM Outer $ ifMultiline
(hsep [intro, head, return, ret, of_, lb, hseparateTight semi bodys, rb])
(vsep [intro <++> head, return <++> ret, of_ <++> lb,
indent ind $ vseparateTight semi bodys, rb])
private
prettyCase : {opts : _} ->
BContext d -> BContext n ->
Qty -> Elim d n -> ScopeTerm d n -> List (CaseArm opts d n) ->
Eff Pretty (Doc opts)
prettyCase dnames tnames qty head ret body =
prettyCase_ dnames tnames ![|caseD <+> prettyQty qty|] head ret body
private
LetBinder : Nat -> Nat -> Type
LetBinder d n = (Qty, BindName, Elim d n)
private
LetExpr : Nat -> Nat -> Nat -> Type
LetExpr d n n' = (Telescope (LetBinder d) n n', Term d n')
-- [todo] factor out this and the untyped version somehow
export
splitLet : Telescope (LetBinder d) n n' -> Term d n' -> Exists (LetExpr d n)
splitLet ys t@(Let qty rhs body _) =
splitLet (ys :< (qty, body.name, rhs)) (assert_smaller t body.term)
splitLet ys t =
Evidence _ (ys, t)
private covering
prettyLets : {opts : LayoutOpts} ->
BContext d -> BContext a -> Telescope (LetBinder d) a b ->
Eff Pretty (SnocList (Doc opts))
prettyLets dnames xs lets = snd <$> go lets where
peelAnn : forall d, n. Elim d n -> Maybe (Term d n, Term d n)
peelAnn (Ann tm ty _) = Just (tm, ty)
peelAnn e = Nothing
letHeader : Qty -> BindName -> Eff Pretty (Doc opts)
letHeader qty x = do
lett <- [|letD <+> prettyQty qty|]
x <- prettyTBind x
pure $ lett <++> x
letBody : forall n. BContext n ->
Doc opts -> Elim d n -> Eff Pretty (Doc opts)
letBody tnames hdr e = case peelAnn e of
Just (tm, ty) => do
ty <- withPrec Outer $ assert_total prettyTerm dnames tnames ty
tm <- withPrec Outer $ assert_total prettyTerm dnames tnames tm
colon <- colonD; eq <- cstD; d <- askAt INDENT
pure $ hangSingle d (hangSingle d hdr (colon <++> ty)) (eq <++> tm)
Nothing => do
e <- withPrec Outer $ assert_total prettyElim dnames tnames e
eq <- cstD; d <- askAt INDENT
inn <- inD
pure $ ifMultiline
(hsep [hdr, eq, e, inn])
(vsep [hdr, indent d $ hsep [eq, e, inn]])
go : forall b. Telescope (LetBinder d) a b ->
Eff Pretty (BContext b, SnocList (Doc opts))
go [<] = pure (xs, [<])
go (lets :< (qty, x, rhs)) = do
(ys, docs) <- go lets
doc <- letBody ys !(letHeader qty x) rhs
pure (ys :< x, docs :< doc)
private
isDefaultDir : Dim d -> Dim d -> Bool
isDefaultDir (K Zero _) (K One _) = True
isDefaultDir _ _ = False
-- [fixme] use telescopes in Scoped
private
toTel : BContext s -> BTelescope n (s + n)
toTel [<] = [<]
toTel (ctx :< x) = toTel ctx :< x
private
prettyTyCasePat : {opts : _} ->
(k : TyConKind) -> BContext (arity k) ->
Eff Pretty (Doc opts)
prettyTyCasePat KTYPE [<] = typeD
prettyTyCasePat KIOState [<] = ioStateD
prettyTyCasePat KPi [< a, b] =
parens . hsep =<< sequence [prettyTBind a, arrowD, prettyTBind b]
prettyTyCasePat KSig [< a, b] =
parens . hsep =<< sequence [prettyTBind a, timesD, prettyTBind b]
prettyTyCasePat KEnum [<] = hl Syntax $ text "{}"
prettyTyCasePat KEq [< a0, a1, a, l, r] =
hsep <$> sequence (eqD :: map prettyTBind [a0, a1, a, l, r])
prettyTyCasePat KNat [<] = natD
prettyTyCasePat KString [<] = stringD
prettyTyCasePat KBOX [< a] = bracks =<< prettyTBind a
prettyLambda : {opts : _} -> BContext d -> BContext n ->
Term d n -> Eff Pretty (Doc opts)
prettyLambda dnames tnames s =
parensIfM Outer =<< do
let MkSplitLams {dnames = ds, tnames = ts, chunks, body} = splitLams s
hangDSingle !(header chunks)
!(assert_total prettyTerm (dnames . ds) (tnames . ts) body)
where
introChar : NameSort -> Eff Pretty (Doc opts)
introChar T = lamD
introChar D = dlamD
prettyBind : NameSort -> BindName -> Eff Pretty (Doc opts)
prettyBind T = prettyTBind
prettyBind D = prettyDBind
header1 : NameSort -> List BindName -> Eff Pretty (Doc opts)
header1 s xs = hsep <$> sequence
[introChar s, sep <$> traverse (prettyBind s) xs, darrowD]
header : NameChunks -> Eff Pretty (Doc opts)
header cs = sep <$> traverse (\(s, xs) => header1 s (toList xs)) (toList cs)
prettyDisp : {opts : _} -> Universe -> Eff Pretty (Maybe (Doc opts))
prettyDisp 0 = pure Nothing
prettyDisp u = map Just $ hl Universe =<<
ifUnicode (text $ superscript $ show u) (text $ "^" ++ show u)
prettyTerm dnames tnames (TYPE l _) = do
type <- hl Syntax . text =<< ifUnicode "" "Type"
level <- prettyDisp l
pure $ maybe type (type <+>) level
prettyTerm dnames tnames (IOState _) =
ioStateD
prettyTerm dnames tnames (Pi qty arg res _) =
parensIfM Outer =<< do
let MkSplitPi {binds, cod} = splitPi [< (qty, res.name, arg)] res.term
arr <- arrowD
lines <- map (<++> arr) <$> prettyPiBinds dnames tnames binds
let tnames = tnames . map pbname binds
cod <- withPrec Outer $ prettyTerm dnames tnames (assert_smaller res cod)
pure $ sepSingle $ toList $ lines :< cod
prettyTerm dnames tnames s@(Lam {}) =
prettyLambda dnames tnames s
prettyTerm dnames tnames (Sig fst snd _) =
parensIfM Times =<< do
let MkSplitSig {binds, last} = splitSig [< (snd.name, fst)] snd.term
times <- timesD
lines <- map (<++> times) <$> prettySigBinds dnames tnames binds
let tnames = tnames . map Builtin.fst binds
last <- withPrec InTimes $
prettyTerm dnames tnames (assert_smaller snd last)
pure $ sepSingle $ toList $ lines :< last
prettyTerm dnames tnames p@(Pair fst snd _) =
parens =<< do
let elems = splitTuple [< fst] snd
lines <- for elems $ \t =>
withPrec Outer $ prettyTerm dnames tnames $ assert_smaller p t
pure $ separateTight !commaD lines
prettyTerm dnames tnames (Enum cases _) =
prettyEnum $ SortedSet.toList cases
prettyTerm dnames tnames (Tag tag _) =
prettyTag tag
prettyTerm dnames tnames (Eq (S _ (N ty)) l r _) =
parensIfM Eq =<< do
l <- withPrec InEq $ prettyTerm dnames tnames l
r <- withPrec InEq $ prettyTerm dnames tnames r
ty <- withPrec InEq $ prettyTerm dnames tnames ty
pure $ sep [l <++> !eqndD, r <++> !colonD, ty]
prettyTerm dnames tnames (Eq ty l r _) =
parensIfM App =<< do
ty <- prettyTypeLine dnames tnames ty
l <- withPrec Arg $ prettyTerm dnames tnames l
r <- withPrec Arg $ prettyTerm dnames tnames r
prettyAppD !eqD [ty, l, r]
prettyTerm dnames tnames s@(DLam {}) =
prettyLambda dnames tnames s
prettyTerm dnames tnames (NAT _) = natD
prettyTerm dnames tnames (Nat n _) = hl Syntax $ pshow n
prettyTerm dnames tnames (Succ p _) =
parensIfM App =<<
prettyAppD !succD [!(withPrec Arg $ prettyTerm dnames tnames p)]
prettyTerm dnames tnames (STRING _) = stringD
prettyTerm dnames tnames (Str s _) = prettyStrLit s
prettyTerm dnames tnames (BOX qty ty _) =
bracks . hcat =<<
sequence [prettyQty qty, dotD,
withPrec Outer $ prettyTerm dnames tnames ty]
prettyTerm dnames tnames (Box val _) =
bracks =<< withPrec Outer (prettyTerm dnames tnames val)
prettyTerm dnames tnames (Let qty rhs body _) = do
let Evidence _ (lets, body) = splitLet [< (qty, body.name, rhs)] body.term
heads <- prettyLets dnames tnames lets
let tnames = tnames . map (\(_, x, _) => x) lets
body <- withPrec Outer $ assert_total prettyTerm dnames tnames body
let lines = toList $ heads :< body
pure $ ifMultiline (hsep lines) (vsep lines)
prettyTerm dnames tnames (E e) =
case the (Elim d n) (pushSubsts' e) of
Ann tm _ _ => assert_total prettyTerm dnames tnames tm
_ => assert_total prettyElim dnames tnames e
prettyTerm dnames tnames t0@(CloT (Sub t ph)) =
prettyTerm dnames tnames $ assert_smaller t0 $ pushSubstsWith' id ph t
prettyTerm dnames tnames t0@(DCloT (Sub t ph)) =
prettyTerm dnames tnames $ assert_smaller t0 $ pushSubstsWith' ph id t
prettyElim dnames tnames (F x u _) = do
x <- prettyFree x
u <- prettyDisp u
pure $ maybe x (x <+>) u
prettyElim dnames tnames (B i _) =
prettyTBind $ tnames !!! i
prettyElim dnames tnames e@(App {}) =
let (f, xs) = splitApps e in
prettyDTApps dnames tnames f xs
prettyElim dnames tnames (CasePair qty pair ret body _) = do
let [< x, y] = body.names
pat <- parens . hsep =<< sequence
[[|prettyTBind x <+> commaD|], prettyTBind y]
prettyCase dnames tnames qty pair ret
[MkCaseArm pat [<] [< x, y] body.term]
prettyElim dnames tnames (Fst pair _) =
parensIfM App =<< do
pair <- prettyTArg dnames tnames (E pair)
prettyAppD !fstD [pair]
prettyElim dnames tnames (Snd pair _) =
parensIfM App =<< do
pair <- prettyTArg dnames tnames (E pair)
prettyAppD !sndD [pair]
prettyElim dnames tnames (CaseEnum qty tag ret arms _) = do
arms <- for (SortedMap.toList arms) $ \(tag, body) =>
pure $ MkCaseArm !(prettyTag tag) [<] [<] body
prettyCase dnames tnames qty tag ret arms
prettyElim dnames tnames (CaseNat qty qtyIH nat ret zero succ _) = do
let zarm = MkCaseArm !zeroD [<] [<] zero
[< p, ih] = succ.names
spat0 <- [|succD <++> prettyTBind p|]
ihpat0 <- map hcat $ sequence [prettyQty qtyIH, dotD, prettyTBind ih]
spat <- if ih.val == Unused
then pure spat0
else pure $ hsep [spat0 <+> !commaD, ihpat0]
let sarm = MkCaseArm spat [<] [< p, ih] succ.term
prettyCase dnames tnames qty nat ret [zarm, sarm]
prettyElim dnames tnames (CaseBox qty box ret body _) = do
pat <- bracks =<< prettyTBind body.name
let arm = MkCaseArm pat [<] [< body.name] body.term
prettyCase dnames tnames qty box ret [arm]
prettyElim dnames tnames e@(DApp {}) =
let (f, xs) = splitApps e in
prettyDTApps dnames tnames f xs
prettyElim dnames tnames (Ann tm ty _) =
case the (Term d n) (pushSubsts' tm) of
E e => assert_total prettyElim dnames tnames e
_ => do
tm <- withPrec AnnL $ assert_total prettyTerm dnames tnames tm
ty <- withPrec Outer $ assert_total prettyTerm dnames tnames ty
parensIfM Outer =<< hangDSingle (tm <++> !annD) ty
prettyElim dnames tnames (Coe ty p q val _) =
parensIfM App =<< do
ty <- prettyTypeLine dnames tnames ty
p <- prettyDArg dnames p
q <- prettyDArg dnames q
val <- prettyTArg dnames tnames val
prettyAppD !coeD [ty, sep [p, q], val]
prettyElim dnames tnames e@(Comp ty p q val r zero one _) =
parensIfM App =<< do
ty <- assert_total $ prettyTypeLine dnames tnames $ SN ty
pq <- sep <$> sequence [prettyDArg dnames p, prettyDArg dnames q]
val <- prettyTArg dnames tnames val
r <- prettyDArg dnames r
arm0 <- [|prettyCompArm dnames tnames Zero zero <+> semiD|]
arm1 <- prettyCompArm dnames tnames One one
ind <- askAt INDENT
layoutComp [ty, pq] val r [arm0, arm1]
prettyElim dnames tnames (TypeCase ty ret arms def _) = do
arms <- for (toList arms) $ \(k ** body) => do
pat <- prettyTyCasePat k body.names
pure $ MkCaseArm pat [<] (toTel body.names) body.term
let darm = MkCaseArm !undD [<] [<] def
prettyCase_ dnames tnames !typecaseD ty (SN ret) $ arms ++ [darm]
prettyElim dnames tnames e0@(CloE (Sub e ph)) =
prettyElim dnames tnames $ assert_smaller e0 $ pushSubstsWith' id ph e
prettyElim dnames tnames e0@(DCloE (Sub e ph)) =
prettyElim dnames tnames $ assert_smaller e0 $ pushSubstsWith' ph id e