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coercions and compositions

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rhiannon morris 2023-04-15 15:13:01 +02:00
parent 468ae7e444
commit a5ccf0215a
25 changed files with 1344 additions and 651 deletions
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14
examples/misc.quox
View file

@ -1,4 +1,3 @@
def0 Pred : 0.★₀ → ★₁ = λ A ⇒ 0.A → ★₀;
def0 All : 0.(A : ★₀) → 0.(Pred A) → ★₁ =
@ -23,3 +22,16 @@ defω funext :
1.(All A (eq-f A P p q)) →
p ≡ q : All A P =
λ A P p q eq ⇒ δ i ⇒ λ x ⇒ eq x @i;
def0 T : ω.{true, false} → ★₀ =
λ b ⇒ caseω b return ★₀ of { 'true ⇒ {tt}; 'false ⇒ {} };
defω absurd :
0.('true ≡ 'false : {true, false}) → 0.(A : ★₀) → A =
λ eq A ⇒
case0 coe [i ⇒ T (eq @i)] @0 @1 'tt return A of { };
defω sym : 0.(A : ★₀) → 0.(x : A) → 0.(y : A) →
1.(x ≡ y : A) → y ≡ x : A =
λ A x y eq ⇒ δ i ⇒
comp [A] @0 @1 (eq @0) @i { 0 j ⇒ eq @j; 1 _ ⇒ eq @0 };

14
lib/Quox/Context.idr
View file

@ -66,6 +66,11 @@ parameters {0 tm : Nat -> Type} (f : forall n. tm n -> a)
toListAcc [<] acc = acc
toListAcc (tel :< t) acc = toListAcc tel (f t :: acc)
export
toSnocVectWith : Context tm n -> SnocVect n a
toSnocVectWith [<] = [<]
toSnocVectWith (tel :< t) = toSnocVectWith tel :< f t
export %inline
toSnocList : Telescope tm _ _ -> SnocList (Exists tm)
toSnocList = toSnocListWith (Evidence _)
@ -82,6 +87,15 @@ export %inline
toList' : Telescope' a _ _ -> List a
toList' = toListWith id
export %inline
toSnocVect : Context tm n -> SnocVect n (Exists tm)
toSnocVect = toSnocVectWith (Evidence _)
export %inline
toSnocVect' : Context' a n -> SnocVect n a
toSnocVect' = toSnocVectWith id
export
fromSnocVect : SnocVect n a -> Context' a n

249
lib/Quox/Equal.idr
View file

@ -70,38 +70,38 @@ sameTyCon (E {}) (E {}) = True
sameTyCon (E {}) _ = False
parameters (defs : Definitions)
||| true if a type is known to be a subsingleton purely by its form.
||| a subsingleton is a type with only zero or one possible values.
||| equality/subtyping accepts immediately on values of subsingleton types.
|||
||| * a function type is a subsingleton if its codomain is.
||| * a pair type is a subsingleton if both its elements are.
||| * all equality types are subsingletons because uip is admissible by
||| boundary separation.
||| * an enum type is a subsingleton if it has zero or one tags.
public export covering
isSubSing : Has ErrorEff fs =>
{n : Nat} -> Term 0 n -> Eff fs Bool
isSubSing ty0 = do
Element ty0 nc <- whnfT defs ty0
case ty0 of
TYPE _ => pure False
Pi {res, _} => isSubSing res.term
Lam {} => pure False
Sig {fst, snd} => isSubSing fst `andM` isSubSing snd.term
Pair {} => pure False
Enum tags => pure $ length (SortedSet.toList tags) <= 1
Tag {} => pure False
Eq {} => pure True
DLam {} => pure False
Nat => pure False
Zero => pure False
Succ {} => pure False
BOX {ty, _} => isSubSing ty
Box {} => pure False
E (s :# _) => isSubSing s
E _ => pure False
||| true if a type is known to be a subsingleton purely by its form.
||| a subsingleton is a type with only zero or one possible values.
||| equality/subtyping accepts immediately on values of subsingleton types.
|||
||| * a function type is a subsingleton if its codomain is.
||| * a pair type is a subsingleton if both its elements are.
||| * equality types are subsingletons because of uip.
||| * an enum type is a subsingleton if it has zero or one tags.
||| * a box type is a subsingleton if its content is
public export covering
isSubSing : Has ErrorEff fs => {n : Nat} ->
Definitions -> EqContext n -> Term 0 n -> Eff fs Bool
isSubSing defs ctx ty0 = do
Element ty0 nc <- whnf defs ctx ty0
case ty0 of
TYPE _ => pure False
Pi _ arg res => isSubSing defs (extendTy Zero res.name arg ctx) res.term
Sig fst snd => isSubSing defs ctx fst `andM`
isSubSing defs (extendTy Zero snd.name fst ctx) snd.term
Enum tags => pure $ length (SortedSet.toList tags) <= 1
Eq {} => pure True
Nat => pure False
BOX _ ty => isSubSing defs ctx ty
E (s :# _) => isSubSing defs ctx s
E _ => pure False
Lam _ => pure False
Pair _ _ => pure False
Tag _ => pure False
DLam _ => pure False
Zero => pure False
Succ _ => pure False
Box _ => pure False
export
@ -112,6 +112,17 @@ ensureTyCon ctx t = case nchoose $ isTyConE t of
Left y => pure y
Right n => throw $ NotType (toTyContext ctx) (t // shift0 ctx.dimLen)
||| performs the minimum work required to recompute the type of an elim.
|||
||| ⚠ **assumes the elim is already typechecked.** ⚠
private covering
computeElimTypeE : (defs : Definitions) -> EqContext n ->
(e : Elim 0 n) -> (0 ne : NotRedex defs e) =>
Equal (Term 0 n)
computeElimTypeE defs ectx e =
let Val n = ectx.termLen in
rethrow $ computeElimType defs (toWhnfContext ectx) e
parameters (defs : Definitions)
mutual
namespace Term
@ -124,9 +135,9 @@ parameters (defs : Definitions)
compare0 ctx ty s t =
wrapErr (WhileComparingT ctx !mode ty s t) $ do
let Val n = ctx.termLen
Element ty nty <- whnfT defs ty
Element s ns <- whnfT defs s
Element t nt <- whnfT defs t
Element ty nty <- whnf defs ctx ty
Element s ns <- whnf defs ctx s
Element t nt <- whnf defs ctx t
tty <- ensureTyCon ctx ty
compare0' ctx ty s t
@ -134,7 +145,7 @@ parameters (defs : Definitions)
||| a lambda "Γ ⊢ λx ⇒ t" that has been converted to "Γ, x ⊢ t".
private %inline
toLamBody : Elim d n -> Term d (S n)
toLamBody e = E $ weakE e :@ BVT 0
toLamBody e = E $ weakE 1 e :@ BVT 0
private covering
compare0' : EqContext n ->
@ -209,7 +220,8 @@ parameters (defs : Definitions)
compare0' _ (Eq {}) _ _ =
-- ✨ uip ✨
--
-- Γ ⊢ e = f : Eq [i ⇒ A] s t
-- ----------------------------
-- Γ ⊢ e = f : Eq [i ⇒ A] s t
pure ()
compare0' ctx Nat s t = local_ Equal $
@ -263,8 +275,8 @@ parameters (defs : Definitions)
compareType : EqContext n -> (s, t : Term 0 n) -> Equal ()
compareType ctx s t = do
let Val n = ctx.termLen
Element s ns <- whnfT defs s
Element t nt <- whnfT defs t
Element s ns <- whnf defs ctx s
Element t nt <- whnf defs ctx t
ts <- ensureTyCon ctx s
tt <- ensureTyCon ctx t
st <- either pure (const $ clashTy ctx s t) $
@ -336,37 +348,12 @@ parameters (defs : Definitions)
-- has been inlined by whnf
Elim.compare0 ctx e f
||| performs the minimum work required to recompute the type of an elim.
|||
||| ⚠ **assumes the elim is already typechecked.** ⚠
private covering
computeElimType : EqContext n -> (e : Elim 0 n) ->
(0 ne : NotRedex defs e) ->
Equal (Term 0 n)
computeElimType ctx (F x) _ = do
def <- lookupFree x defs
let Val n = ctx.termLen
pure $ def.type
computeElimType ctx (B i) _ = pure $ ctx.tctx !! i
computeElimType ctx (f :@ s) ne = do
(_, arg, res) <- expectPiE defs ctx !(computeElimType ctx f (noOr1 ne))
pure $ sub1 res (s :# arg)
computeElimType ctx (CasePair {pair, ret, _}) _ = pure $ sub1 ret pair
computeElimType ctx (CaseEnum {tag, ret, _}) _ = pure $ sub1 ret tag
computeElimType ctx (CaseNat {nat, ret, _}) _ = pure $ sub1 ret nat
computeElimType ctx (CaseBox {box, ret, _}) _ = pure $ sub1 ret box
computeElimType ctx (f :% p) ne = do
(ty, _, _) <- expectEqE defs ctx !(computeElimType ctx f (noOr1 ne))
pure $ dsub1 ty p
computeElimType ctx (TypeCase {ret, _}) _ = pure ret
computeElimType ctx (_ :# ty) _ = pure ty
private covering
replaceEnd : EqContext n ->
(e : Elim 0 n) -> DimConst -> (0 ne : NotRedex defs e) ->
Equal (Elim 0 n)
replaceEnd ctx e p ne = do
(ty, l, r) <- expectEqE defs ctx !(computeElimType ctx e ne)
(ty, l, r) <- expectEq defs ctx !(computeElimTypeE defs ctx e)
pure $ ends l r p :# dsub1 ty (K p)
namespace Elim
@ -382,10 +369,10 @@ parameters (defs : Definitions)
compare0 ctx e f =
wrapErr (WhileComparingE ctx !mode e f) $ do
let Val n = ctx.termLen
Element e ne <- whnfT defs e
Element f nf <- whnfT defs f
Element e ne <- whnf defs ctx e
Element f nf <- whnf defs ctx f
-- [fixme] there is a better way to do this "isSubSing" stuff for sure
unless !(isSubSing defs !(computeElimType ctx e ne)) $
unless !(isSubSing defs ctx !(computeElimTypeE defs ctx e)) $
compare0' ctx e f ne nf
private covering
@ -411,7 +398,8 @@ parameters (defs : Definitions)
compare0' ctx (e :@ s) (f :@ t) ne nf =
local_ Equal $ do
compare0 ctx e f
(_, arg, _) <- expectPiE defs ctx !(computeElimType ctx e (noOr1 ne))
(_, arg, _) <- expectPi defs ctx =<<
computeElimTypeE defs ctx e @{noOr1 ne}
Term.compare0 ctx arg s t
compare0' ctx e@(_ :@ _) f _ _ = clashE ctx e f
@ -419,9 +407,9 @@ parameters (defs : Definitions)
(CasePair fpi f fret fbody) ne nf =
local_ Equal $ do
compare0 ctx e f
ety <- computeElimType ctx e (noOr1 ne)
ety <- computeElimTypeE defs ctx e @{noOr1 ne}
compareType (extendTy Zero eret.name ety ctx) eret.term fret.term
(fst, snd) <- expectSigE defs ctx ety
(fst, snd) <- expectSig defs ctx ety
let [< x, y] = ebody.names
Term.compare0 (extendTyN [< (epi, x, fst), (epi, y, snd.term)] ctx)
(substCasePairRet ety eret)
@ -433,9 +421,9 @@ parameters (defs : Definitions)
(CaseEnum fpi f fret farms) ne nf =
local_ Equal $ do
compare0 ctx e f
ety <- computeElimType ctx e (noOr1 ne)
ety <- computeElimTypeE defs ctx e @{noOr1 ne}
compareType (extendTy Zero eret.name ety ctx) eret.term fret.term
for_ !(expectEnumE defs ctx ety) $ \t =>
for_ !(expectEnum defs ctx ety) $ \t =>
compare0 ctx (sub1 eret $ Tag t :# ety)
!(lookupArm t earms) !(lookupArm t farms)
expectEqualQ epi fpi
@ -450,7 +438,7 @@ parameters (defs : Definitions)
(CaseNat fpi fpi' f fret fzer fsuc) ne nf =
local_ Equal $ do
compare0 ctx e f
ety <- computeElimType ctx e (noOr1 ne)
ety <- computeElimTypeE defs ctx e @{noOr1 ne}
compareType (extendTy Zero eret.name ety ctx) eret.term fret.term
compare0 ctx (sub1 eret (Zero :# Nat)) ezer fzer
let [< p, ih] = esuc.names
@ -465,9 +453,9 @@ parameters (defs : Definitions)
(CaseBox fpi f fret fbody) ne nf =
local_ Equal $ do
compare0 ctx e f
ety <- computeElimType ctx e (noOr1 ne)
ety <- computeElimTypeE defs ctx e @{noOr1 ne}
compareType (extendTy Zero eret.name ety ctx) eret.term fret.term
(q, ty) <- expectBOXE defs ctx ety
(q, ty) <- expectBOX defs ctx ety
compare0 (extendTy (epi * q) ebody.name ty ctx)
(substCaseBoxRet ety eret)
ebody.term fbody.term
@ -475,50 +463,93 @@ parameters (defs : Definitions)
compare0' ctx e@(CaseBox {}) f _ _ = clashE ctx e f
compare0' ctx (s :# a) (t :# b) _ _ =
Term.compare0 ctx !(bigger a b) s t
where
bigger : forall a. a -> a -> Equal a
bigger l r = mode <&> \case Super => l; _ => r
let ty = case !mode of Super => a; _ => b in
Term.compare0 ctx ty s t
compare0' ctx (TypeCase ty1 ret1 univ1 pi1 sig1 enum1 eq1 nat1 box1)
(TypeCase ty2 ret2 univ2 pi2 sig2 enum2 eq2 nat2 box2)
compare0' ctx (Coe ty1 p1 q1 (E val1)) (Coe ty2 p2 q2 (E val2)) ne nf = do
compareType ctx (dsub1 ty1 p1) (dsub1 ty2 p2)
compareType ctx (dsub1 ty1 q1) (dsub1 ty2 q2)
compare0 ctx val1 val2
compare0' ctx e@(Coe {}) f _ _ = clashE ctx e f
compare0' ctx (Comp _ _ _ _ (K _) _ _) _ ne _ = void $ absurd $ noOr2 ne
compare0' ctx (Comp _ _ _ _ (B i) _ _) _ _ _ = absurd i
compare0' ctx _ (Comp _ _ _ _ (K _) _ _) _ nf = void $ absurd $ noOr2 nf
compare0' ctx (TypeCase ty1 ret1 arms1 def1)
(TypeCase ty2 ret2 arms2 def2)
ne _ =
local_ Equal $ do
compare0 ctx ty1 ty2
u <- expectTYPEE defs ctx =<< computeElimType ctx ty1 (noOr1 ne)
u <- expectTYPE defs ctx =<<
computeElimTypeE defs ctx ty1 @{noOr1 ne}
compareType ctx ret1 ret2
compare0 ctx univ1 univ2 ret1
let [< piA, piB] = pi1.names
piCtx = extendTyN
[< (Zero, piA, TYPE u),
(Zero, piB, Arr Zero (BVT 0) (TYPE u))] ctx
ret1_2 = weakT ret1 {by = 2}
compare0 piCtx pi1.term pi2.term ret1_2
let [< sigA, sigB] = sig1.names
sigCtx = extendTyN
[< (Zero, sigA, TYPE u),
(Zero, sigB, Arr Zero (BVT 0) (TYPE u))] ctx
compare0 sigCtx sig1.term sig2.term ret1_2
compare0 ctx enum1 enum2 ret1
let [< eqA0, eqA1, eqA, eqL, eqR] = eq1.names
eqCtx = extendTyN
[< (Zero, eqA0, TYPE u),
(Zero, eqA1, TYPE u),
(Zero, eqA, Eq0 (TYPE u) (BVT 1) (BVT 0)),
(Zero, eqL, BVT 2),
(Zero, eqR, BVT 2)] ctx
ret1_5 = weakT ret1 {by = 5}
compare0 eqCtx eq1.term eq2.term ret1_5
compare0 ctx nat1 nat2 ret1
let boxCtx = extendTy Zero box1.name (TYPE u) ctx
ret1_1 = weakT ret1
compare0 boxCtx box1.term box2.term ret1_1
compareType ctx def1 def2
for_ allKinds $ \k =>
compareArm ctx k ret1 u
(lookupPrecise k arms1) (lookupPrecise k arms2) def1
compare0' ctx e@(TypeCase {}) f _ _ = clashE ctx e f
compare0' ctx (s :# a) f _ _ = Term.compare0 ctx a s (E f)
compare0' ctx e (t :# b) _ _ = Term.compare0 ctx b (E e) t
compare0' ctx e@(_ :# _) f _ _ = clashE ctx e f
||| compare two type-case branches, which came from the arms of the given
||| kind. `ret` is the return type of the case expression, and `u` is the
||| universe the head is in.
private covering
compareArm : EqContext n -> (k : TyConKind) ->
(ret : Term 0 n) -> (u : Universe) ->
(b1, b2 : Maybe (TypeCaseArmBody k 0 n)) ->
(def : Term 0 n) ->
Equal ()
compareArm {b1 = Nothing, b2 = Nothing, _} = pure ()
compareArm ctx k ret u b1 b2 def =
let def = SN def in
compareArm_ ctx k ret u (fromMaybe def b1) (fromMaybe def b2)
private covering
compareArm_ : EqContext n -> (k : TyConKind) ->
(ret : Term 0 n) -> (u : Universe) ->
(b1, b2 : TypeCaseArmBody k 0 n) ->
Equal ()
compareArm_ ctx KTYPE ret u b1 b2 =
compare0 ctx ret b1.term b2.term
compareArm_ ctx KPi ret u b1 b2 = do
let [< a, b] = b1.names
ctx = extendTyN
[< (Zero, a, TYPE u),
(Zero, b, Arr Zero (BVT 0) (TYPE u))] ctx
compare0 ctx (weakT 2 ret) b1.term b2.term
compareArm_ ctx KSig ret u b1 b2 = do
let [< a, b] = b1.names
ctx = extendTyN
[< (Zero, a, TYPE u),
(Zero, b, Arr Zero (BVT 0) (TYPE u))] ctx
compare0 ctx (weakT 2 ret) b1.term b2.term
compareArm_ ctx KEnum ret u b1 b2 =
compare0 ctx ret b1.term b2.term
compareArm_ ctx KEq ret u b1 b2 = do
let [< a0, a1, a, l, r] = b1.names
ctx = extendTyN
[< (Zero, a0, TYPE u),
(Zero, a1, TYPE u),
(Zero, a, Eq0 (TYPE u) (BVT 1) (BVT 0)),
(Zero, l, BVT 2),
(Zero, r, BVT 2)] ctx
compare0 ctx (weakT 5 ret) b1.term b2.term
compareArm_ ctx KNat ret u b1 b2 =
compare0 ctx ret b1.term b2.term
compareArm_ ctx KBOX ret u b1 b2 = do
let ctx = extendTy Zero b1.name (TYPE u) ctx
compare0 ctx (weakT 1 ret) b1.term b1.term
parameters {auto _ : (Has DefsReader fs, Has ErrorEff fs)} (ctx : TyContext d n)
-- [todo] only split on the dvars that are actually used anywhere in

26
lib/Quox/Parser/FromParser.idr
View file

@ -99,13 +99,13 @@ mutual
Pair <$> fromPTermWith ds ns s <*> fromPTermWith ds ns t
Case pi pair (r, ret) (CasePair (x, y) body) =>
map E $ Base.CasePair pi
map E $ CasePair pi
<$> fromPTermElim ds ns pair
<*> fromPTermTScope ds ns [< r] ret
<*> fromPTermTScope ds ns [< x, y] body
Case pi tag (r, ret) (CaseEnum arms) =>
map E $ Base.CaseEnum pi
map E $ CaseEnum pi
<$> fromPTermElim ds ns tag
<*> fromPTermTScope ds ns [< r] ret
<*> assert_total fromPTermEnumArms ds ns arms
@ -115,7 +115,7 @@ mutual
Succ n => [|Succ $ fromPTermWith ds ns n|]
Case pi nat (r, ret) (CaseNat zer (s, pi', ih, suc)) =>
Prelude.map E $ Base.CaseNat pi pi'
map E $ CaseNat pi pi'
<$> fromPTermElim ds ns nat
<*> fromPTermTScope ds ns [< r] ret
<*> fromPTermWith ds ns zer
@ -143,7 +143,7 @@ mutual
Box val => Box <$> fromPTermWith ds ns val
Case pi box (r, ret) (CaseBox b body) =>
Prelude.map E $ CaseBox pi
map E $ CaseBox pi
<$> fromPTermElim ds ns box
<*> fromPTermTScope ds ns [< r] ret
<*> fromPTermTScope ds ns [< b] body
@ -157,6 +157,24 @@ mutual
s :# a =>
map E $ (:#) <$> fromPTermWith ds ns s <*> fromPTermWith ds ns a
Coe (i, ty) p q val =>
map E $ Coe
<$> fromPTermDScope ds ns [< i] ty
<*> fromPDimWith ds p
<*> fromPDimWith ds q
<*> fromPTermWith ds ns val
-- [todo] direct translation for homo comp?
Comp (i, ty) p q val r (j0, val0) (j1, val1) =>
map E $ CompH
<$> fromPTermDScope ds ns [< i] ty
<*> fromPDimWith ds p
<*> fromPDimWith ds q
<*> fromPTermWith ds ns val
<*> fromPDimWith ds r
<*> fromPTermDScope ds ns [< j0] val0
<*> fromPTermDScope ds ns [< j1] val1
private
fromPTermEnumArms : Has (Except Error) fs =>
Context' BName d -> Context' BName n ->

1
lib/Quox/Parser/Lexer.idr
View file

@ -197,6 +197,7 @@ reserved =
Sym "★" `Or` Word "Type",
Word "ℕ" `Or` Word "Nat",
Word1 "zero", Word1 "succ",
Word1 "coe", Word1 "comp",
Word1 "def",
Word1 "def0",
Word "defω" `Or` Word "def#",

38
lib/Quox/Parser/Parser.idr
View file

@ -177,7 +177,7 @@ optNameBinder = [|join $ optional $ bname <* darr|]
mutual
export covering
term : Grammar True PTerm
term = lamTerm <|> caseTerm <|> bindTerm <|> annTerm
term = lamTerm <|> caseTerm <|> coeTerm <|> compTerm <|> bindTerm <|> annTerm
private covering
lamTerm : Grammar True PTerm
@ -190,6 +190,30 @@ mutual
(resC "return" *> optBinderTerm)
(resC "of" *> caseBody)|]
private covering
coeTerm : Grammar True PTerm
coeTerm = resC "coe" *> [|Coe typeLine dimArg dimArg aTerm|]
private covering
compTerm : Grammar True PTerm
compTerm = resC "comp" *> do
head <- [|Comp typeLine dimArg dimArg aTerm dimArg|]
uncurry head <$> compBody
where
compBranch : Grammar True (DimConst, BName, PTerm)
compBranch = [|(,,) dimConst bname (resC "⇒" *> term)|]
zeroOne : (DimConst, a) -> (DimConst, a) -> Grammar False (a, a)
zeroOne (Zero, x) (One, y) = pure (x, y)
zeroOne (One, x) (Zero, y) = pure (y, x)
zeroOne _ _ = fatalError "body of comp needs one 0 branch and one 1 branch"
compBody : Grammar True ((BName, PTerm), (BName, PTerm))
compBody = braces $ do
et0 <- compBranch <* resC ";"
et1 <- compBranch <* optional (resC ";")
zeroOne et0 et1
private covering
caseBody : Grammar True PCaseBody
caseBody = braces $
@ -251,14 +275,14 @@ mutual
private covering
appTerm : Grammar True PTerm
appTerm = resC "★" *> [|TYPE nat|]
<|> resC "Eq" *> [|Eq (bracks optBinderTerm) aTerm aTerm|]
<|> resC "Eq" *> [|Eq typeLine aTerm aTerm|]
<|> resC "succ" *> [|Succ aTerm|]
<|> [|apply aTerm (many appArg)|]
where
data PArg = TermArg PTerm | DimArg PDim
appArg : Grammar True PArg
appArg = [|DimArg $ resC "@" *> dim|] <|> [|TermArg aTerm|]
appArg = [|DimArg dimArg|] <|> [|TermArg aTerm|]
apply : PTerm -> List PArg -> PTerm
apply = foldl apply1 where
@ -266,6 +290,14 @@ mutual
apply1 f (TermArg x) = f :@ x
apply1 f (DimArg p) = f :% p
private covering
typeLine : Grammar True (BName, PTerm)
typeLine = bracks optBinderTerm
private covering
dimArg : Grammar True PDim
dimArg = resC "@" *> dim
private covering
aTerm : Grammar True PTerm
aTerm = [|Enum $ braces $ commaSep bareTag|]

3
lib/Quox/Parser/Syntax.idr
View file

@ -54,6 +54,9 @@ namespace PTerm
| V PName
| (:#) PTerm PTerm
| Coe (BName, PTerm) PDim PDim PTerm
| Comp (BName, PTerm) PDim PDim PTerm PDim (BName, PTerm) (BName, PTerm)
%name PTerm s, t
public export

2
lib/Quox/Pretty.idr
View file

@ -87,7 +87,7 @@ bracks = delims "[" "]"
||| includes spaces inside the braces
export %inline
braces : Doc HL -> Doc HL
braces doc = hl Delim "{" <++> doc <++> hl Delim "}"
braces doc = hl Delim "{" <++> nest 2 doc <++> hl Delim "}"
export %inline
parensIf : Bool -> Doc HL -> Doc HL

711
lib/Quox/Reduce.idr
View file

@ -3,6 +3,8 @@ module Quox.Reduce
import Quox.No
import Quox.Syntax
import Quox.Definition
import Quox.Typing.Context
import Quox.Typing.Error
import Data.SnocVect
import Data.Maybe
import Data.List
@ -10,36 +12,35 @@ import Data.List
%default total
||| errors that might happen if you pass an ill typed expression into
||| whnf. don't do that please
public export
data WhnfError = MissingEnumArm TagVal (List TagVal)
public export
0 RedexTest : TermLike -> Type
RedexTest tm = {d, n : Nat} -> Definitions -> tm d n -> Bool
public export
interface Whnf (0 tm : TermLike) (0 isRedex : RedexTest tm) (0 err : Type) | tm
interface Whnf (0 tm : TermLike) (0 isRedex : RedexTest tm) | tm
where
whnf : {d, n : Nat} -> (defs : Definitions) ->
tm d n -> Either err (Subset (tm d n) (No . isRedex defs))
whnf : {d, n : Nat} -> (defs : Definitions) -> (ctx : WhnfContext d n) ->
tm d n -> Either Error (Subset (tm d n) (No . isRedex defs))
public export %inline
whnf0 : {d, n : Nat} -> {0 isRedex : RedexTest tm} -> Whnf tm isRedex =>
(defs : Definitions) -> WhnfContext d n -> tm d n ->
Either Error (tm d n)
whnf0 defs ctx t = fst <$> whnf defs ctx t
public export
0 IsRedex, NotRedex : {isRedex : RedexTest tm} -> Whnf tm isRedex err =>
0 IsRedex, NotRedex : {isRedex : RedexTest tm} -> Whnf tm isRedex =>
Definitions -> Pred (tm d n)
IsRedex defs = So . isRedex defs
NotRedex defs = No . isRedex defs
public export
0 NonRedex : (tm : TermLike) -> {isRedex : RedexTest tm} ->
Whnf tm isRedex err =>
(d, n : Nat) -> (defs : Definitions) -> Type
Whnf tm isRedex => (d, n : Nat) -> (defs : Definitions) -> Type
NonRedex tm d n defs = Subset (tm d n) (NotRedex defs)
public export %inline
nred : {0 isRedex : RedexTest tm} -> (0 _ : Whnf tm isRedex err) =>
nred : {0 isRedex : RedexTest tm} -> (0 _ : Whnf tm isRedex) =>
(t : tm d n) -> (0 nr : NotRedex defs t) =>
NonRedex tm d n defs
nred t = Element t nr
@ -48,32 +49,38 @@ nred t = Element t nr
public export %inline
isLamHead : Elim {} -> Bool
isLamHead (Lam {} :# Pi {}) = True
isLamHead (Coe {}) = True
isLamHead _ = False
public export %inline
isDLamHead : Elim {} -> Bool
isDLamHead (DLam {} :# Eq {}) = True
isDLamHead (Coe {}) = True
isDLamHead _ = False
public export %inline
isPairHead : Elim {} -> Bool
isPairHead (Pair {} :# Sig {}) = True
isPairHead (Coe {}) = True
isPairHead _ = False
public export %inline
isTagHead : Elim {} -> Bool
isTagHead (Tag t :# Enum _) = True
isTagHead (Coe {}) = True
isTagHead _ = False
public export %inline
isNatHead : Elim {} -> Bool
isNatHead (Zero :# Nat) = True
isNatHead (Succ n :# Nat) = True
isNatHead (Coe {}) = True
isNatHead _ = False
public export %inline
isBoxHead : Elim {} -> Bool
isBoxHead (Box {} :# BOX {}) = True
isBoxHead (Coe {}) = True
isBoxHead _ = False
public export %inline
@ -88,36 +95,41 @@ isAnn _ = False
||| true if a term is syntactically a type.
public export %inline
isTyCon : (t : Term {}) -> Bool
isTyCon (TYPE {}) = True
isTyCon (Pi {}) = True
isTyCon (Lam {}) = False
isTyCon (Sig {}) = True
isTyCon (Pair {}) = False
isTyCon (Enum {}) = True
isTyCon (Tag {}) = False
isTyCon (Eq {}) = True
isTyCon (DLam {}) = False
isTyCon Nat = True
isTyCon Zero = False
isTyCon (Succ {}) = False
isTyCon (BOX {}) = True
isTyCon (Box {}) = False
isTyCon (E {}) = False
isTyCon (CloT {}) = False
isTyCon (DCloT {}) = False
isTyCon : Term {} -> Bool
isTyCon (TYPE {}) = True
isTyCon (Pi {}) = True
isTyCon (Lam {}) = False
isTyCon (Sig {}) = True
isTyCon (Pair {}) = False
isTyCon (Enum {}) = True
isTyCon (Tag {}) = False
isTyCon (Eq {}) = True
isTyCon (DLam {}) = False
isTyCon Nat = True
isTyCon Zero = False
isTyCon (Succ {}) = False
isTyCon (BOX {}) = True
isTyCon (Box {}) = False
isTyCon (E {}) = False
isTyCon (CloT {}) = False
isTyCon (DCloT {}) = False
||| true if a term is syntactically a type, or a neutral.
public export %inline
isTyConE : (t : Term {}) -> Bool
isTyConE : Term {} -> Bool
isTyConE s = isTyCon s || isE s
||| true if a term is syntactically a type.
public export %inline
isAnnTyCon : (t : Elim {}) -> Bool
isAnnTyCon : Elim {} -> Bool
isAnnTyCon (ty :# TYPE _) = isTyCon ty
isAnnTyCon _ = False
public export %inline
isK : Dim d -> Bool
isK (K _) = True
isK _ = False
mutual
public export
@ -135,102 +147,332 @@ mutual
isRedexE defs nat || isNatHead nat
isRedexE defs (CaseBox {box, _}) =
isRedexE defs box || isBoxHead box
isRedexE defs (f :% _) =
isRedexE defs f || isDLamHead f
isRedexE defs (f :% p) =
isRedexE defs f || isDLamHead f || isK p
isRedexE defs (t :# a) =
isE t || isRedexT defs t || isRedexT defs a
isRedexE defs (TypeCase {ty, _}) =
isRedexE defs ty || isAnnTyCon ty
isRedexE defs (Coe {val, _}) =
isRedexT defs val || not (isE val)
isRedexE defs (Comp {ty, r, _}) =
isRedexT defs ty || isK r
isRedexE defs (TypeCase {ty, ret, _}) =
isRedexE defs ty || isRedexT defs ret || isAnnTyCon ty
isRedexE _ (CloE {}) = True
isRedexE _ (DCloE {}) = True
public export
isRedexT : RedexTest Term
isRedexT _ (CloT {}) = True
isRedexT _ (DCloT {}) = True
isRedexT defs (E e) = isAnn e || isRedexE defs e
isRedexT _ _ = False
isRedexT _ (CloT {}) = True
isRedexT _ (DCloT {}) = True
isRedexT defs (E e) = isAnn e || isRedexE defs e
isRedexT _ _ = False
public export
tycaseRhs : (k : TyConKind) -> TypeCaseArms d n ->
Maybe (ScopeTermN (arity k) d n)
tycaseRhs k arms = lookupPrecise k arms
public export
tycaseRhsDef : Term d n -> (k : TyConKind) -> TypeCaseArms d n ->
ScopeTermN (arity k) d n
tycaseRhsDef def k arms = fromMaybe (SN def) $ tycaseRhs k arms
public export
tycaseRhs0 : (k : TyConKind) -> TypeCaseArms d n ->
(0 eq : arity k = 0) => Maybe (Term d n)
tycaseRhs0 k arms {eq} with (tycaseRhs k arms) | (arity k)
tycaseRhs0 k arms {eq = Refl} | res | 0 = map (.term) res
public export
tycaseRhsDef0 : Term d n -> (k : TyConKind) -> TypeCaseArms d n ->
(0 eq : arity k = 0) => Term d n
tycaseRhsDef0 def k arms = fromMaybe def $ tycaseRhs0 k arms
private
weakDS : (by : Nat) -> DScopeTerm d n -> DScopeTerm d (by + n)
weakDS by (S names (Y body)) = S names $ Y $ weakT by body
weakDS by (S names (N body)) = S names $ N $ weakT by body
private
dweakS : (by : Nat) -> ScopeTerm d n -> ScopeTerm (by + d) n
dweakS by (S names (Y body)) = S names $ Y $ dweakT by body
dweakS by (S names (N body)) = S names $ N $ dweakT by body
private
coeScoped : {s : Nat} -> DScopeTerm d n -> Dim d -> Dim d ->
ScopeTermN s d n -> ScopeTermN s d n
coeScoped ty p q (S names (Y body)) =
S names $ Y $ E $ Coe (weakDS s ty) p q body
coeScoped ty p q (S names (N body)) =
S names $ N $ E $ Coe ty p q body
mutual
parameters {d, n : Nat} (defs : Definitions) (ctx : WhnfContext d n)
||| performs the minimum work required to recompute the type of an elim.
|||
||| ⚠ **assumes the elim is already typechecked.** ⚠
export covering
computeElimType : (e : Elim d n) -> (0 ne : No (isRedexE defs e)) =>
Either Error (Term d n)
computeElimType (F x) = do
let Just def = lookup x defs | Nothing => Left $ NotInScope x
pure $ def.type
computeElimType (B i) = pure $ ctx.tctx !! i
computeElimType (f :@ s) {ne} = do
-- can't use `expectPi` (or `expectEq` below) without making this
-- mutual block from hell even worse lol
Pi {arg, res, _} <- whnf0 defs ctx =<< computeElimType f {ne = noOr1 ne}
| t => Left $ ExpectedPi ctx.names t
pure $ sub1 res (s :# arg)
computeElimType (CasePair {pair, ret, _}) = pure $ sub1 ret pair
computeElimType (CaseEnum {tag, ret, _}) = pure $ sub1 ret tag
computeElimType (CaseNat {nat, ret, _}) = pure $ sub1 ret nat
computeElimType (CaseBox {box, ret, _}) = pure $ sub1 ret box
computeElimType (f :% p) {ne} = do
Eq {ty, _} <- whnf0 defs ctx =<< computeElimType f {ne = noOr1 ne}
| t => Left $ ExpectedEq ctx.names t
pure $ dsub1 ty p
computeElimType (Coe {ty, q, _}) = pure $ dsub1 ty q
computeElimType (Comp {ty, _}) = pure ty
computeElimType (TypeCase {ret, _}) = pure ret
computeElimType (_ :# ty) = pure ty
parameters {d, n : Nat} (defs : Definitions) (ctx : WhnfContext (S d) n)
||| for π.(x : A) → B, returns (A, B);
||| for an elim returns a pair of type-cases that will reduce to that;
||| for other intro forms error
private covering
tycasePi : (t : Term (S d) n) -> (0 tnf : No (isRedexT defs t)) =>
Either Error (Term (S d) n, ScopeTerm (S d) n)
tycasePi (Pi {arg, res, _}) = pure (arg, res)
tycasePi (E e) {tnf} = do
ty <- computeElimType defs ctx e @{noOr2 tnf}
let arg = E $ typeCase1 e ty KPi [< "Arg", "Ret"] (BVT 1)
res' = typeCase1 e (Arr Zero arg ty) KPi [< "Arg", "Ret"] (BVT 0)
res = SY [< "Arg"] $ E $ weakE 1 res' :@ BVT 0
pure (arg, res)
tycasePi t = Left $ ExpectedPi ctx.names t
||| for (x : A) × B, returns (A, B);
||| for an elim returns a pair of type-cases that will reduce to that;
||| for other intro forms error
private covering
tycaseSig : (t : Term (S d) n) -> (0 tnf : No (isRedexT defs t)) =>
Either Error (Term (S d) n, ScopeTerm (S d) n)
tycaseSig (Sig {fst, snd, _}) = pure (fst, snd)
tycaseSig (E e) {tnf} = do
ty <- computeElimType defs ctx e @{noOr2 tnf}
let fst = E $ typeCase1 e ty KSig [< "Fst", "Snd"] (BVT 1)
snd' = typeCase1 e (Arr Zero fst ty) KSig [< "Fst", "Snd"] (BVT 0)
snd = SY [< "Fst"] $ E $ weakE 1 snd' :@ BVT 0
pure (fst, snd)
tycaseSig t = Left $ ExpectedSig ctx.names t
||| for [π. A], returns A;
||| for an elim returns a type-case that will reduce to that;
||| for other intro forms error
private covering
tycaseBOX : (t : Term (S d) n) -> (0 tnf : No (isRedexT defs t)) =>
Either Error (Term (S d) n)
tycaseBOX (BOX _ a) = pure a
tycaseBOX (E e) {tnf} = do
ty <- computeElimType defs ctx e @{noOr2 tnf}
pure $ E $ typeCase1 e ty KBOX [< "Ty"] (BVT 0)
tycaseBOX t = Left $ ExpectedBOX ctx.names t
||| for Eq [i ⇒ A] l r, returns (A‹0/i›, A‹1/i›, A, l, r);
||| for an elim returns five type-cases that will reduce to that;
||| for other intro forms error
private covering
tycaseEq : (t : Term (S d) n) -> (0 tnf : No (isRedexT defs t)) =>
Either Error (Term (S d) n, Term (S d) n, DScopeTerm (S d) n,
Term (S d) n, Term (S d) n)
tycaseEq (Eq {ty, l, r}) = pure (ty.zero, ty.one, ty, l, r)
tycaseEq (E e) {tnf} = do
ty <- computeElimType defs ctx e @{noOr2 tnf}
let names = [< "A0", "A1", "A", "L", "R"]
a0 = E $ typeCase1 e ty KEq names (BVT 4)
a1 = E $ typeCase1 e ty KEq names (BVT 3)
a' = typeCase1 e (Eq0 ty a0 a1) KEq names (BVT 2)
a = SY [< "i"] $ E $ dweakE 1 a' :% BV 0
l = E $ typeCase1 e a0 KEq names (BVT 1)
r = E $ typeCase1 e a1 KEq names (BVT 0)
pure (a0, a1, a, l, r)
tycaseEq t = Left $ ExpectedEq ctx.names t
parameters {d, n : Nat} (defs : Definitions) (ctx : WhnfContext d n)
||| reduce a function application `Coe ty p q val :@ s`
private covering
piCoe : (ty : DScopeTerm d n) -> (p, q : Dim d) -> (val, s : Term d n) ->
Either Error (Subset (Elim d n) (No . isRedexE defs))
piCoe sty@(S i ty) p q val s = do
-- (coe [i ⇒ π.(x : A) → B] @p @q t) s ⇝
-- coe [i ⇒ B[𝒔‹i›/x] @p @q ((t ∷ (π.(x : A) → B)‹p/i›) 𝒔‹p›)
-- where 𝒔‹j› ≔ coe [i ⇒ A] @q @j s
--
-- type-case is used to expose A,B if the type is neutral
let ctx1 = extendDimN i ctx
Element ty tynf <- whnf defs ctx1 ty.term
(arg, res) <- tycasePi defs ctx1 ty
let s0 = Coe (SY i arg) q p s
body = E $ (val :# (ty // one p)) :@ E s0
s1 = Coe (SY i (arg // (BV 0 ::: shift 2))) (weakD 1 q) (BV 0)
(s // shift 1)
whnf defs ctx $ Coe (SY i $ sub1 res s1) p q body
||| reduce a pair elimination `CasePair pi (Coe ty p q val) ret body`
private covering
sigCoe : (qty : Qty) ->
(ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) ->
(ret : ScopeTerm d n) -> (body : ScopeTermN 2 d n) ->
Either Error (Subset (Elim d n) (No . isRedexE defs))
sigCoe qty sty@(S i ty) p q val ret body = do
-- caseπ (coe [i ⇒ (x : A) × B] @p @q s) return z ⇒ C of { (a, b) ⇒ e }
-- ⇝
-- caseπ s ∷ ((x : A) × B)‹p/i› return z ⇒ C
-- of { (a, b) ⇒
-- e[(coe [i ⇒ A] @p @q a)/a,
-- (coe [i ⇒ B[(coe [j ⇒ A‹j/i›] @p @i a)/x]] @p @q b)/b] }
--
-- type-case is used to expose A,B if the type is neutral
let ctx1 = extendDimN i ctx
Element ty tynf <- whnf defs ctx1 ty.term
(tfst, tsnd) <- tycaseSig defs ctx1 ty
let a' = Coe (SY i $ weakT 2 tfst) p q (BVT 1)
tsnd' = tsnd.term //
(Coe (SY i $ weakT 2 $ tfst // (BV 0 ::: shift 2))
(weakD 1 p) (BV 0) (BVT 1) ::: shift 2)
b' = Coe (SY i tsnd') p q (BVT 0)
whnf defs ctx $ CasePair qty (val :# (ty // one p)) ret $
SY body.names $ body.term // (a' ::: b' ::: shift 2)
||| reduce a dimension application `Coe ty p q val :% r`
private covering
eqCoe : (ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) ->
(r : Dim d) ->
Either Error (Subset (Elim d n) (No . isRedexE defs))
eqCoe sty@(S j ty) p q val r = do
-- (coe [j ⇒ Eq [i ⇒ A] L R] @p @q eq) @r
-- ⇝
-- comp [j ⇒ A‹r/i›] @p @q (eq ∷ (Eq [i ⇒ A] L R)‹p/j›)
-- { (r=0) j ⇒ L; (r=1) j ⇒ R }
let ctx1 = extendDimN j ctx
Element ty tynf <- whnf defs ctx1 ty.term
(a0, a1, a, s, t) <- tycaseEq defs ctx1 ty
let a' = SY j $ dsub1 a (weakD 1 r)
val' = E $ (val :# (ty // one p)) :% r
whnf defs ctx $ CompH a' p q val' r (SY j s) (SY j t)
||| reduce a pair elimination `CaseBox pi (Coe ty p q val) ret body`
private covering
boxCoe : (qty : Qty) ->
(ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) ->
(ret : ScopeTerm d n) -> (body : ScopeTerm d n) ->
Either Error (Subset (Elim d n) (No . isRedexE defs))
boxCoe qty sty@(S i ty) p q val ret body = do
-- caseπ (coe [i ⇒ [ρ. A]] @p @q s) return z ⇒ C of { [a] ⇒ e }
-- ⇝
-- caseπ s ∷ [ρ. A]‹p/i› return z ⇒ C
-- of { [a] ⇒ e[(coe [i ⇒ A] p q a)/a] }
let ctx1 = extendDimN i ctx
Element ty tynf <- whnf defs ctx1 ty.term
ta <- tycaseBOX defs ctx1 ty
let a' = Coe (SY i $ weakT 1 ta) p q $ BVT 0
whnf defs ctx $ CaseBox qty (val :# (ty // one p)) ret $
SY body.names $ body.term // (a' ::: shift 1)
export covering
Whnf Elim Reduce.isRedexE WhnfError where
whnf defs (F x) with (lookupElim x defs) proof eq
_ | Just y = whnf defs y
Whnf Elim Reduce.isRedexE where
whnf defs ctx (F x) with (lookupElim x defs) proof eq
_ | Just y = whnf defs ctx y
_ | Nothing = pure $ Element (F x) $ rewrite eq in Ah
whnf _ (B i) = pure $ nred $ B i
whnf _ _ (B i) = pure $ nred $ B i
-- ((λ x ⇒ t) ∷ (π.x : A) → B) s ⇝ t[s∷A/x] ∷ B[s∷A/x]
whnf defs (f :@ s) = do
Element f fnf <- whnf defs f
whnf defs ctx (f :@ s) = do
Element f fnf <- whnf defs ctx f
case nchoose $ isLamHead f of
Left _ =>
let Lam body :# Pi {arg, res, _} = f
s = s :# arg
in
whnf defs $ sub1 body s :# sub1 res s
Left _ => case f of
Lam body :# Pi {arg, res, _} =>
let s = s :# arg in
whnf defs ctx $ sub1 body s :# sub1 res s
Coe ty p q val => piCoe defs ctx ty p q val s
Right nlh => pure $ Element (f :@ s) $ fnf `orNo` nlh
-- case (s, t) ∷ (x : A) × B return p ⇒ C of { (a, b) ⇒ u } ⇝
-- u[s∷A/a, t∷B[s∷A/x]] ∷ C[(s, t)∷((x : A) × B)/p]
whnf defs (CasePair pi pair ret body) = do
Element pair pairnf <- whnf defs pair
whnf defs ctx (CasePair pi pair ret body) = do
Element pair pairnf <- whnf defs ctx pair
case nchoose $ isPairHead pair of
Left _ =>
let Pair {fst, snd} :# Sig {fst = tfst, snd = tsnd, _} = pair
fst = fst :# tfst
snd = snd :# sub1 tsnd fst
in
whnf defs $ subN body [< fst, snd] :# sub1 ret pair
Left _ => case pair of
Pair {fst, snd} :# Sig {fst = tfst, snd = tsnd, _} =>
let fst = fst :# tfst
snd = snd :# sub1 tsnd fst
in
whnf defs ctx $ subN body [< fst, snd] :# sub1 ret pair
Coe ty p q val => do
sigCoe defs ctx pi ty p q val ret body
Right np =>
pure $ Element (CasePair pi pair ret body)
(pairnf `orNo` np)
pure $ Element (CasePair pi pair ret body) $ pairnf `orNo` np
-- case 'a ∷ {a,…} return p ⇒ C of { 'a ⇒ u } ⇝
-- u ∷ C['a∷{a,…}/p]
whnf defs (CaseEnum pi tag ret arms) = do
Element tag tagnf <- whnf defs tag
whnf defs ctx (CaseEnum pi tag ret arms) = do
Element tag tagnf <- whnf defs ctx tag
case nchoose $ isTagHead tag of
Left t =>
let Tag t :# Enum ts = tag
ty = sub1 ret tag
in
case lookup t arms of
Just arm => whnf defs $ arm :# ty
Nothing => Left $ MissingEnumArm t (keys arms)
Left t => case tag of
Tag t :# Enum ts =>
let ty = sub1 ret tag in
case lookup t arms of
Just arm => whnf defs ctx $ arm :# ty
Nothing => Left $ MissingEnumArm t (keys arms)
Coe ty p q val =>
-- there is nowhere an equality can be hiding inside an Enum
whnf defs ctx $ CaseEnum pi (val :# dsub1 ty q) ret arms
Right nt =>
pure $ Element (CaseEnum pi tag ret arms) $ tagnf `orNo` nt
-- case zero ∷ ℕ return p ⇒ C of { zero ⇒ u; … } ⇝
-- u ∷ C[zero∷ℕ/p]
--
-- case succ n ∷ ℕ return p ⇒ C of { succ n' [π.ih] ⇒ u; … } ⇝
-- case succ n ∷ ℕ return p ⇒ C of { succ n', π.ih ⇒ u; … } ⇝
-- u[n∷ℕ/n', (case n ∷ ℕ ⋯)/ih] ∷ C[succ n ∷ ℕ/p]
whnf defs (CaseNat pi piIH nat ret zer suc) = do
Element nat natnf <- whnf defs nat
whnf defs ctx (CaseNat pi piIH nat ret zer suc) = do
Element nat natnf <- whnf defs ctx nat
case nchoose $ isNatHead nat of
Left _ =>
let ty = sub1 ret nat in
case nat of
Zero :# Nat => whnf defs (zer :# ty)
Zero :# Nat => whnf defs ctx (zer :# ty)
Succ n :# Nat =>
let nn = n :# Nat
tm = subN suc [< nn, CaseNat pi piIH nn ret zer suc]
in
whnf defs $ tm :# ty
whnf defs ctx $ tm :# ty
Coe ty p q val =>
-- same deal as Enum
whnf defs ctx $ CaseNat pi piIH (val :# dsub1 ty q) ret zer suc
Right nn =>
pure $ Element (CaseNat pi piIH nat ret zer suc) $ natnf `orNo` nn
-- case [t] ∷ [π.A] return p ⇒ C of { [x] ⇒ u } ⇝
-- u[t∷A/x] ∷ C[[t] ∷ [π.A]/p]
whnf defs (CaseBox pi box ret body) = do
Element box boxnf <- whnf defs box
whnf defs ctx (CaseBox pi box ret body) = do
Element box boxnf <- whnf defs ctx box
case nchoose $ isBoxHead box of
Left _ =>
let Box val :# BOX q bty = box
ty = sub1 ret box
in
whnf defs $ sub1 body (val :# bty) :# ty
Left _ => case box of
Box val :# BOX q bty =>
let ty = sub1 ret box in
whnf defs ctx $ sub1 body (val :# bty) :# ty
Coe ty p q val =>
boxCoe defs ctx pi ty p q val ret body
Right nb =>
pure $ Element (CaseBox pi box ret body) $ boxnf `orNo` nb
@ -238,114 +480,231 @@ mutual
-- ((δ 𝑖 ⇒ s) ∷ Eq [𝑗 ⇒ A] t u) @1 ⇝ u ∷ A‹1/𝑗›
-- ((δ 𝑖 ⇒ s) ∷ Eq [𝑗 ⇒ A] t u) @𝑘 ⇝ s‹𝑘/𝑖› ∷ A‹𝑘/𝑗›
-- (if 𝑘 is a variable)
whnf defs (f :% p) = do
Element f fnf <- whnf defs f
whnf defs ctx (f :% p) = do
Element f fnf <- whnf defs ctx f
case nchoose $ isDLamHead f of
Left _ =>
let DLam body :# Eq {ty = ty, l, r, _} = f
body = endsOr l r (dsub1 body p) p
in
whnf defs $ body :# dsub1 ty p
Right ndlh =>
pure $ Element (f :% p) $ fnf `orNo` ndlh
Left _ => case f of
DLam body :# Eq {ty = ty, l, r, _} =>
let body = endsOr l r (dsub1 body p) p in
whnf defs ctx $ body :# dsub1 ty p
Coe ty p' q' val =>
eqCoe defs ctx ty p' q' val p
Right ndlh => case p of
K e => do
Eq {l, r, ty, _} <- whnf0 defs ctx =<< computeElimType defs ctx f
| ty => Left $ ExpectedEq ctx.names ty
whnf defs ctx $ ends (l :# ty.zero) (r :# ty.one) e
B _ => pure $ Element (f :% p) $ fnf `orNo` ndlh `orNo` Ah
-- e ∷ A ⇝ e
whnf defs (s :# a) = do
Element s snf <- whnf defs s
whnf defs ctx (s :# a) = do
Element s snf <- whnf defs ctx s
case nchoose $ isE s of
Left _ => let E e = s in pure $ Element e $ noOr2 snf
Right ne => do
Element a anf <- whnf defs a
Element a anf <- whnf defs ctx a
pure $ Element (s :# a) $ ne `orNo` snf `orNo` anf
-- (type-case ★ᵢ ∷ _ return Q of { ★ ⇒ s; ⋯ }) ⇝ s ∷ Q
--
-- (type-case π.(x : A) → B ∷ ★ᵢ return Q of { (a → b) ⇒ s; ⋯ }) ⇝
-- s[(A ∷ ★ᵢ)/a, ((λ x ⇒ B) ∷ 0.A → ★ᵢ)/b] ∷ ★ᵢ
--
-- (type-case (x : A) × B ∷ ★ᵢ return Q of { (a × b) ⇒ s; ⋯ }) ⇝
-- s[(A ∷ ★ᵢ)/a, ((λ x ⇒ B) ∷ 0.A → ★ᵢ)/b] ∷ ★ᵢ
--
-- (type-case {⋯} ∷ _ return Q of { {} ⇒ s; ⋯ }) ⇝ s ∷ Q
--
-- (type-case Eq [i ⇒ A] L R ∷ ★ᵢ return Q of {
-- Eq a₀ a₁ a l r ⇒ s; ⋯ }) ⇝
-- s[(A‹0/i› ∷ ★ᵢ)/a₀, (A‹1/i› ∷ ★ᵢ)/a₁,
-- ((δ i ⇒ A) ∷ Eq [★ᵢ] A‹0/i› A‹1/i›)/a,
-- (L ∷ A‹0/i›)/l, (R ∷ A‹1/i›)/r] ∷ Q
--
-- (type-case ℕ ∷ _ return Q of { ℕ ⇒ s; ⋯ }) ⇝ s ∷ Q
--
-- (type-case [π.A] ∷ ★ᵢ return Q of { [a] ⇒ s; ⋯ }) ⇝ s[(A ∷ ★ᵢ)/a] ∷ Q
whnf defs (TypeCase {ty, ret, univ, pi, sig, enum, eq, nat, box}) = do
Element ty tynf <- whnf defs ty
whnf defs ctx (Coe (S _ (N ty)) _ _ val) =
whnf defs ctx $ val :# ty
whnf defs ctx (Coe (S [< i] ty) p q val) = do
Element ty tynf <- whnf defs (extendDim i ctx) ty.term
Element val valnf <- whnf defs ctx val
pushCoe defs ctx i ty p q val
whnf defs ctx (Comp ty p q val r zero one) =
-- comp [A] @p @p s { ⋯ } ⇝ s ∷ A
if p == q then whnf defs ctx $ val :# ty else
case nchoose (isK r) of
-- comp [A] @p @q s { (0=0) j ⇒ t; ⋯ } ⇝ t‹q/j› ∷ A
-- comp [A] @p @q s { (1=1) j ⇒ t; ⋯ } ⇝ t‹q/j› ∷ A
Left y => case r of
K Zero => whnf defs ctx $ dsub1 zero q :# ty
K One => whnf defs ctx $ dsub1 one q :# ty
Right nk => do
Element ty tynf <- whnf defs ctx ty
pure $ Element (Comp ty p q val r zero one) $ tynf `orNo` nk
-- [todo] anything other than just the boundaries??
whnf defs ctx (TypeCase ty ret arms def) = do
Element ty tynf <- whnf defs ctx ty
Element ret retnf <- whnf defs ctx ret
case nchoose $ isAnnTyCon ty of
Left y =>
let ty :# TYPE u = ty in
case ty of
TYPE _ =>
whnf defs $ univ :# ret
Pi _ arg res =>
let arg = arg :# TYPE u
res = toLam res :# Arr Zero (TYPE u) (TYPE u)
in
whnf defs $ subN pi [< arg, res] :# ret
Sig fst snd =>
let fst = fst :# TYPE u
snd = toLam snd :# Arr Zero (TYPE u) (TYPE u)
in
whnf defs $ subN sig [< fst, snd] :# ret
Enum _ =>
whnf defs $ enum :# ret
Eq a l r =>
let a0' = a.zero; a1' = a.one
a0 = a0' :# TYPE u
a1 = a1' :# TYPE u
a = toDLam a :# Eq0 (TYPE u) a0' a1'
l = l :# a0'
r = r :# a1'
in
whnf defs $ subN eq [< a0, a1, a, l, r] :# ret
Nat =>
whnf defs $ nat :# ret
BOX _ s =>
whnf defs $ sub1 box (s :# TYPE u) :# ret
Right nt => pure $
Element (TypeCase {ty, ret, univ, pi, sig, enum, eq, nat, box}) $
tynf `orNo` nt
where
toLam : {s : Nat} -> ScopeTermN s d n -> Term d n
toLam (S names body) = names :\\ body.term
Left y => let ty :# TYPE u = ty in
reduceTypeCase defs ctx ty u ret arms def
Right nt => pure $ Element (TypeCase ty ret arms def) $
tynf `orNo` retnf `orNo` nt
toDLam : {s : Nat} -> DScopeTermN s d n -> Term d n
toDLam (S names body) = names :\\% body.term
whnf defs (CloE el th) = whnf defs $ pushSubstsWith' id th el
whnf defs (DCloE el th) = whnf defs $ pushSubstsWith' th id el
whnf defs ctx (CloE el th) = whnf defs ctx $ pushSubstsWith' id th el
whnf defs ctx (DCloE el th) = whnf defs ctx $ pushSubstsWith' th id el
export covering
Whnf Term Reduce.isRedexT WhnfError where
whnf _ t@(TYPE {}) = pure $ nred t
whnf _ t@(Pi {}) = pure $ nred t
whnf _ t@(Lam {}) = pure $ nred t
whnf _ t@(Sig {}) = pure $ nred t
whnf _ t@(Pair {}) = pure $ nred t
whnf _ t@(Enum {}) = pure $ nred t
whnf _ t@(Tag {}) = pure $ nred t
whnf _ t@(Eq {}) = pure $ nred t
whnf _ t@(DLam {}) = pure $ nred t
whnf _ Nat = pure $ nred Nat
whnf _ Zero = pure $ nred Zero
whnf _ t@(Succ {}) = pure $ nred t
whnf _ t@(BOX {}) = pure $ nred t
whnf _ t@(Box {}) = pure $ nred t
Whnf Term Reduce.isRedexT where
whnf _ _ t@(TYPE {}) = pure $ nred t
whnf _ _ t@(Pi {}) = pure $ nred t
whnf _ _ t@(Lam {}) = pure $ nred t
whnf _ _ t@(Sig {}) = pure $ nred t
whnf _ _ t@(Pair {}) = pure $ nred t
whnf _ _ t@(Enum {}) = pure $ nred t
whnf _ _ t@(Tag {}) = pure $ nred t
whnf _ _ t@(Eq {}) = pure $ nred t
whnf _ _ t@(DLam {}) = pure $ nred t
whnf _ _ Nat = pure $ nred Nat
whnf _ _ Zero = pure $ nred Zero
whnf _ _ t@(Succ {}) = pure $ nred t
whnf _ _ t@(BOX {}) = pure $ nred t
whnf _ _ t@(Box {}) = pure $ nred t
-- s ∷ A ⇝ s (in term context)
whnf defs (E e) = do
Element e enf <- whnf defs e
whnf defs ctx (E e) = do
Element e enf <- whnf defs ctx e
case nchoose $ isAnn e of
Left _ => let tm :# _ = e in pure $ Element tm $ noOr1 $ noOr2 enf
Right na => pure $ Element (E e) $ na `orNo` enf
whnf defs (CloT tm th) = whnf defs $ pushSubstsWith' id th tm
whnf defs (DCloT tm th) = whnf defs $ pushSubstsWith' th id tm
whnf defs ctx (CloT tm th) = whnf defs ctx $ pushSubstsWith' id th tm
whnf defs ctx (DCloT tm th) = whnf defs ctx $ pushSubstsWith' th id tm
||| reduce a type-case applied to a type constructor
private covering
reduceTypeCase : {d, n : Nat} -> (defs : Definitions) -> WhnfContext d n ->
(ty : Term d n) -> (u : Universe) -> (ret : Term d n) ->
(arms : TypeCaseArms d n) -> (def : Term d n) ->
(0 _ : So (isTyCon ty)) =>
Either Error (Subset (Elim d n) (No . isRedexE defs))
reduceTypeCase defs ctx ty u ret arms def = case ty of
-- (type-case ★ᵢ ∷ _ return Q of { ★ ⇒ s; ⋯ }) ⇝ s ∷ Q
TYPE _ =>
whnf defs ctx $ tycaseRhsDef0 def KTYPE arms :# ret
-- (type-case π.(x : A) → B ∷ ★ᵢ return Q of { (a → b) ⇒ s; ⋯ }) ⇝
-- s[(A ∷ ★ᵢ)/a, ((λ x ⇒ B) ∷ 0.A → ★ᵢ)/b] ∷ ★ᵢ
Pi _ arg res =>
let arg = arg :# TYPE u
res = Lam res :# Arr Zero (TYPE u) (TYPE u)
in
whnf defs ctx $ subN (tycaseRhsDef def KPi arms) [< arg, res] :# ret
-- (type-case (x : A) × B ∷ ★ᵢ return Q of { (a × b) ⇒ s; ⋯ }) ⇝
-- s[(A ∷ ★ᵢ)/a, ((λ x ⇒ B) ∷ 0.A → ★ᵢ)/b] ∷ ★ᵢ
Sig fst snd =>
let fst = fst :# TYPE u
snd = Lam snd :# Arr Zero (TYPE u) (TYPE u)
in
whnf defs ctx $ subN (tycaseRhsDef def KSig arms) [< fst, snd] :# ret
-- (type-case {⋯} ∷ _ return Q of { {} ⇒ s; ⋯ }) ⇝ s ∷ Q
Enum _ =>
whnf defs ctx $ tycaseRhsDef0 def KEnum arms :# ret
-- (type-case Eq [i ⇒ A] L R ∷ ★ᵢ return Q
-- of { Eq a₀ a₁ a l r ⇒ s; ⋯ }) ⇝
-- s[(A‹0/i› ∷ ★ᵢ)/a₀, (A‹1/i› ∷ ★ᵢ)/a₁,
-- ((δ i ⇒ A) ∷ Eq [★ᵢ] A‹0/i› A‹1/i›)/a,
-- (L ∷ A‹0/i›)/l, (R ∷ A‹1/i›)/r] ∷ Q
Eq a l r =>
let a0 = a.zero; a1 = a.one in
whnf defs ctx $
subN (tycaseRhsDef def KEq arms)
[< a0 :# TYPE u, a1 :# TYPE u,
DLam a :# Eq0 (TYPE u) a0 a1, l :# a0, r :# a1]
:# ret
-- (type-case ℕ ∷ _ return Q of { ℕ ⇒ s; ⋯ }) ⇝ s ∷ Q
Nat =>
whnf defs ctx $ tycaseRhsDef0 def KNat arms :# ret
-- (type-case [π.A] ∷ ★ᵢ return Q of { [a] ⇒ s; ⋯ }) ⇝ s[(A ∷ ★ᵢ)/a] ∷ Q
BOX _ s =>
whnf defs ctx $ sub1 (tycaseRhsDef def KBOX arms) (s :# TYPE u) :# ret
||| pushes a coercion inside a whnf-ed term
private covering
pushCoe : {n, d : Nat} -> (defs : Definitions) -> WhnfContext d n ->
BaseName ->
(ty : Term (S d) n) -> (0 tynf : No (isRedexT defs ty)) =>
Dim d -> Dim d ->
(s : Term d n) -> (0 snf : No (isRedexT defs s)) =>
Either Error (NonRedex Elim d n defs)
pushCoe defs ctx i ty p q s =
if p == q then whnf defs ctx $ s :# (ty // one q) else
case s of
-- (coe [_ ⇒ ★ᵢ] @_ @_ ty) ⇝ (ty ∷ ★ᵢ)
TYPE {} => pure $ nred $ s :# TYPE !(unwrapTYPE ty)
Pi {} => pure $ nred $ s :# TYPE !(unwrapTYPE ty)
Sig {} => pure $ nred $ s :# TYPE !(unwrapTYPE ty)
Enum {} => pure $ nred $ s :# TYPE !(unwrapTYPE ty)
Eq {} => pure $ nred $ s :# TYPE !(unwrapTYPE ty)
Nat => pure $ nred $ s :# TYPE !(unwrapTYPE ty)
BOX {} => pure $ nred $ s :# TYPE !(unwrapTYPE ty)
-- just η expand it. then whnf for (:@) will handle it later
-- this is how @xtt does it
Lam body => do
let body' = Coe (SY [< i] ty) p q (Lam body)
term' = Lam (SY [< "y"] $ E $ weakE 1 body' :@ BVT 0)
type' = ty // one q
whnf defs ctx $ term' :# type'
{-
-- maybe:
-- (coe [i ⇒ π.(x : A) → B] @p @q (λ x ⇒ s)) ⇝
-- (λ x ⇒ coe [i ⇒ B[(coe [j ⇒ A‹j/i›] @q @i x)/x]] @p @q s)
-- ∷ (π.(x: A‹q/i›) → B‹q/i›)
Lam body => do
let Pi {qty, arg, res} = ty
| _ => Left $ ?err
let arg' = SY [< "j"] $ weakT 1 $ arg // (BV 0 ::: shift 2)
res' = SY [< i] $ res.term //
(Coe arg' (weakD 1 q) (BV 0) (BVT 0) ::: shift 1)
body = SY body.names $ E $ Coe res' p q body.term
pure $ Element (Lam body :# Pi qty (arg // one q) (res // one q)) Ah
-}
-- (coe [i ⇒ (x : A) × B] @p @q (s, t)) ⇝
-- (coe [i ⇒ A] @p @q s,
-- coe [i ⇒ B[(coe [j ⇒ A‹j/i›] @p @i s)/x]] @p @q t)
-- ∷ (x : A‹q/i›) × B‹q/i›
--
-- can't use η here because... it doesn't exist
Pair fst snd => do
let Sig {fst = tfst, snd = tsnd} = ty
| _ => Left $ ExpectedSig (extendDim i ctx.names) ty
let fst' = E $ Coe (SY [< i] tfst) p q fst
tfst' = SY [< "j"] $ tfst `CanDSubst.(//)` (BV 0 ::: shift 2)
tsnd' = SY [< i] $ sub1 tsnd $
Coe tfst' (weakD 1 p) (BV 0) $ dweakT 1 fst
snd' = E $ Coe tsnd' p q snd
pure $
Element (Pair fst' snd' :# Sig (tfst // one q) (tsnd // one q)) Ah
-- η expand like λ
DLam body => do
let body' = Coe (SY [< i] ty) p q (DLam body)
term' = DLam (SY [< "j"] $ E $ dweakE 1 body' :% BV 0)
type' = ty // one q
whnf defs ctx $ term' :# type'
-- (coe [_ ⇒ {⋯}] @_ @_ t) ⇝ (t ∷ {⋯})
Tag tag => do
let Enum ts = ty
| _ => Left $ ExpectedEnum (extendDim i ctx.names) ty
pure $ Element (Tag tag :# Enum ts) Ah
-- (coe [_ ⇒ ℕ] @_ @_ n) ⇝ (n ∷ ℕ)
Zero => pure $ Element (Zero :# Nat) Ah
Succ t => pure $ Element (Succ t :# Nat) Ah
-- (coe [i ⇒ [π.A]] @p @q [s]) ⇝
-- [coe [i ⇒ A] @p @q s] ∷ [π. A‹q/i›]
Box val => do
let BOX {qty, ty = a} = ty
| _ => Left $ ExpectedBOX (extendDim i ctx.names) ty
let a = SY [< i] a
pure $ Element (Box (E $ Coe a p q s) :# BOX qty (dsub1 a q)) Ah
E e => pure $ Element (Coe (SY [< i] ty) p q (E e)) (snf `orNo` Ah)
where
unwrapTYPE : Term (S d) n -> Either Error Universe
unwrapTYPE (TYPE u) = pure u
unwrapTYPE ty = Left $ ExpectedTYPE (extendDim i ctx.names) ty

6
lib/Quox/Syntax/Dim.idr
View file

@ -22,7 +22,7 @@ data DimConst = Zero | One
||| `ends l r e` returns `l` if `e` is `Zero`, or `r` if it is `One`.
public export
ends : a -> a -> DimConst -> a
ends : Lazy a -> Lazy a -> DimConst -> a
ends l r Zero = l
ends l r One = r
@ -130,5 +130,5 @@ BV i = B $ V i
export
weakD : {default 1 by : Nat} -> Dim d -> Dim (by + d)
weakD p = p // shift by
weakD : (by : Nat) -> Dim d -> Dim (by + d)
weakD by p = p // shift by

7
lib/Quox/Syntax/DimEq.idr
View file

@ -63,6 +63,11 @@ ifConsistent : Applicative f => (eqs : DimEq d) -> f a -> f (IfConsistent eqs a)
ifConsistent ZeroIsOne act = pure Nothing
ifConsistent (C _) act = Just <$> act
public export
toMaybe : IfConsistent eqs a -> Maybe a
toMaybe Nothing = Nothing
toMaybe (Just x) = Just x
export
fromGround' : Context' DimConst d -> DimEq' d
@ -245,7 +250,7 @@ PrettyHL (DimEq' d) where
go [<] = pure [<]
go (eqs :< Nothing) = local {dnames $= tail} $ go eqs
go (eqs :< Just p) = do
eq <- prettyCst (BV {d = 1} 0) (weakD p)
eq <- prettyCst (BV {d = 1} 0) (weakD 1 p)
eqs <- local {dnames $= tail} $ go eqs
pure $ eqs :< eq

73
lib/Quox/Syntax/Term/Base.idr
View file

@ -5,6 +5,7 @@ import public Quox.Syntax.Shift
import public Quox.Syntax.Subst
import public Quox.Syntax.Qty
import public Quox.Syntax.Dim
import public Quox.Syntax.Term.TyConKind
import public Quox.Name
import public Quox.Context
@ -17,33 +18,35 @@ import Data.Nat
import public Data.So
import Data.String
import public Data.SortedMap
import public Data.SortedMap.Dependent
import public Data.SortedSet
%default total
public export
0 TermLike : Type
TermLike : Type
TermLike = Nat -> Nat -> Type
public export
0 TSubstLike : Type
TSubstLike : Type
TSubstLike = Nat -> Nat -> Nat -> Type
public export
0 Universe : Type
Universe : Type
Universe = Nat
public export
0 TagVal : Type
TagVal : Type
TagVal = String
infixl 8 :#
infixl 9 :@, :%
mutual
public export
0 TSubst : TSubstLike
TSubst d = Subst $ Elim d
TSubst : TSubstLike
TSubst d = Subst $ \n => Elim d n
||| first argument `d` is dimension scope size;
||| second `n` is term scope size
@ -138,16 +141,19 @@ mutual
||| type-annotated term
(:#) : (tm, ty : Term d n) -> Elim d n
||| match on types (needed for coercions :mario_flop:)
TypeCase : (ty : Elim d n) ->
(ret : Term d n) ->
(univ : Term d n) ->
(pi : ScopeTermN 2 d n) ->
(sig : ScopeTermN 2 d n) ->
(enum : Term d n) ->
(eq : ScopeTermN 5 d n) ->
(nat : Term d n) ->
(box : ScopeTerm d n) ->
||| coerce a value along a type equality, or show its coherence
||| [@xtt; §2.1.1]
Coe : (ty : DScopeTerm d n) -> (p, q : Dim d) ->
(val : Term d n) -> Elim d n
||| "generalised composition" [@xtt; §2.1.2]
Comp : (ty : Term d n) -> (p, q : Dim d) ->
(val : Term d n) -> (r : Dim d) ->
(zero, one : DScopeTerm d n) -> Elim d n
||| match on types. needed for b.s. of coercions [@xtt; §2.2]
TypeCase : (ty : Elim d n) -> (ret : Term d n) ->
(arms : TypeCaseArms d n) -> (def : Term d n) ->
Elim d n
||| term closure/suspended substitution
@ -158,9 +164,22 @@ mutual
Elim dto n
public export
0 CaseEnumArms : TermLike
CaseEnumArms : TermLike
CaseEnumArms d n = SortedMap TagVal (Term d n)
public export
TypeCaseArms : TermLike
TypeCaseArms d n = SortedDMap TyConKind (\k => TypeCaseArmBody k d n)
public export
TypeCaseArm : TermLike
TypeCaseArm d n = (k ** TypeCaseArmBody k d n)
public export
TypeCaseArmBody : TyConKind -> TermLike
TypeCaseArmBody k = ScopeTermN (arity k)
||| a scoped term with names
public export
record Scoped (s : Nat) (f : Nat -> Type) (n : Nat) where
@ -174,15 +193,16 @@ mutual
N : (body : f n) -> ScopedBody s f n
public export
0 ScopeTermN, DScopeTermN : Nat -> TermLike
ScopeTermN, DScopeTermN : Nat -> TermLike
ScopeTermN s d n = Scoped s (Term d) n
DScopeTermN s d n = Scoped s (\d => Term d n) d
public export
0 ScopeTerm, DScopeTerm : TermLike
ScopeTerm, DScopeTerm : TermLike
ScopeTerm = ScopeTermN 1
DScopeTerm = DScopeTermN 1
%name Term s, t, r
%name Elim e, f
%name Scoped body
@ -260,6 +280,19 @@ makeNat : Nat -> Term d n
makeNat 0 = Zero
makeNat (S k) = Succ $ makeNat k
public export
public export %inline
enum : List TagVal -> Term d n
enum = Enum . SortedSet.fromList
public export %inline
typeCase : Elim d n -> Term d n ->
List (TypeCaseArm d n) -> Term d n -> Elim d n
typeCase ty ret arms def = TypeCase ty ret (fromList arms) def
public export %inline
typeCase1 : Elim d n -> Term d n ->
(k : TyConKind) -> NContext (arity k) -> Term d (arity k + n) ->
{default Nat def : Term d n} ->
Elim d n
typeCase1 ty ret k ns body {def} =
typeCase ty ret [(k ** SY ns body)] def

137
lib/Quox/Syntax/Term/Pretty.idr
View file

@ -15,22 +15,22 @@ export %inline
typeD, arrowD, darrowD, timesD, lamD, eqndD, dlamD, annD, natD :
Pretty.HasEnv m => m (Doc HL)
typeD = hlF Syntax $ ifUnicode "★" "Type"
arrowD = hlF Syntax $ ifUnicode "→" "->"
darrowD = hlF Syntax $ ifUnicode "⇒" "=>"
timesD = hlF Syntax $ ifUnicode "×" "**"
arrowD = hlF Delim $ ifUnicode "→" "->"
darrowD = hlF Delim $ ifUnicode "⇒" "=>"
timesD = hlF Delim $ ifUnicode "×" "**"
lamD = hlF Syntax $ ifUnicode "λ" "fun"
eqndD = hlF Syntax $ ifUnicode "≡" "=="
eqndD = hlF Delim $ ifUnicode "≡" "=="
dlamD = hlF Syntax $ ifUnicode "δ" "dfun"
annD = hlF Syntax $ ifUnicode "∷" "::"
annD = hlF Delim $ ifUnicode "∷" "::"
natD = hlF Syntax $ ifUnicode "ℕ" "Nat"
export %inline
eqD, colonD, commaD, semiD, caseD, typecaseD, returnD,
ofD, dotD, zeroD, succD : Doc HL
ofD, dotD, zeroD, succD, coeD, compD : Doc HL
eqD = hl Syntax "Eq"
colonD = hl Syntax ":"
commaD = hl Syntax ","
semiD = hl Syntax ";"
colonD = hl Delim ":"
commaD = hl Delim ","
semiD = hl Delim ";"
caseD = hl Syntax "case"
typecaseD = hl Syntax "type-case"
ofD = hl Syntax "of"
@ -38,6 +38,8 @@ returnD = hl Syntax "return"
dotD = hl Delim "."
zeroD = hl Syntax "zero"
succD = hl Syntax "succ"
coeD = hl Syntax "coe"
compD = hl Syntax "compD"
export
@ -138,10 +140,10 @@ prettyTuple = map (parens . align . separate commaD) . traverse prettyM
export
prettyArms : PrettyHL a => Pretty.HasEnv m =>
List (SnocList BaseName, Doc HL, a) -> m (Doc HL)
prettyArms =
BinderSort -> List (SnocList BaseName, Doc HL, a) -> m (Doc HL)
prettyArms s =
map (braces . aseparate semiD) .
traverse (\(xs, l, r) => prettyArm T xs l r)
traverse (\(xs, l, r) => prettyArm s xs l r)
export
prettyCase' : (PrettyHL a, PrettyHL b, PrettyHL c, Pretty.HasEnv m) =>
@ -153,7 +155,7 @@ prettyCase' intro elim r ret arms = do
ret <- case r of
Unused => pretty0M ret
_ => prettyLams Nothing T [< r] ret
arms <- prettyArms arms
arms <- prettyArms T arms
pure $ asep [intro <++> elim, returnD <++> ret, ofD <++> arms]
export
@ -192,6 +194,12 @@ export
prettyBoxVal : PrettyHL a => Pretty.HasEnv m => a -> m (Doc HL)
prettyBoxVal val = bracks <$> pretty0M val
export
prettyCompPat : Pretty.HasEnv m => Dim d -> DimConst -> BaseName -> m (Doc HL)
prettyCompPat s e j = pure $
hsep [parens (hsep [!(pretty0M s), hl Syntax "=", !(pretty0M e)]),
!(pretty0M $ DV j)]
export
toNatLit : Term d n -> Maybe Nat
toNatLit Zero = Just 0
@ -210,58 +218,77 @@ parameters (showSubsts : Bool)
where
prettyM (TYPE l) =
parensIfM App $ !typeD <+> hl Syntax !(prettyUnivSuffix l)
prettyM (Pi qty s (S _ (N t))) = do
dom <- pretty0M $ MkWithQty qty s
cod <- withPrec AnnR $ prettyM t
parensIfM AnnR $ asep [dom <++> !arrowD, cod]
prettyM (Pi qty s (S [< x] (Y t))) =
prettyBindType (Just qty) x s !arrowD t
prettyM (Lam (S x t)) =
let GotLams {names, body, _} = getLams' x t.term Refl in
prettyLams (Just !lamD) T (toSnocList' names) body
prettyM (Sig s (S _ (N t))) = do
s <- withPrec InTimes $ prettyM s
t <- withPrec Times $ prettyM t
parensIfM Times $ asep [s <++> !timesD, t]
prettyM (Sig s (S [< x] (Y t))) =
prettyBindType Nothing x s !timesD t
prettyM (Pair s t) =
let GotPairs {init, last, _} = getPairs' [< s] t in
prettyTuple $ toList $ init :< last
prettyM (Enum tags) =
pure $ delims "{" "}" . aseparate comma $ map prettyTagBare $
Prelude.toList tags
prettyM (Tag t) =
pure $ prettyTag t
prettyM (Eq (S _ (N ty)) l r) = do
l <- withPrec InEq $ prettyM l
r <- withPrec InEq $ prettyM r
ty <- withPrec InEq $ prettyM ty
parensIfM Eq $ asep [l <++> !eqndD, r <++> colonD, ty]
prettyM (Eq (S [< i] (Y ty)) l r) = do
prettyApps Nothing (L eqD)
[epretty $ MkTypeLine i ty, epretty l, epretty r]
prettyM (DLam (S i t)) =
let GotDLams {names, body, _} = getDLams' i t.term Refl in
prettyLams (Just !dlamD) D (toSnocList' names) body
prettyM Nat = natD
prettyM Zero = pure $ hl Syntax "0"
prettyM (Succ n) =
case toNatLit n of
Just n => pure $ hl Syntax $ pretty $ S n
Nothing => prettyApps Nothing (L succD) [n]
prettyM (BOX pi ty) = do
pi <- pretty0M pi
ty <- pretty0M ty
pure $ bracks $ hcat [pi, dotD, align ty]
prettyM (Box val) = prettyBoxVal val
prettyM (E e) = prettyM e
prettyM (CloT s th) =
if showSubsts then
parensIfM SApp . hang 2 =<<
[|withPrec SApp (prettyM s) <%> prettyTSubst th|]
else
prettyM $ pushSubstsWith' id th s
prettyM (DCloT s th) =
if showSubsts then
parensIfM SApp . hang 2 =<<
@ -274,61 +301,97 @@ parameters (showSubsts : Bool)
where
prettyM (F x) =
hl' Free <$> prettyM x
prettyM (B i) =
prettyVar TVar TVarErr (!ask).tnames i
prettyM (e :@ s) =
let GotArgs {fun, args, _} = getArgs' e [s] in
prettyApps Nothing fun args
prettyM (CasePair pi p (S [< r] ret) (S [< x, y] body)) = do
pat <- parens . separate commaD <$> traverse (hlF TVar . prettyM) [x, y]
prettyCase pi p r ret.term [([< x, y], pat, body.term)]
prettyM (CaseEnum pi t (S [< r] ret) arms) =
prettyCase pi t r ret.term
[([<], prettyTag t, b) | (t, b) <- SortedMap.toList arms]
prettyM (CaseNat pi pi' nat (S [< r] ret) zer (S [< s, ih] suc)) =
prettyCase pi nat r ret.term
[([<], zeroD, eterm zer),
([< s, ih], !succPat, eterm suc.term)]
where
succPat : m (Doc HL)
succPat = case (ih, pi') of
(Unused, Zero) => pure $ succD <++> !(pretty0M s)
_ => pure $ asep [succD <++> !(pretty0M s) <+> comma,
!(pretty0M $ MkWithQty pi' ih)]
where
succPat : m (Doc HL)
succPat = case (ih, pi') of
(Unused, Zero) => pure $ succD <++> !(pretty0M s)
_ => pure $ asep [succD <++> !(pretty0M s) <+> comma,
!(pretty0M $ MkWithQty pi' ih)]
prettyM (CaseBox pi box (S [< r] ret) (S [< u] body)) =
prettyCase pi box r ret.term
[([< u], !(prettyBoxVal $ TV u), body.term)]
prettyM (e :% d) =
let GotDArgs {fun, args, _} = getDArgs' e [d] in
prettyApps (Just "@") fun args
prettyM (s :# a) = do
s <- withPrec AnnL $ prettyM s
a <- withPrec AnnR $ prettyM a
parensIfM AnnR $ hang 2 $ s <++> !annD <%%> a
prettyM (TypeCase ty ret univ
(S [< piA, piB] pi) (S [< sigA, sigB] sig) enum
(S [< eqA0, eqA1, eqA, eqL, eqR] eq)
nat (S [< boxA] box)) = do
let v : BaseName -> Doc HL := pretty0 True . TV
pipat <- pure $ parens $ hsep [v piA, !arrowD, v piB]
sigpat <- pure $ parens $ hsep [v sigA, !timesD, v sigB]
eqpat <- prettyApps Nothing (L eqD)
[TV eqA0, TV eqA1, TV eqA, TV eqL, TV eqR]
boxpat <- pure $ bracks $ v boxA
prettyCase' typecaseD ty Unused ret
[([<], !typeD, eterm univ),
([< piA, piB], pipat, eterm pi.term),
([< sigA, sigB], sigpat, eterm sig.term),
([<], hl Syntax "{}", eterm enum),
([< eqA0, eqA1, eqA, eqL, eqR], eqpat, eterm eq.term),
([<], !natD, eterm nat),
([< boxA], boxpat, eterm box.term)]
prettyM (Coe (S [< i] ty) p q val) =
let ty = case ty of
Y ty => epretty $ MkTypeLine i ty
N ty => epretty ty
in
prettyApps' (L coeD)
[(Nothing, ty),
(Just "@", epretty p),
(Just "@", epretty q),
(Nothing, epretty val)]
prettyM (Comp ty p q val r (S [< z] zero) (S [< o] one)) = do
apps <- prettyApps' (L compD)
[(Nothing, epretty ty),
(Just "@", epretty p),
(Just "@", epretty q),
(Nothing, epretty val)]
arms <- prettyArms D
[([< z], !(prettyCompPat r Zero z), zero.term),
([< o], !(prettyCompPat r One o), one.term)]
pure $ apps <++> arms
prettyM (TypeCase ty ret arms def) = do
arms <- traverse fromArm (toList arms)
prettyCase' typecaseD ty Unused ret $
arms ++ [([<], hl Syntax "_", eterm def)]
where
v : BaseName -> Doc HL
v = pretty0 True . TV
tyCasePat : (k : TyConKind) -> NContext (arity k) -> m (Doc HL)
tyCasePat KTYPE [<] = typeD
tyCasePat KPi [< a, b] = pure $ parens $ hsep [v a, !arrowD, v b]
tyCasePat KSig [< a, b] = pure $ parens $ hsep [v a, !arrowD, v b]
tyCasePat KEnum [<] = pure $ hl Syntax "{}"
tyCasePat KEq vars = prettyApps Nothing (L eqD) $ map TV $ toList' vars
tyCasePat KNat [<] = natD
tyCasePat KBOX [< a] = pure $ bracks $ v a
fromArm : TypeCaseArm d n ->
m (SnocList BaseName, Doc HL, Exists (Term d))
fromArm (k ** S ns t) =
pure (toSnocList' ns, !(tyCasePat k ns), eterm t.term)
prettyM (CloE e th) =
if showSubsts then
parensIfM SApp . hang 2 =<<
[|withPrec SApp (prettyM e) <%> prettyTSubst th|]
else
prettyM $ pushSubstsWith' id th e
prettyM (DCloE e th) =
if showSubsts then
parensIfM SApp . hang 2 =<<

56
lib/Quox/Syntax/Term/Subst.idr
View file

@ -130,21 +130,21 @@ comp th ps ph = map (// th) ps . ph
public export %inline
dweakT : {by : Nat} -> Term d n -> Term (by + d) n
dweakT t = t // shift by
dweakT : (by : Nat) -> Term d n -> Term (by + d) n
dweakT by t = t // shift by
public export %inline
dweakE : {by : Nat} -> Elim d n -> Elim (by + d) n
dweakE t = t // shift by
dweakE : (by : Nat) -> Elim d n -> Elim (by + d) n
dweakE by t = t // shift by
public export %inline
weakT : {default 1 by : Nat} -> Term d n -> Term d (by + n)
weakT t = t // shift by
weakT : (by : Nat) -> Term d n -> Term d (by + n)
weakT by t = t // shift by
public export %inline
weakE : {default 1 by : Nat} -> Elim d n -> Elim d (by + n)
weakE t = t // shift by
weakE : (by : Nat) -> Elim d n -> Elim d (by + n)
weakE by t = t // shift by
parameters {s : Nat}
@ -152,7 +152,7 @@ parameters {s : Nat}
export %inline
(.term) : ScopedBody s (Term d) n -> Term d (s + n)
(Y b).term = b
(N b).term = weakT b {by = s}
(N b).term = weakT s b
namespace ScopeTermN
export %inline
@ -163,7 +163,7 @@ parameters {s : Nat}
export %inline
(.term) : ScopedBody s (\d => Term d n) d -> Term (s + d) n
(Y b).term = b
(N b).term = dweakT b {by = s}
(N b).term = dweakT s b
namespace DScopeTermN
export %inline
@ -305,13 +305,37 @@ mutual
nclo $ (f // th // ph) :% (d // th)
pushSubstsWith th ph (s :# a) =
nclo $ (s // th // ph) :# (a // th // ph)
pushSubstsWith th ph (TypeCase ty ret univ pi sig enum eq nat box) =
nclo $ TypeCase (ty // th // ph) (ret // th // ph)
(univ // th // ph) (pi // th // ph)
(sig // th // ph) (enum // th // ph)
(eq // th // ph) (nat // th // ph)
(box // th // ph)
pushSubstsWith th ph (Coe ty p q val) =
nclo $ Coe (ty // th // ph) (p // th) (q // th) (val // th // ph)
pushSubstsWith th ph (Comp ty p q val r zero one) =
nclo $ Comp (ty // th // ph) (p // th) (q // th)
(val // th // ph) (r // th)
(zero // th // ph) (one // th // ph)
pushSubstsWith th ph (TypeCase ty ret arms def) =
nclo $ TypeCase (ty // th // ph) (ret // th // ph)
(map (\t => t // th // ph) arms) (def // th // ph)
pushSubstsWith th ph (CloE e ps) =
pushSubstsWith th (comp th ps ph) e
pushSubstsWith th ph (DCloE e ps) =
pushSubstsWith (ps . th) ph e
||| heterogeneous composition, using Comp and Coe (and subst)
|||
||| comp [i ⇒ A] @p @q s { (r=0) j ⇒ t₀; (r=1) j ⇒ t₁ }
||| ≔
||| comp [A‹q/i›] @p @q (coe [i ⇒ A] @p @q s) {
||| (r=0) j ⇒ coe [i ⇒ A] @j @q t₀;
||| (r=1) j ⇒ coe [i ⇒ A] @j @q t₁
||| }
public export %inline
CompH : (ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) ->
(r : Dim d) -> (zero, one : DScopeTerm d n) -> Elim d n
CompH {ty, p, q, val, r, zero, one} =
let ty' = SY ty.names $ ty.term // (B VZ ::: shift 2) in
Comp {
ty = dsub1 ty q, p, q,
val = E $ Coe ty p q val, r,
zero = SY zero.names $ E $ Coe ty' (B VZ) (weakD 1 q) zero.term,
one = SY one.names $ E $ Coe ty' (B VZ) (weakD 1 q) one.term
}

34
lib/Quox/Syntax/Term/TyConKind.idr Normal file
View file

@ -0,0 +1,34 @@
module Quox.Syntax.Term.TyConKind
import Decidable.Equality
import Derive.Prelude
import Generics.Derive
%language ElabReflection
%default total
public export
data TyConKind = KTYPE | KPi | KSig | KEnum | KEq | KNat | KBOX
%name TyConKind k
%runElab derive "TyConKind" [Eq.Eq, Ord.Ord, Show.Show, Generic, Meta, DecEq]
||| a list of all `TyConKind`s
public export %inline
allKinds : List TyConKind
allKinds = %runElab do
-- as a script so it stays up to date if there are more tycon kinds
cs <- getCons $ fst !(lookupName "TyConKind")
traverse (check . var) cs
||| in `type-case`, how many variables are bound in this branch
public export %inline
arity : TyConKind -> Nat
arity KTYPE = 0
arity KPi = 2
arity KSig = 2
arity KEnum = 0
arity KEq = 5
arity KNat = 0
arity KBOX = 1

74
lib/Quox/Typechecker.idr
View file

@ -56,6 +56,20 @@ addNames0 : Context (Term d . (+ n)) s -> NContext s -> CtxExtension d n (s + n)
addNames0 [<] [<] = [<]
addNames0 (ts :< t) (xs :< x) = addNames0 ts xs :< (Zero, x, t)
export
typecaseTel : (k : TyConKind) -> Universe -> CtxExtension0' (arity k) d n
typecaseTel k u = case k of
KTYPE => [<]
-- A : ★ᵤ, B : 0.A → ★ᵤ
KPi => [< TYPE u, Arr Zero (BVT 0) (TYPE u)]
KSig => [< TYPE u, Arr Zero (BVT 0) (TYPE u)]
KEnum => [<]
-- A₀ : ★ᵤ, A₁ : ★ᵤ, A : (A₀ ≡ A₁ : ★ᵤ), L : A₀, R : A₀
KEq => [< TYPE u, TYPE u, Eq0 (TYPE u) (BVT 1) (BVT 0), BVT 2, BVT 2]
KNat => [<]
-- A : ★ᵤ
KBOX => [< TYPE u]
mutual
||| "Ψ | Γ ⊢ σ · s ⇐ A ⊳ Σ"
@ -291,7 +305,7 @@ mutual
ScopeTermN s d n -> Term d n -> TC ()
check0ScopeN ctx ext (S _ (N body)) ty = check0 ctx body ty
check0ScopeN ctx ext (S names (Y body)) ty =
check0 (extendTyN (addNames0 ext names) ctx) body (weakT {by = s} ty)
check0 (extendTyN (addNames0 ext names) ctx) body (weakT s ty)
private covering
check0Scope : TyContext d n -> Term d n ->
@ -332,11 +346,11 @@ mutual
pure $ lookupBound sg.fst i ctx.tctx
where
lookupBound : forall n. Qty -> Var n -> TContext d n -> InferResult' d n
lookupBound pi VZ (ctx :< ty) =
InfRes {type = weakT ty, qout = zeroFor ctx :< pi}
lookupBound pi VZ (ctx :< type) =
InfRes {type = weakT 1 type, qout = zeroFor ctx :< pi}
lookupBound pi (VS i) (ctx :< _) =
let InfRes {type, qout} = lookupBound pi i ctx in
InfRes {type = weakT type, qout = qout :< Zero}
InfRes {type = weakT 1 type, qout = qout :< Zero}
infer' ctx sg (fun :@ arg) = do
-- if Ψ | Γ ⊢ σ · f ⇒ (π·x : A) → B ⊳ Σ₁
@ -367,7 +381,7 @@ mutual
bodyctx = extendTyN [< (pisg, x, tfst), (pisg, y, tsnd.term)] ctx
bodyty = substCasePairRet pairres.type ret
bodyout <- checkC bodyctx sg body.term bodyty >>= popQs [< pisg, pisg]
-- then Ψ | Γ ⊢ σ · case ⋯ ⇒ ret[pair/p] ⊳ πΣ₁ + Σ₂
-- then Ψ | Γ ⊢ σ · caseπ ⋯ ⇒ ret[pair/p] ⊳ πΣ₁ + Σ₂
pure $ InfRes {
type = sub1 ret pair,
qout = pi * pairres.qout + bodyout
@ -390,7 +404,7 @@ mutual
armres <- for arms $ \(a, s) =>
checkC ctx sg s (sub1 ret (Tag a :# tres.type))
let Just armout = lubs ctx armres
| _ => throw $ BadCaseQtys ctx $
| _ => throw $ BadQtys "case arms" ctx $
zipWith (\qs, (t, rhs) => (qs, Tag t)) armres arms
pure $ InfRes {
type = sub1 ret t,
@ -417,7 +431,7 @@ mutual
expectCompatQ qih (pi' * sg.fst)
-- [fixme] better error here
expectCompatQ (qp + qih) pisg
-- then Ψ | Γ ⊢ case ⋯ ⇒ A[n] ⊳ πΣn + Σz + ωΣs
-- then Ψ | Γ ⊢ caseπ ⋯ ⇒ A[n] ⊳ πΣn + Σz + ωΣs
pure $ InfRes {
type = sub1 ret n,
qout = pi * nres.qout + zerout + Any * sucout
@ -435,7 +449,7 @@ mutual
bodyCtx = extendTy qpisg body.name ty ctx
bodyType = substCaseBoxRet ty ret
bodyout <- checkC bodyCtx sg body.term bodyType >>= popQ qpisg
-- then Ψ | Γ ⊢ case ⋯ ⇒ R[b/x] ⊳ Σ₁ + Σ₂
-- then Ψ | Γ ⊢ caseπ ⋯ ⇒ R[b/x] ⊳ Σ₁ + Σ₂
pure $ InfRes {
type = sub1 ret box,
qout = boxres.qout + bodyout
@ -448,23 +462,43 @@ mutual
-- then Ψ | Γ ⊢ σ · f p ⇒ A‹p/𝑖› ⊳ Σ
pure $ InfRes {type = dsub1 ty dim, qout}
infer' ctx sg (TypeCase ty ret univ pi sig enum eq nat box) = do
infer' ctx sg (Coe (S [< i] ty) p q val) = do
let ty = ty.term
checkType (extendDim i ctx) ty Nothing
qout <- checkC ctx sg val (ty // one p)
pure $ InfRes {type = ty // one q, qout}
infer' ctx sg (Comp ty p q val r (S [< j0] val0) (S [< j1] val1)) = do
checkType ctx ty Nothing
qout <- checkC ctx sg val ty
let ty' = dweakT 1 ty; val' = dweakT 1 val; p' = weakD 1 p
ctx0 = extendDim j0 $ eqDim r (K Zero) ctx
val0 = val0.term
qout0 <- check ctx0 sg val0 ty'
equal (eqDim (BV 0) p' ctx0) ty' val0 val'
let ctx1 = extendDim j0 $ eqDim r (K One) ctx
val1 = val1.term
qout1 <- check ctx1 sg val1 ty'
equal (eqDim (BV 0) p' ctx1) ty' val1 val'
let qout0' = toMaybe $ map (, val0 // one p) qout0
qout1' = toMaybe $ map (, val1 // one p) qout1
qouts = (qout, val) :: catMaybes [qout0', qout1']
let Just qout = lubs ctx $ map fst qouts
| Nothing => throw $ BadQtys "composition" ctx qouts
pure $ InfRes {type = ty, qout}
infer' ctx sg (TypeCase ty ret arms def) = do
-- if σ = 0
expectEqualQ Zero sg.fst
-- if Ψ, Γ ⊢₀ e ⇒ Type u
u <- expectTYPE !ask ctx . type =<< inferC ctx szero ty
-- if Ψ, Γ ⊢₀ C ⇐ Type
-- (non-dependent return type)
-- if Ψ, Γ ⊢₀ C ⇐ Type (non-dependent return type)
checkTypeC ctx ret Nothing
-- if all the cases have type C
check0 ctx univ ret
check0ScopeN ctx [< TYPE u, Arr Zero (BVT 0) (TYPE u)] pi ret
check0ScopeN ctx [< TYPE u, Arr Zero (BVT 0) (TYPE u)] sig ret
check0 ctx enum ret
check0ScopeN ctx [< TYPE u, TYPE u, Eq0 (TYPE u) (BVT 1) (BVT 0),
BVT 2, BVT 2] eq ret
check0 ctx nat ret
check0Scope ctx (TYPE u) box ret
-- if Ψ, Γ' ⊢₀ A ⇐ C for each rhs A
for_ allKinds $ \k =>
for_ (lookupPrecise k arms) $ \(S names t) =>
check0 (extendTyN (addNames0 (typecaseTel k u) names) ctx)
t.term (weakT (arity k) ret)
-- then Ψ, Γ ⊢₀ type-case ⋯ ⇒ C
pure $ InfRes {type = ret, qout = zeroFor ctx}

162
lib/Quox/Typing.idr
View file

@ -8,9 +8,15 @@ import public Quox.Syntax
import public Quox.Definition
import public Quox.Reduce
import Language.Reflection
import Control.Eff
%default total
%language ElabReflection
private TTName : Type
TTName = TT.Name
%hide TT.Name
public export
@ -50,146 +56,94 @@ substCaseSuccRet retty = retty.term // (Succ (BVT 1) :# Nat ::: shift 2)
public export
substCaseBoxRet : Term d n -> ScopeTerm d n -> Term d (S n)
substCaseBoxRet dty retty =
retty.term // (Box (BVT 0) :# weakT dty ::: shift 1)
retty.term // (Box (BVT 0) :# weakT 1 dty ::: shift 1)
parameters (defs : Definitions) {auto _ : Has ErrorEff fs}
export covering %inline
whnfT : {0 isRedex : RedexTest tm} -> Whnf tm isRedex WhnfError =>
{d, n : Nat} -> tm d n -> Eff fs (NonRedex tm d n defs)
whnfT = either (throw . WhnfError) pure . whnf defs
namespace TyContext
parameters (ctx : TyContext d n)
export covering
whnf : {0 isRedex : RedexTest tm} -> Whnf tm isRedex =>
tm d n -> Eff fs (NonRedex tm d n defs)
whnf = let Val n = ctx.termLen; Val d = ctx.dimLen in
rethrow . whnf defs (toWhnfContext ctx)
parameters {d2, n : Nat} (ctx : Lazy (TyContext d1 n))
(th : Lazy (DSubst d2 d1))
export covering %inline
expectTYPE_ : Term d2 n -> Eff fs Universe
expectTYPE_ s = case fst !(whnfT s) of
TYPE l => pure l
_ => throw $ ExpectedTYPE ctx (s // th)
private covering %macro
expect : (forall d, n. NameContexts d n -> Term d n -> Error) ->
TTImp -> TTImp -> Elab (Term d n -> Eff fs a)
expect k l r = do
f <- check `(\case ~(l) => Just ~(r); _ => Nothing)
pure $ \t => maybe (throw $ k ctx.names t) pure . f . fst =<< whnf t
export covering %inline
expectPi_ : Term d2 n -> Eff fs (Qty, Term d2 n, ScopeTerm d2 n)
expectPi_ s = case fst !(whnfT s) of
Pi {qty, arg, res, _} => pure (qty, arg, res)
_ => throw $ ExpectedPi ctx (s // th)
export covering %inline
expectSig_ : Term d2 n -> Eff fs (Term d2 n, ScopeTerm d2 n)
expectSig_ s = case fst !(whnfT s) of
Sig {fst, snd, _} => pure (fst, snd)
_ => throw $ ExpectedSig ctx (s // th)
export covering %inline
expectEnum_ : Term d2 n -> Eff fs (SortedSet TagVal)
expectEnum_ s = case fst !(whnfT s) of
Enum tags => pure tags
_ => throw $ ExpectedEnum ctx (s // th)
export covering %inline
expectEq_ : Term d2 n ->
Eff fs (DScopeTerm d2 n, Term d2 n, Term d2 n)
expectEq_ s = case fst !(whnfT s) of
Eq {ty, l, r, _} => pure (ty, l, r)
_ => throw $ ExpectedEq ctx (s // th)
export covering %inline
expectNat_ : Term d2 n -> Eff fs ()
expectNat_ s = case fst !(whnfT s) of
Nat => pure ()
_ => throw $ ExpectedNat ctx (s // th)
export covering %inline
expectBOX_ : Term d2 n -> Eff fs (Qty, Term d2 n)
expectBOX_ s = case fst !(whnfT s) of
BOX q a => pure (q, a)
_ => throw $ ExpectedBOX ctx (s // th)
-- [fixme] refactor this stuff
parameters (ctx : TyContext d n)
export covering %inline
expectTYPE : Term d n -> Eff fs Universe
expectTYPE =
let Val d = ctx.dimLen; Val n = ctx.termLen in
expectTYPE_ ctx id
expectTYPE = expect ExpectedTYPE `(TYPE l) `(l)
export covering %inline
expectPi : Term d n -> Eff fs (Qty, Term d n, ScopeTerm d n)
expectPi =
let Val d = ctx.dimLen; Val n = ctx.termLen in
expectPi_ ctx id
expectPi = expect ExpectedPi `(Pi {qty, arg, res}) `((qty, arg, res))
export covering %inline
expectSig : Term d n -> Eff fs (Term d n, ScopeTerm d n)
expectSig =
let Val d = ctx.dimLen; Val n = ctx.termLen in
expectSig_ ctx id
expectSig = expect ExpectedSig `(Sig {fst, snd}) `((fst, snd))
export covering %inline
expectEnum : Term d n -> Eff fs (SortedSet TagVal)
expectEnum =
let Val d = ctx.dimLen; Val n = ctx.termLen in
expectEnum_ ctx id
expectEnum = expect ExpectedEnum `(Enum ts) `(ts)
export covering %inline
expectEq : Term d n -> Eff fs (DScopeTerm d n, Term d n, Term d n)
expectEq =
let Val d = ctx.dimLen; Val n = ctx.termLen in
expectEq_ ctx id
expectEq = expect ExpectedEq `(Eq {ty, l, r}) `((ty, l, r))
export covering %inline
expectNat : Term d n -> Eff fs ()
expectNat =
let Val d = ctx.dimLen; Val n = ctx.termLen in
expectNat_ ctx id
expectNat = expect ExpectedNat `(Nat) `(())
export covering %inline
expectBOX : Term d n -> Eff fs (Qty, Term d n)
expectBOX =
let Val d = ctx.dimLen; Val n = ctx.termLen in
expectBOX_ ctx id
expectBOX = expect ExpectedBOX `(BOX {qty, ty}) `((qty, ty))
parameters (ctx : EqContext n)
export covering %inline
expectTYPEE : Term 0 n -> Eff fs Universe
expectTYPEE t =
let Val n = ctx.termLen in
expectTYPE_ (toTyContext ctx) (shift0 ctx.dimLen) t
namespace EqContext
parameters (ctx : EqContext n)
export covering
whnf : {0 isRedex : RedexTest tm} -> Whnf tm isRedex =>
tm 0 n -> Eff fs (NonRedex tm 0 n defs)
whnf = let Val n = ctx.termLen in rethrow . whnf defs (toWhnfContext ctx)
private covering %macro
expect : (forall d, n. NameContexts d n -> Term d n -> Error) ->
TTImp -> TTImp -> Elab (Term 0 n -> Eff fs a)
expect k l r = do
f <- check `(\case ~(l) => Just ~(r); _ => Nothing)
pure $ \t =>
let err = throw $ k ctx.names (t // shift0 ctx.dimLen) in
maybe err pure . f . fst =<< whnf t
export covering %inline
expectPiE : Term 0 n -> Eff fs (Qty, Term 0 n, ScopeTerm 0 n)
expectPiE t =
let Val n = ctx.termLen in
expectPi_ (toTyContext ctx) (shift0 ctx.dimLen) t
expectTYPE : Term 0 n -> Eff fs Universe
expectTYPE = expect ExpectedTYPE `(TYPE l) `(l)
export covering %inline
expectSigE : Term 0 n -> Eff fs (Term 0 n, ScopeTerm 0 n)
expectSigE t =
let Val n = ctx.termLen in
expectSig_ (toTyContext ctx) (shift0 ctx.dimLen) t
expectPi : Term 0 n -> Eff fs (Qty, Term 0 n, ScopeTerm 0 n)
expectPi = expect ExpectedPi `(Pi {qty, arg, res}) `((qty, arg, res))
export covering %inline
expectEnumE : Term 0 n -> Eff fs (SortedSet TagVal)
expectEnumE t =
let Val n = ctx.termLen in
expectEnum_ (toTyContext ctx) (shift0 ctx.dimLen) t
expectSig : Term 0 n -> Eff fs (Term 0 n, ScopeTerm 0 n)
expectSig = expect ExpectedSig `(Sig {fst, snd}) `((fst, snd))
export covering %inline
expectEqE : Term 0 n -> Eff fs (DScopeTerm 0 n, Term 0 n, Term 0 n)
expectEqE t =
let Val n = ctx.termLen in
expectEq_ (toTyContext ctx) (shift0 ctx.dimLen) t
expectEnum : Term 0 n -> Eff fs (SortedSet TagVal)
expectEnum = expect ExpectedEnum `(Enum ts) `(ts)
export covering %inline
expectNatE : Term 0 n -> Eff fs ()
expectNatE t =
let Val n = ctx.termLen in
expectNat_ (toTyContext ctx) (shift0 ctx.dimLen) t
expectEq : Term 0 n -> Eff fs (DScopeTerm 0 n, Term 0 n, Term 0 n)
expectEq = expect ExpectedEq `(Eq {ty, l, r}) `((ty, l, r))
export covering %inline
expectBOXE : Term 0 n -> Eff fs (Qty, Term 0 n)
expectBOXE t =
let Val n = ctx.termLen in
expectBOX_ (toTyContext ctx) (shift0 ctx.dimLen) t
expectNat : Term 0 n -> Eff fs ()
expectNat = expect ExpectedNat `(Nat) `(())
export covering %inline
expectBOX : Term 0 n -> Eff fs (Qty, Term 0 n)
expectBOX = expect ExpectedBOX `(BOX {qty, ty}) `((qty, ty))

37
lib/Quox/Typing/Context.idr
View file

@ -51,6 +51,14 @@ record EqContext n where
%name EqContext ctx
public export
record WhnfContext d n where
constructor MkWhnfContext
dnames : NContext d
tnames : NContext n
tctx : TContext d n
%name WhnfContext ctx
namespace TContext
export %inline
pushD : TContext d n -> TContext (S d) n
@ -111,6 +119,11 @@ namespace TyContext
eqDim : Dim d -> Dim d -> TyContext d n -> TyContext d n
eqDim p q = {dctx $= set p q, dimLen $= id, termLen $= id}
export
toWhnfContext : TyContext d n -> WhnfContext d n
toWhnfContext (MkTyContext {dnames, tnames, tctx, _}) =
MkWhnfContext {dnames, tnames, tctx}
namespace QOutput
export %inline
@ -190,6 +203,30 @@ namespace EqContext
dnames, tnames, qtys
}
export
toWhnfContext : (ectx : EqContext n) -> WhnfContext 0 n
toWhnfContext (MkEqContext {tnames, tctx, _}) =
MkWhnfContext {dnames = [<], tnames, tctx}
namespace WhnfContext
public export %inline
empty : WhnfContext 0 0
empty = MkWhnfContext [<] [<] [<]
export
extendDimN : {s : Nat} -> NContext s -> WhnfContext d n ->
WhnfContext (s + d) n
extendDimN ns (MkWhnfContext {dnames, tnames, tctx}) =
MkWhnfContext {
dnames = dnames ++ toSnocVect' ns,
tctx = dweakT s <$> tctx,
tnames
}
export
extendDim : BaseName -> WhnfContext d n -> WhnfContext (S d) n
extendDim i = extendDimN [< i]
private
data CtxBinder a = MkCtxBinder BaseName a

183
lib/Quox/Typing/Error.idr
View file

@ -1,7 +1,6 @@
module Quox.Typing.Error
import Quox.Syntax
import Quox.Reduce
import Quox.Typing.Context
import Quox.Typing.EqMode
import Quox.Pretty
@ -10,19 +9,62 @@ import Data.List
import Control.Eff
public export
record NameContexts d n where
constructor MkNameContexts
dnames : NContext d
tnames : NContext n
namespace NameContexts
export
empty : NameContexts 0 0
empty = MkNameContexts [<] [<]
export
extendDimN : NContext s -> NameContexts d n -> NameContexts (s + d) n
extendDimN xs = {dnames $= (++ toSnocVect' xs)}
export
extendDim : BaseName -> NameContexts d n -> NameContexts (S d) n
extendDim i = extendDimN [< i]
namespace TyContext
public export
(.names) : TyContext d n -> NameContexts d n
(MkTyContext {dnames, tnames, _}).names =
MkNameContexts {dnames, tnames}
namespace EqContext
public export
(.names) : (e : EqContext n) -> NameContexts e.dimLen n
(MkEqContext {dnames, tnames, _}).names =
MkNameContexts {dnames, tnames}
public export
(.names0) : EqContext n -> NameContexts 0 n
(MkEqContext {tnames, _}).names0 =
MkNameContexts {dnames = [<], tnames}
namespace WhnfContext
public export
(.names) : WhnfContext d n -> NameContexts d n
(MkWhnfContext {dnames, tnames, _}).names =
MkNameContexts {dnames, tnames}
public export
data Error
= ExpectedTYPE (TyContext d n) (Term d n)
| ExpectedPi (TyContext d n) (Term d n)
| ExpectedSig (TyContext d n) (Term d n)
| ExpectedEnum (TyContext d n) (Term d n)
| ExpectedEq (TyContext d n) (Term d n)
| ExpectedNat (TyContext d n) (Term d n)
| ExpectedBOX (TyContext d n) (Term d n)
= ExpectedTYPE (NameContexts d n) (Term d n)
| ExpectedPi (NameContexts d n) (Term d n)
| ExpectedSig (NameContexts d n) (Term d n)
| ExpectedEnum (NameContexts d n) (Term d n)
| ExpectedEq (NameContexts d n) (Term d n)
| ExpectedNat (NameContexts d n) (Term d n)
| ExpectedBOX (NameContexts d n) (Term d n)
| BadUniverse Universe Universe
| TagNotIn TagVal (SortedSet TagVal)
| BadCaseEnum (SortedSet TagVal) (SortedSet TagVal)
| BadCaseQtys (TyContext d n) (List (QOutput n, Term d n))
| BadQtys String (TyContext d n) (List (QOutput n, Term d n))
-- first term arg of ClashT is the type
| ClashT (EqContext n) EqMode (Term 0 n) (Term 0 n) (Term 0 n)
@ -35,6 +77,8 @@ data Error
| NotType (TyContext d n) (Term d n)
| WrongType (EqContext n) (Term 0 n) (Term 0 n)
| MissingEnumArm TagVal (List TagVal)
-- extra context
| WhileChecking
(TyContext d n) Qty
@ -59,8 +103,6 @@ data Error
(EqContext n) EqMode
(Elim 0 n) (Elim 0 n)
Error
| WhnfError WhnfError
%name Error err
public export
@ -157,62 +199,71 @@ isTypeInUniverse (Just k) = "is a type in universe" <++> prettyUniverse k
parameters (unicode : Bool)
private
termt : TyContext d n -> Term d n -> Doc HL
termt ctx = hang 4 . prettyTerm unicode ctx.dnames ctx.tnames
termn : NameContexts d n -> Term d n -> Doc HL
termn ctx = hang 4 . prettyTerm unicode ctx.dnames ctx.tnames
private
terme : EqContext n -> Term 0 n -> Doc HL
terme ctx = hang 4 . prettyTerm unicode [<] ctx.tnames
dstermn : {s : Nat} -> NameContexts d n -> DScopeTermN s d n -> Doc HL
dstermn ctx (S i t) = termn (extendDimN i ctx) t.term
private
dissectCaseQtys : TyContext d n ->
NContext n' -> List (QOutput n', z) ->
List (Doc HL)
dissectCaseQtys ctx [<] arms = []
dissectCaseQtys ctx (tel :< x) arms =
let qs = map (head . fst) arms
tl = dissectCaseQtys ctx tel (map (mapFst tail) arms)
filterSameQtys : NContext n -> List (QOutput n, z) ->
Exists $ \n' => (NContext n', List (QOutput n', z))
filterSameQtys [<] qts = Evidence 0 ([<], qts)
filterSameQtys (ns :< n) qts =
let (qs, qts) = unzip $ map (\(qs :< q, t) => (q, qs, t)) qts
Evidence l (ns, qts) = filterSameQtys ns qts
in
if allSame qs then tl else
("-" <++> asep [hsep [pretty0 unicode $ TV x, "is used with quantities"],
hseparate comma $ map (pretty0 unicode) qs]) :: tl
if allSame qs
then Evidence l (ns, qts)
else Evidence (S l) (ns :< n, zipWith (\(qs, t), q => (qs :< q, t)) qts qs)
where
allSame : List Qty -> Bool
allSame [] = True
allSame (q :: qs) = all (== q) qs
export
prettyWhnfError : WhnfError -> Doc HL
prettyWhnfError = \case
MissingEnumArm tag tags =>
sep [hsep ["the tag", hl Tag $ pretty tag, "is not contained in"],
termt empty $ Enum $ fromList tags]
private
printCaseQtys : TyContext d n ->
NContext n' -> List (QOutput n', Term d n) ->
List (Doc HL)
printCaseQtys ctx ns qts =
let Evidence l (ns, qts) = filterSameQtys ns qts in
map (line ns) qts
where
commaList : PrettyHL a => Context' a l -> Doc HL
commaList = hseparate comma . map (pretty0 unicode) . toList'
line : NContext l -> (QOutput l, Term d n) -> Doc HL
line ns (qs, t) =
"-" <++> asep ["the term", termn ctx.names t,
"uses variables", commaList $ TV <$> ns,
"with quantities", commaList qs]
-- [todo] only show some contexts, probably
export
prettyError : (showContext : Bool) -> Error -> Doc HL
prettyError showContext = \case
ExpectedTYPE ctx s =>
sep ["expected a type universe, but got", termt ctx s]
sep ["expected a type universe, but got", termn ctx s]
ExpectedPi ctx s =>
sep ["expected a function type, but got", termt ctx s]
sep ["expected a function type, but got", termn ctx s]
ExpectedSig ctx s =>
sep ["expected a pair type, but got", termt ctx s]
sep ["expected a pair type, but got", termn ctx s]
ExpectedEnum ctx s =>
sep ["expected an enumeration type, but got", termt ctx s]
sep ["expected an enumeration type, but got", termn ctx s]
ExpectedEq ctx s =>
sep ["expected an equality type, but got", termt ctx s]
sep ["expected an equality type, but got", termn ctx s]
ExpectedNat ctx s {d, n} =>
sep ["expected the type", pretty0 unicode $ Nat {d, n},
"but got", termt ctx s]
"but got", termn ctx s]
ExpectedBOX ctx s =>
sep ["expected a box type, but got", termt ctx s]
sep ["expected a box type, but got", termn ctx s]
BadUniverse k l =>
sep ["the universe level", prettyUniverse k,
@ -220,32 +271,32 @@ parameters (unicode : Bool)
TagNotIn tag set =>
sep [sep ["tag", prettyTag tag, "is not contained in"],
termt empty (Enum set)]
termn empty (Enum set)]
BadCaseEnum type arms =>
sep ["case expression has head of type", termt empty (Enum type),
"but cases for", termt empty (Enum arms)]
sep ["case expression has head of type", termn empty (Enum type),
"but cases for", termn empty (Enum arms)]
BadCaseQtys ctx arms =>
BadQtys what ctx arms =>
hang 4 $ sep $
"inconsistent variable usage in case arms" ::
dissectCaseQtys ctx ctx.tnames arms
("inconsistent variable usage in" <++> fromString what) ::
printCaseQtys ctx ctx.tnames arms
ClashT ctx mode ty s t =>
inEContext ctx $
sep ["the term", terme ctx s,
hsep ["is not", prettyMode mode], terme ctx t,
"at type", terme ctx ty]
sep ["the term", termn ctx.names0 s,
hsep ["is not", prettyMode mode], termn ctx.names0 t,
"at type", termn ctx.names0 ty]
ClashTy ctx mode a b =>
inEContext ctx $
sep ["the type", terme ctx a,
hsep ["is not", prettyMode mode], terme ctx b]
sep ["the type", termn ctx.names0 a,
hsep ["is not", prettyMode mode], termn ctx.names0 b]
ClashE ctx mode e f =>
inEContext ctx $
sep ["the term", terme ctx $ E e,
hsep ["is not", prettyMode mode], terme ctx $ E f]
sep ["the term", termn ctx.names0 $ E e,
hsep ["is not", prettyMode mode], termn ctx.names0 $ E f]
ClashU mode k l =>
sep ["the universe level", prettyUniverse k,
@ -260,46 +311,48 @@ parameters (unicode : Bool)
NotType ctx s =>
inTContext ctx $
sep ["the term", termt ctx s, "is not a type"]
sep ["the term", termn ctx.names s, "is not a type"]
WrongType ctx ty s =>
inEContext ctx $
sep ["the term", terme ctx s,
"cannot have type", terme ctx ty]
sep ["the term", termn ctx.names0 s,
"cannot have type", termn ctx.names0 ty]
MissingEnumArm tag tags =>
sep [hsep ["the tag", hl Tag $ pretty tag, "is not contained in"],
termn empty $ Enum $ fromList tags]
WhileChecking ctx pi s a err =>
vsep [inTContext ctx $
sep ["while checking", termt ctx s,
"has type", termt ctx a,
sep ["while checking", termn ctx.names s,
"has type", termn ctx.names a,
hsep ["with quantity", pretty0 unicode pi]],
prettyError showContext err]
WhileCheckingTy ctx a k err =>
vsep [inTContext ctx $
sep ["while checking", termt ctx a,
sep ["while checking", termn ctx.names a,
isTypeInUniverse k],
prettyError showContext err]
WhileInferring ctx pi e err =>
vsep [inTContext ctx $
sep ["while inferring the type of", termt ctx $ E e,
sep ["while inferring the type of", termn ctx.names $ E e,
hsep ["with quantity", pretty0 unicode pi]],
prettyError showContext err]
WhileComparingT ctx mode a s t err =>
vsep [inEContext ctx $
sep ["while checking that", terme ctx s,
hsep ["is", prettyMode mode], terme ctx t,
"at type", terme ctx a],
sep ["while checking that", termn ctx.names0 s,
hsep ["is", prettyMode mode], termn ctx.names0 t,
"at type", termn ctx.names0 a],
prettyError showContext err]
WhileComparingE ctx mode e f err =>
vsep [inEContext ctx $
sep ["while checking that", terme ctx $ E e,
hsep ["is", prettyMode mode], terme ctx $ E f],
sep ["while checking that", termn ctx.names0 $ E e,
hsep ["is", prettyMode mode], termn ctx.names0 $ E f],
prettyError showContext err]
WhnfError err => prettyWhnfError err
where
inTContext : TyContext d n -> Doc HL -> Doc HL
inTContext ctx doc =

3
lib/quox-lib.ipkg
View file

@ -5,7 +5,7 @@ authors = "rhiannon morris"
sourceloc = "https://git.rhiannon.website/rhi/quox"
license = "acsl"
depends = base, contrib, elab-util, snocvect, eff
depends = base, contrib, elab-util, sop, snocvect, eff
modules =
Quox.BoolExtra,
@ -21,6 +21,7 @@ modules =
Quox.Syntax.Shift,
Quox.Syntax.Subst,
Quox.Syntax.Term,
Quox.Syntax.Term.TyConKind,
Quox.Syntax.Term.Base,
Quox.Syntax.Term.Pretty,
Quox.Syntax.Term.Split,

47
tests/TermImpls.idr
View file

@ -25,14 +25,14 @@ mutual
TYPE _ == _ = False
Pi qty1 arg1 res1 == Pi qty2 arg2 res2 =
qty1 == qty2 && arg1 == arg2 && res1.term == res2.term
qty1 == qty2 && arg1 == arg2 && res1 == res2
Pi {} == _ = False
Lam body1 == Lam body2 = body1.term == body2.term
Lam body1 == Lam body2 = body1 == body2
Lam {} == _ = False
Sig fst1 snd1 == Sig fst2 snd2 =
fst1 == fst2 && snd1.term == snd2.term
fst1 == fst2 && snd1 == snd2
Sig {} == _ = False
Pair fst1 snd1 == Pair fst2 snd2 = fst1 == fst2 && snd1 == snd2
@ -45,10 +45,10 @@ mutual
Tag _ == _ = False
Eq ty1 l1 r1 == Eq ty2 l2 r2 =
ty1.term == ty2.term && l1 == l2 && r1 == r2
ty1 == ty2 && l1 == l2 && r1 == r2
Eq {} == _ = False
DLam body1 == DLam body2 = body1.term == body2.term
DLam body1 == DLam body2 = body1 == body2
DLam {} == _ = False
Nat == Nat = True
@ -93,20 +93,20 @@ mutual
(_ :@ _) == _ = False
CasePair q1 p1 r1 b1 == CasePair q2 p2 r2 b2 =
q1 == q2 && p1 == p2 && r1.term == r2.term && b1.term == b2.term
q1 == q2 && p1 == p2 && r1 == r2 && b1 == b2
CasePair {} == _ = False
CaseEnum q1 t1 r1 a1 == CaseEnum q2 t2 r2 a2 =
q1 == q2 && t1 == t2 && r1.term == r2.term && a1 == a2
q1 == q2 && t1 == t2 && r1 == r2 && a1 == a2
CaseEnum {} == _ = False
CaseNat q1 q1' n1 r1 z1 s1 == CaseNat q2 q2' n2 r2 z2 s2 =
q1 == q2 && q1' == q2' && n1 == n2 &&
r1.term == r2.term && z1 == z2 && s1.term == s2.term
r1 == r2 && z1 == z2 && s1 == s2
CaseNat {} == _ = False
CaseBox q1 x1 r1 b1 == CaseBox q2 x2 r2 b2 =
q1 == q2 && x1 == x2 && r1.term == r2.term && b1.term == b2.term
q1 == q2 && x1 == x2 && r1 == r2 && b1 == b2
CaseBox {} == _ = False
(fun1 :% dim1) == (fun2 :% dim2) = fun1 == fun2 && dim1 == dim2
@ -115,17 +115,18 @@ mutual
(tm1 :# ty1) == (tm2 :# ty2) = tm1 == tm2 && ty1 == ty2
(_ :# _) == _ = False
TypeCase ty1 ret1 univ1 pi1 sig1 enum1 eq1 nat1 box1
==
TypeCase ty2 ret2 univ2 pi2 sig2 enum2 eq2 nat2 box2 =
ty1 == ty2 && ret1 == ret2 &&
pi1.term == pi2.term &&
sig1.term == sig2.term &&
enum1 == enum2 &&
eq1.term == eq2.term &&
nat1 == nat2 &&
box1.term == box2.term
Coe ty1 p1 q1 val1 == Coe ty2 p2 q2 val2 =
ty1 == ty2 && p1 == p2 && q1 == q2 && val1 == val2
Coe {} == _ = False
Comp ty1 p1 q1 val1 r1 zero1 one1 == Comp ty2 p2 q2 val2 r2 zero2 one2 =
ty1 == ty2 && p1 == p2 && q1 == q2 &&
val1 == val2 && r1 == r2 && zero1 == zero2 && one1 == one2
Comp {} == _ = False
TypeCase ty1 ret1 arms1 def1 == TypeCase ty2 ret2 arms2 def2 =
ty1 == ty2 && ret1 == ret2 &&
arms1 == arms2 && def1 == def2
TypeCase {} == _ = False
CloE el1 th1 == CloE el2 th2 =
@ -140,6 +141,14 @@ mutual
Nothing => False
DCloE {} == _ = False
export covering
{s : Nat} -> Eq (ScopeTermN s d n) where
b1 == b2 = b1.term == b2.term
export covering
{s : Nat} -> Eq (DScopeTermN s d n) where
b1 == b2 = b1.term == b2.term
export covering
Show (Term d n) where
showPrec d t = showParens (d /= Open) $ prettyStr True t

27
tests/Tests/PrettyTerm.idr
View file

@ -155,30 +155,9 @@ tests = "pretty printing terms" :- [
"type-case" :- [
testPrettyE [<] [<]
{label = "type-case ℕ ∷ ★₀ return ★₀ of { ⋯ }"}
(TypeCase (Nat :# TYPE 0) (TYPE 0) Nat (SN Nat) (SN Nat) Nat
(SN Nat) Nat (SN Nat))
"""
type-case ℕ ∷ ★₀ return ★₀ of {
★ ⇒ ℕ;
(_ → _) ⇒ ℕ;
(_ × _) ⇒ ℕ;
{} ⇒ ℕ;
Eq _ _ _ _ _ ⇒ ℕ;
ℕ ⇒ ℕ;
[_] ⇒ ℕ
}
"""
"""
type-case Nat :: Type0 return Type0 of {
Type => Nat;
(_ -> _) => Nat;
(_ ** _) => Nat;
{} => Nat;
Eq _ _ _ _ _ => Nat;
Nat => Nat;
[_] => Nat
}
"""
(TypeCase (Nat :# TYPE 0) (TYPE 0) empty Nat)
"type-case ℕ ∷ ★₀ return ★₀ of { _ ⇒ ℕ }"
"type-case Nat :: Type0 return Type0 of { _ => Nat }"
],
"annotations" :- [

79
tests/Tests/Reduce.idr
View file

@ -7,108 +7,113 @@ import TypingImpls
import TAP
parameters {0 isRedex : RedexTest tm} {auto _ : Whnf tm isRedex err}
{auto _ : ToInfo err}
{auto _ : forall d, n. Eq (tm d n)}
{auto _ : forall d, n. Show (tm d n)}
parameters {0 isRedex : RedexTest tm} {auto _ : Whnf tm isRedex} {d, n : Nat}
{auto _ : (Eq (tm d n), Show (tm d n))}
{default empty defs : Definitions}
{default 0 d, n : Nat}
testWhnf : String -> tm d n -> tm d n -> Test
testWhnf label from to = test "\{label} (whnf)" $ do
result <- bimap toInfo fst $ whnf defs from
private
testWhnf : String -> WhnfContext d n -> tm d n -> tm d n -> Test
testWhnf label ctx from to = test "\{label} (whnf)" $ do
result <- bimap toInfo fst $ whnf defs ctx from
unless (result == to) $ Left [("exp", show to), ("got", show result)]
testNoStep : String -> tm d n -> Test
testNoStep label e = testWhnf label e e
private
testNoStep : String -> WhnfContext d n -> tm d n -> Test
testNoStep label ctx e = testWhnf label ctx e e
private
ctx : Context (\n => (BaseName, Term 0 n)) n -> WhnfContext 0 n
ctx xs = let (ns, ts) = unzip xs in MkWhnfContext [<] ns ts
export
tests : Test
tests = "whnf" :- [
"head constructors" :- [
testNoStep "★₀" $ TYPE 0,
testNoStep "[A] ⊸ [B]" $
testNoStep "★₀" empty $ TYPE 0,
testNoStep "[A] ⊸ [B]" empty $
Arr One (FT "A") (FT "B"),
testNoStep "(x: [A]) ⊸ [B [x]]" $
testNoStep "(x: [A]) ⊸ [B [x]]" empty $
Pi One (FT "A") (S [< "x"] $ Y $ E $ F "B" :@ BVT 0),
testNoStep "λx. [x]" $
testNoStep "λx. [x]" empty $
Lam $ S [< "x"] $ Y $ BVT 0,
testNoStep "[f [a]]" $
testNoStep "[f [a]]" empty $
E $ F "f" :@ FT "a"
],
"neutrals" :- [
testNoStep "x" {n = 1} $ BV 0,
testNoStep "a" $ F "a",
testNoStep "f [a]" $ F "f" :@ FT "a",
testNoStep "★₀ ∷ ★₁" $ TYPE 0 :# TYPE 1
testNoStep "x" (ctx [< ("A", Nat)]) $ BV 0,
testNoStep "a" empty $ F "a",
testNoStep "f [a]" empty $ F "f" :@ FT "a",
testNoStep "★₀ ∷ ★₁" empty $ TYPE 0 :# TYPE 1
],
"redexes" :- [
testWhnf "[a] ∷ [A]"
testWhnf "[a] ∷ [A]" empty
(FT "a" :# FT "A")
(F "a"),
testWhnf "[★₁ ∷ ★₃]"
testWhnf "[★₁ ∷ ★₃]" empty
(E (TYPE 1 :# TYPE 3))
(TYPE 1),
testWhnf "(λx. [x] ∷ [A] ⊸ [A]) [a]"
testWhnf "(λx. [x] ∷ [A] ⊸ [A]) [a]" empty
((([< "x"] :\\ BVT 0) :# Arr One (FT "A") (FT "A")) :@ FT "a")
(F "a")
],
"definitions" :- [
testWhnf "a (transparent)"
testWhnf "a (transparent)" empty
{defs = fromList [("a", mkDef gzero (TYPE 1) (TYPE 0))]}
(F "a") (TYPE 0 :# TYPE 1)
],
"elim closure" :- [
testWhnf "x{}" {n = 1}
testWhnf "x{}" (ctx [< ("A", Nat)])
(CloE (BV 0) id)
(BV 0),
testWhnf "x{a/x}"
testWhnf "x{a/x}" empty
(CloE (BV 0) (F "a" ::: id))
(F "a"),
testWhnf "x{x/x,a/y}" {n = 1}
testWhnf "x{x/x,a/y}" (ctx [< ("A", Nat)])
(CloE (BV 0) (BV 0 ::: F "a" ::: id))
(BV 0),
testWhnf "x{(y{a/y})/x}"
testWhnf "x{(y{a/y})/x}" empty
(CloE (BV 0) ((CloE (BV 0) (F "a" ::: id)) ::: id))
(F "a"),
testWhnf "(x y){f/x,a/y}"
testWhnf "(x y){f/x,a/y}" empty
(CloE (BV 0 :@ BVT 1) (F "f" ::: F "a" ::: id))
(F "f" :@ FT "a"),
testWhnf "([y] ∷ [x]){A/x}" {n = 1}
testWhnf "([y] ∷ [x]){A/x}" (ctx [< ("A", Nat)])
(CloE (BVT 1 :# BVT 0) (F "A" ::: id))
(BV 0),
testWhnf "([y] ∷ [x]){A/x,a/y}"
testWhnf "([y] ∷ [x]){A/x,a/y}" empty
(CloE (BVT 1 :# BVT 0) (F "A" ::: F "a" ::: id))
(F "a")
],
"term closure" :- [
testWhnf "(λy. x){a/x}"
testWhnf "(λy. x){a/x}" empty
(CloT (Lam $ S [< "y"] $ N $ BVT 0) (F "a" ::: id))
(Lam $ S [< "y"] $ N $ FT "a"),
testWhnf "(λy. y){a/x}"
testWhnf "(λy. y){a/x}" empty
(CloT ([< "y"] :\\ BVT 0) (F "a" ::: id))
([< "y"] :\\ BVT 0)
],
"looking inside […]" :- [
testWhnf "[(λx. x ∷ A ⊸ A) [a]]"
testWhnf "[(λx. x ∷ A ⊸ A) [a]]" empty
(E $ (([< "x"] :\\ BVT 0) :# Arr One (FT "A") (FT "A")) :@ FT "a")
(FT "a")
],
"nested redex" :- [
note "whnf only looks at top level redexes",
testNoStep "λy. [(λx. [x] ∷ [A] ⊸ [A]) [y]]" $
testNoStep "λy. [(λx. [x] ∷ [A] ⊸ [A]) [y]]" empty $
[< "y"] :\\ E ((([< "x"] :\\ BVT 0) :# Arr One (FT "A") (FT "A")) :@ BVT 0),
testNoStep "f [(λx. [x] ∷ [A] ⊸ [A]) [a]]" $
testNoStep "f [(λx. [x] ∷ [A] ⊸ [A]) [a]]" empty $
F "a" :@
E ((([< "x"] :\\ BVT 0) :# Arr One (FT "A") (FT "A")) :@ FT "a"),
testNoStep "λx. [y [x]]{x/x,a/y}" {n = 1} $
testNoStep "λx. [y [x]]{x/x,a/y}" (ctx [< ("A", Nat)]) $
[< "x"] :\\ CloT (E $ BV 1 :@ BVT 0) (BV 0 ::: F "a" ::: id),
testNoStep "f ([y [x]]{x/x,a/y})" {n = 1} $
testNoStep "f ([y [x]]{x/x,a/y})" (ctx [< ("A", Nat)]) $
F "f" :@ CloT (E $ BV 1 :@ BVT 0) (BV 0 ::: F "a" ::: id)
]
]

3
tests/Tests/Typechecker.idr
View file

@ -451,8 +451,7 @@ tests = "typechecker" :- [
"type-case" :- [
testTC "0 · type-case ℕ ∷ ★₀ return ★₀ of { _ ⇒ ℕ } ⇒ ★₀" $
inferAs empty szero
(TypeCase (Nat :# TYPE 0) (TYPE 0) Nat (SN Nat) (SN Nat) Nat
(SN Nat) Nat (SN Nat))
(TypeCase (Nat :# TYPE 0) (TYPE 0) empty Nat)
(TYPE 0)
],

9
tests/TypingImpls.idr
View file

@ -9,17 +9,10 @@ import Derive.Prelude
%language ElabReflection
%runElab derive "Reduce.WhnfError" [Show]
%runElab deriveIndexed "TyContext" [Show]
%runElab deriveIndexed "EqContext" [Show]
%runElab deriveIndexed "NameContexts" [Show]
%runElab derive "Error" [Show]
export
ToInfo WhnfError where
toInfo (MissingEnumArm t ts) =
[("type", "MissingEnumArm"),
("tag", show t),
("list", show ts)]
export
ToInfo Error where toInfo err = [("err", show $ prettyError True True err)]