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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 Pred : 0.★₀ → ★₁ = λ A ⇒ 0.A → ★₀;
def0 All : 0.(A : ★₀) → 0.(Pred A) → ★₁ = def0 All : 0.(A : ★₀) → 0.(Pred A) → ★₁ =
@ -23,3 +22,16 @@ defω funext :
1.(All A (eq-f A P p q)) → 1.(All A (eq-f A P p q)) →
p ≡ q : All A P = p ≡ q : All A P =
λ A P p q eq ⇒ δ i ⇒ λ x ⇒ eq x @i; 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 [<] acc = acc
toListAcc (tel :< t) acc = toListAcc tel (f t :: 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 export %inline
toSnocList : Telescope tm _ _ -> SnocList (Exists tm) toSnocList : Telescope tm _ _ -> SnocList (Exists tm)
toSnocList = toSnocListWith (Evidence _) toSnocList = toSnocListWith (Evidence _)
@ -82,6 +87,15 @@ export %inline
toList' : Telescope' a _ _ -> List a toList' : Telescope' a _ _ -> List a
toList' = toListWith id 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 export
fromSnocVect : SnocVect n a -> Context' a n 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 sameTyCon (E {}) _ = False
parameters (defs : Definitions) ||| true if a type is known to be a subsingleton purely by its form.
||| 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.
||| a subsingleton is a type with only zero or one possible values. ||| equality/subtyping accepts immediately on values of subsingleton types.
||| equality/subtyping accepts immediately on values of subsingleton types. |||
||| ||| * a function type is a subsingleton if its codomain is.
||| * a function type is a subsingleton if its codomain is. ||| * a pair type is a subsingleton if both its elements are.
||| * a pair type is a subsingleton if both its elements are. ||| * equality types are subsingletons because of uip.
||| * all equality types are subsingletons because uip is admissible by ||| * an enum type is a subsingleton if it has zero or one tags.
||| boundary separation. ||| * a box type is a subsingleton if its content is
||| * an enum type is a subsingleton if it has zero or one tags. public export covering
public export covering isSubSing : Has ErrorEff fs => {n : Nat} ->
isSubSing : Has ErrorEff fs => Definitions -> EqContext n -> Term 0 n -> Eff fs Bool
{n : Nat} -> Term 0 n -> Eff fs Bool isSubSing defs ctx ty0 = do
isSubSing ty0 = do Element ty0 nc <- whnf defs ctx ty0
Element ty0 nc <- whnfT defs ty0 case ty0 of
case ty0 of TYPE _ => pure False
TYPE _ => pure False Pi _ arg res => isSubSing defs (extendTy Zero res.name arg ctx) res.term
Pi {res, _} => isSubSing res.term Sig fst snd => isSubSing defs ctx fst `andM`
Lam {} => pure False isSubSing defs (extendTy Zero snd.name fst ctx) snd.term
Sig {fst, snd} => isSubSing fst `andM` isSubSing snd.term Enum tags => pure $ length (SortedSet.toList tags) <= 1
Pair {} => pure False Eq {} => pure True
Enum tags => pure $ length (SortedSet.toList tags) <= 1 Nat => pure False
Tag {} => pure False BOX _ ty => isSubSing defs ctx ty
Eq {} => pure True E (s :# _) => isSubSing defs ctx s
DLam {} => pure False E _ => pure False
Nat => pure False Lam _ => pure False
Zero => pure False Pair _ _ => pure False
Succ {} => pure False Tag _ => pure False
BOX {ty, _} => isSubSing ty DLam _ => pure False
Box {} => pure False Zero => pure False
E (s :# _) => isSubSing s Succ _ => pure False
E _ => pure False Box _ => pure False
export export
@ -112,6 +112,17 @@ ensureTyCon ctx t = case nchoose $ isTyConE t of
Left y => pure y Left y => pure y
Right n => throw $ NotType (toTyContext ctx) (t // shift0 ctx.dimLen) 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) parameters (defs : Definitions)
mutual mutual
namespace Term namespace Term
@ -124,9 +135,9 @@ parameters (defs : Definitions)
compare0 ctx ty s t = compare0 ctx ty s t =
wrapErr (WhileComparingT ctx !mode ty s t) $ do wrapErr (WhileComparingT ctx !mode ty s t) $ do
let Val n = ctx.termLen let Val n = ctx.termLen
Element ty nty <- whnfT defs ty Element ty nty <- whnf defs ctx ty
Element s ns <- whnfT defs s Element s ns <- whnf defs ctx s
Element t nt <- whnfT defs t Element t nt <- whnf defs ctx t
tty <- ensureTyCon ctx ty tty <- ensureTyCon ctx ty
compare0' ctx ty s t 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". ||| a lambda "Γ ⊢ λx ⇒ t" that has been converted to "Γ, x ⊢ t".
private %inline private %inline
toLamBody : Elim d n -> Term d (S n) 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 private covering
compare0' : EqContext n -> compare0' : EqContext n ->
@ -209,7 +220,8 @@ parameters (defs : Definitions)
compare0' _ (Eq {}) _ _ = compare0' _ (Eq {}) _ _ =
-- ✨ uip ✨ -- ✨ uip ✨
-- --
-- Γ ⊢ e = f : Eq [i ⇒ A] s t -- ----------------------------
-- Γ ⊢ e = f : Eq [i ⇒ A] s t
pure () pure ()
compare0' ctx Nat s t = local_ Equal $ compare0' ctx Nat s t = local_ Equal $
@ -263,8 +275,8 @@ parameters (defs : Definitions)
compareType : EqContext n -> (s, t : Term 0 n) -> Equal () compareType : EqContext n -> (s, t : Term 0 n) -> Equal ()
compareType ctx s t = do compareType ctx s t = do
let Val n = ctx.termLen let Val n = ctx.termLen
Element s ns <- whnfT defs s Element s ns <- whnf defs ctx s
Element t nt <- whnfT defs t Element t nt <- whnf defs ctx t
ts <- ensureTyCon ctx s ts <- ensureTyCon ctx s
tt <- ensureTyCon ctx t tt <- ensureTyCon ctx t
st <- either pure (const $ clashTy ctx s t) $ st <- either pure (const $ clashTy ctx s t) $
@ -336,37 +348,12 @@ parameters (defs : Definitions)
-- has been inlined by whnf -- has been inlined by whnf
Elim.compare0 ctx e f 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 private covering
replaceEnd : EqContext n -> replaceEnd : EqContext n ->
(e : Elim 0 n) -> DimConst -> (0 ne : NotRedex defs e) -> (e : Elim 0 n) -> DimConst -> (0 ne : NotRedex defs e) ->
Equal (Elim 0 n) Equal (Elim 0 n)
replaceEnd ctx e p ne = do 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) pure $ ends l r p :# dsub1 ty (K p)
namespace Elim namespace Elim
@ -382,10 +369,10 @@ parameters (defs : Definitions)
compare0 ctx e f = compare0 ctx e f =
wrapErr (WhileComparingE ctx !mode e f) $ do wrapErr (WhileComparingE ctx !mode e f) $ do
let Val n = ctx.termLen let Val n = ctx.termLen
Element e ne <- whnfT defs e Element e ne <- whnf defs ctx e
Element f nf <- whnfT defs f Element f nf <- whnf defs ctx f
-- [fixme] there is a better way to do this "isSubSing" stuff for sure -- [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 compare0' ctx e f ne nf
private covering private covering
@ -411,7 +398,8 @@ parameters (defs : Definitions)
compare0' ctx (e :@ s) (f :@ t) ne nf = compare0' ctx (e :@ s) (f :@ t) ne nf =
local_ Equal $ do local_ Equal $ do
compare0 ctx e f 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 Term.compare0 ctx arg s t
compare0' ctx e@(_ :@ _) f _ _ = clashE ctx e f compare0' ctx e@(_ :@ _) f _ _ = clashE ctx e f
@ -419,9 +407,9 @@ parameters (defs : Definitions)
(CasePair fpi f fret fbody) ne nf = (CasePair fpi f fret fbody) ne nf =
local_ Equal $ do local_ Equal $ do
compare0 ctx e f 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 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 let [< x, y] = ebody.names
Term.compare0 (extendTyN [< (epi, x, fst), (epi, y, snd.term)] ctx) Term.compare0 (extendTyN [< (epi, x, fst), (epi, y, snd.term)] ctx)
(substCasePairRet ety eret) (substCasePairRet ety eret)
@ -433,9 +421,9 @@ parameters (defs : Definitions)
(CaseEnum fpi f fret farms) ne nf = (CaseEnum fpi f fret farms) ne nf =
local_ Equal $ do local_ Equal $ do
compare0 ctx e f 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 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) compare0 ctx (sub1 eret $ Tag t :# ety)
!(lookupArm t earms) !(lookupArm t farms) !(lookupArm t earms) !(lookupArm t farms)
expectEqualQ epi fpi expectEqualQ epi fpi
@ -450,7 +438,7 @@ parameters (defs : Definitions)
(CaseNat fpi fpi' f fret fzer fsuc) ne nf = (CaseNat fpi fpi' f fret fzer fsuc) ne nf =
local_ Equal $ do local_ Equal $ do
compare0 ctx e f 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 compareType (extendTy Zero eret.name ety ctx) eret.term fret.term
compare0 ctx (sub1 eret (Zero :# Nat)) ezer fzer compare0 ctx (sub1 eret (Zero :# Nat)) ezer fzer
let [< p, ih] = esuc.names let [< p, ih] = esuc.names
@ -465,9 +453,9 @@ parameters (defs : Definitions)
(CaseBox fpi f fret fbody) ne nf = (CaseBox fpi f fret fbody) ne nf =
local_ Equal $ do local_ Equal $ do
compare0 ctx e f 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 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) compare0 (extendTy (epi * q) ebody.name ty ctx)
(substCaseBoxRet ety eret) (substCaseBoxRet ety eret)
ebody.term fbody.term ebody.term fbody.term
@ -475,50 +463,93 @@ parameters (defs : Definitions)
compare0' ctx e@(CaseBox {}) f _ _ = clashE ctx e f compare0' ctx e@(CaseBox {}) f _ _ = clashE ctx e f
compare0' ctx (s :# a) (t :# b) _ _ = compare0' ctx (s :# a) (t :# b) _ _ =
Term.compare0 ctx !(bigger a b) s t let ty = case !mode of Super => a; _ => b in
where Term.compare0 ctx ty s t
bigger : forall a. a -> a -> Equal a
bigger l r = mode <&> \case Super => l; _ => r
compare0' ctx (TypeCase ty1 ret1 univ1 pi1 sig1 enum1 eq1 nat1 box1) compare0' ctx (Coe ty1 p1 q1 (E val1)) (Coe ty2 p2 q2 (E val2)) ne nf = do
(TypeCase ty2 ret2 univ2 pi2 sig2 enum2 eq2 nat2 box2) 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 _ = ne _ =
local_ Equal $ do local_ Equal $ do
compare0 ctx ty1 ty2 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 compareType ctx ret1 ret2
compare0 ctx univ1 univ2 ret1 compareType ctx def1 def2
let [< piA, piB] = pi1.names for_ allKinds $ \k =>
piCtx = extendTyN compareArm ctx k ret1 u
[< (Zero, piA, TYPE u), (lookupPrecise k arms1) (lookupPrecise k arms2) def1
(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
compare0' ctx e@(TypeCase {}) f _ _ = clashE ctx e f compare0' ctx e@(TypeCase {}) f _ _ = clashE ctx e f
compare0' ctx (s :# a) f _ _ = Term.compare0 ctx a s (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 (t :# b) _ _ = Term.compare0 ctx b (E e) t
compare0' ctx e@(_ :# _) f _ _ = clashE ctx e f 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) parameters {auto _ : (Has DefsReader fs, Has ErrorEff fs)} (ctx : TyContext d n)
-- [todo] only split on the dvars that are actually used anywhere in -- [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 <$> fromPTermWith ds ns s <*> fromPTermWith ds ns t Pair <$> fromPTermWith ds ns s <*> fromPTermWith ds ns t
Case pi pair (r, ret) (CasePair (x, y) body) => Case pi pair (r, ret) (CasePair (x, y) body) =>
map E $ Base.CasePair pi map E $ CasePair pi
<$> fromPTermElim ds ns pair <$> fromPTermElim ds ns pair
<*> fromPTermTScope ds ns [< r] ret <*> fromPTermTScope ds ns [< r] ret
<*> fromPTermTScope ds ns [< x, y] body <*> fromPTermTScope ds ns [< x, y] body
Case pi tag (r, ret) (CaseEnum arms) => Case pi tag (r, ret) (CaseEnum arms) =>
map E $ Base.CaseEnum pi map E $ CaseEnum pi
<$> fromPTermElim ds ns tag <$> fromPTermElim ds ns tag
<*> fromPTermTScope ds ns [< r] ret <*> fromPTermTScope ds ns [< r] ret
<*> assert_total fromPTermEnumArms ds ns arms <*> assert_total fromPTermEnumArms ds ns arms
@ -115,7 +115,7 @@ mutual
Succ n => [|Succ $ fromPTermWith ds ns n|] Succ n => [|Succ $ fromPTermWith ds ns n|]
Case pi nat (r, ret) (CaseNat zer (s, pi', ih, suc)) => Case pi nat (r, ret) (CaseNat zer (s, pi', ih, suc)) =>
Prelude.map E $ Base.CaseNat pi pi' map E $ CaseNat pi pi'
<$> fromPTermElim ds ns nat <$> fromPTermElim ds ns nat
<*> fromPTermTScope ds ns [< r] ret <*> fromPTermTScope ds ns [< r] ret
<*> fromPTermWith ds ns zer <*> fromPTermWith ds ns zer
@ -143,7 +143,7 @@ mutual
Box val => Box <$> fromPTermWith ds ns val Box val => Box <$> fromPTermWith ds ns val
Case pi box (r, ret) (CaseBox b body) => Case pi box (r, ret) (CaseBox b body) =>
Prelude.map E $ CaseBox pi map E $ CaseBox pi
<$> fromPTermElim ds ns box <$> fromPTermElim ds ns box
<*> fromPTermTScope ds ns [< r] ret <*> fromPTermTScope ds ns [< r] ret
<*> fromPTermTScope ds ns [< b] body <*> fromPTermTScope ds ns [< b] body
@ -157,6 +157,24 @@ mutual
s :# a => s :# a =>
map E $ (:#) <$> fromPTermWith ds ns s <*> fromPTermWith ds ns 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 private
fromPTermEnumArms : Has (Except Error) fs => fromPTermEnumArms : Has (Except Error) fs =>
Context' BName d -> Context' BName n -> Context' BName d -> Context' BName n ->

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

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

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

@ -177,7 +177,7 @@ optNameBinder = [|join $ optional $ bname <* darr|]
mutual mutual
export covering export covering
term : Grammar True PTerm term : Grammar True PTerm
term = lamTerm <|> caseTerm <|> bindTerm <|> annTerm term = lamTerm <|> caseTerm <|> coeTerm <|> compTerm <|> bindTerm <|> annTerm
private covering private covering
lamTerm : Grammar True PTerm lamTerm : Grammar True PTerm
@ -190,6 +190,30 @@ mutual
(resC "return" *> optBinderTerm) (resC "return" *> optBinderTerm)
(resC "of" *> caseBody)|] (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 private covering
caseBody : Grammar True PCaseBody caseBody : Grammar True PCaseBody
caseBody = braces $ caseBody = braces $
@ -251,14 +275,14 @@ mutual
private covering private covering
appTerm : Grammar True PTerm appTerm : Grammar True PTerm
appTerm = resC "★" *> [|TYPE nat|] appTerm = resC "★" *> [|TYPE nat|]
<|> resC "Eq" *> [|Eq (bracks optBinderTerm) aTerm aTerm|] <|> resC "Eq" *> [|Eq typeLine aTerm aTerm|]
<|> resC "succ" *> [|Succ aTerm|] <|> resC "succ" *> [|Succ aTerm|]
<|> [|apply aTerm (many appArg)|] <|> [|apply aTerm (many appArg)|]
where where
data PArg = TermArg PTerm | DimArg PDim data PArg = TermArg PTerm | DimArg PDim
appArg : Grammar True PArg appArg : Grammar True PArg
appArg = [|DimArg $ resC "@" *> dim|] <|> [|TermArg aTerm|] appArg = [|DimArg dimArg|] <|> [|TermArg aTerm|]
apply : PTerm -> List PArg -> PTerm apply : PTerm -> List PArg -> PTerm
apply = foldl apply1 where apply = foldl apply1 where
@ -266,6 +290,14 @@ mutual
apply1 f (TermArg x) = f :@ x apply1 f (TermArg x) = f :@ x
apply1 f (DimArg p) = f :% p 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 private covering
aTerm : Grammar True PTerm aTerm : Grammar True PTerm
aTerm = [|Enum $ braces $ commaSep bareTag|] aTerm = [|Enum $ braces $ commaSep bareTag|]

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

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

2
lib/Quox/Pretty.idr
View file

@ -87,7 +87,7 @@ bracks = delims "[" "]"
||| includes spaces inside the braces ||| includes spaces inside the braces
export %inline export %inline
braces : Doc HL -> Doc HL braces : Doc HL -> Doc HL
braces doc = hl Delim "{" <++> doc <++> hl Delim "}" braces doc = hl Delim "{" <++> nest 2 doc <++> hl Delim "}"
export %inline export %inline
parensIf : Bool -> Doc HL -> Doc HL 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.No
import Quox.Syntax import Quox.Syntax
import Quox.Definition import Quox.Definition
import Quox.Typing.Context
import Quox.Typing.Error
import Data.SnocVect import Data.SnocVect
import Data.Maybe import Data.Maybe
import Data.List import Data.List
@ -10,36 +12,35 @@ import Data.List
%default total %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 public export
0 RedexTest : TermLike -> Type 0 RedexTest : TermLike -> Type
RedexTest tm = {d, n : Nat} -> Definitions -> tm d n -> Bool RedexTest tm = {d, n : Nat} -> Definitions -> tm d n -> Bool
public export 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 where
whnf : {d, n : Nat} -> (defs : Definitions) -> whnf : {d, n : Nat} -> (defs : Definitions) -> (ctx : WhnfContext d n) ->
tm d n -> Either err (Subset (tm d n) (No . isRedex defs)) 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 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) Definitions -> Pred (tm d n)
IsRedex defs = So . isRedex defs IsRedex defs = So . isRedex defs
NotRedex defs = No . isRedex defs NotRedex defs = No . isRedex defs
public export public export
0 NonRedex : (tm : TermLike) -> {isRedex : RedexTest tm} -> 0 NonRedex : (tm : TermLike) -> {isRedex : RedexTest tm} ->
Whnf tm isRedex err => Whnf tm isRedex => (d, n : Nat) -> (defs : Definitions) -> Type
(d, n : Nat) -> (defs : Definitions) -> Type
NonRedex tm d n defs = Subset (tm d n) (NotRedex defs) NonRedex tm d n defs = Subset (tm d n) (NotRedex defs)
public export %inline 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) => (t : tm d n) -> (0 nr : NotRedex defs t) =>
NonRedex tm d n defs NonRedex tm d n defs
nred t = Element t nr nred t = Element t nr
@ -48,32 +49,38 @@ nred t = Element t nr
public export %inline public export %inline
isLamHead : Elim {} -> Bool isLamHead : Elim {} -> Bool
isLamHead (Lam {} :# Pi {}) = True isLamHead (Lam {} :# Pi {}) = True
isLamHead (Coe {}) = True
isLamHead _ = False isLamHead _ = False
public export %inline public export %inline
isDLamHead : Elim {} -> Bool isDLamHead : Elim {} -> Bool
isDLamHead (DLam {} :# Eq {}) = True isDLamHead (DLam {} :# Eq {}) = True
isDLamHead (Coe {}) = True
isDLamHead _ = False isDLamHead _ = False
public export %inline public export %inline
isPairHead : Elim {} -> Bool isPairHead : Elim {} -> Bool
isPairHead (Pair {} :# Sig {}) = True isPairHead (Pair {} :# Sig {}) = True
isPairHead (Coe {}) = True
isPairHead _ = False isPairHead _ = False
public export %inline public export %inline
isTagHead : Elim {} -> Bool isTagHead : Elim {} -> Bool
isTagHead (Tag t :# Enum _) = True isTagHead (Tag t :# Enum _) = True
isTagHead (Coe {}) = True
isTagHead _ = False isTagHead _ = False
public export %inline public export %inline
isNatHead : Elim {} -> Bool isNatHead : Elim {} -> Bool
isNatHead (Zero :# Nat) = True isNatHead (Zero :# Nat) = True
isNatHead (Succ n :# Nat) = True isNatHead (Succ n :# Nat) = True
isNatHead (Coe {}) = True
isNatHead _ = False isNatHead _ = False
public export %inline public export %inline
isBoxHead : Elim {} -> Bool isBoxHead : Elim {} -> Bool
isBoxHead (Box {} :# BOX {}) = True isBoxHead (Box {} :# BOX {}) = True
isBoxHead (Coe {}) = True
isBoxHead _ = False isBoxHead _ = False
public export %inline public export %inline
@ -88,36 +95,41 @@ isAnn _ = False
||| true if a term is syntactically a type. ||| true if a term is syntactically a type.
public export %inline public export %inline
isTyCon : (t : Term {}) -> Bool isTyCon : Term {} -> Bool
isTyCon (TYPE {}) = True isTyCon (TYPE {}) = True
isTyCon (Pi {}) = True isTyCon (Pi {}) = True
isTyCon (Lam {}) = False isTyCon (Lam {}) = False
isTyCon (Sig {}) = True isTyCon (Sig {}) = True
isTyCon (Pair {}) = False isTyCon (Pair {}) = False
isTyCon (Enum {}) = True isTyCon (Enum {}) = True
isTyCon (Tag {}) = False isTyCon (Tag {}) = False
isTyCon (Eq {}) = True isTyCon (Eq {}) = True
isTyCon (DLam {}) = False isTyCon (DLam {}) = False
isTyCon Nat = True isTyCon Nat = True
isTyCon Zero = False isTyCon Zero = False
isTyCon (Succ {}) = False isTyCon (Succ {}) = False
isTyCon (BOX {}) = True isTyCon (BOX {}) = True
isTyCon (Box {}) = False isTyCon (Box {}) = False
isTyCon (E {}) = False isTyCon (E {}) = False
isTyCon (CloT {}) = False isTyCon (CloT {}) = False
isTyCon (DCloT {}) = False isTyCon (DCloT {}) = False
||| true if a term is syntactically a type, or a neutral. ||| true if a term is syntactically a type, or a neutral.
public export %inline public export %inline
isTyConE : (t : Term {}) -> Bool isTyConE : Term {} -> Bool
isTyConE s = isTyCon s || isE s isTyConE s = isTyCon s || isE s
||| true if a term is syntactically a type. ||| true if a term is syntactically a type.
public export %inline public export %inline
isAnnTyCon : (t : Elim {}) -> Bool isAnnTyCon : Elim {} -> Bool
isAnnTyCon (ty :# TYPE _) = isTyCon ty isAnnTyCon (ty :# TYPE _) = isTyCon ty
isAnnTyCon _ = False isAnnTyCon _ = False
public export %inline
isK : Dim d -> Bool
isK (K _) = True
isK _ = False
mutual mutual
public export public export
@ -135,102 +147,332 @@ mutual
isRedexE defs nat || isNatHead nat isRedexE defs nat || isNatHead nat
isRedexE defs (CaseBox {box, _}) = isRedexE defs (CaseBox {box, _}) =
isRedexE defs box || isBoxHead box isRedexE defs box || isBoxHead box
isRedexE defs (f :% _) = isRedexE defs (f :% p) =
isRedexE defs f || isDLamHead f isRedexE defs f || isDLamHead f || isK p
isRedexE defs (t :# a) = isRedexE defs (t :# a) =
isE t || isRedexT defs t || isRedexT defs a isE t || isRedexT defs t || isRedexT defs a
isRedexE defs (TypeCase {ty, _}) = isRedexE defs (Coe {val, _}) =
isRedexE defs ty || isAnnTyCon ty 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 _ (CloE {}) = True
isRedexE _ (DCloE {}) = True isRedexE _ (DCloE {}) = True
public export public export
isRedexT : RedexTest Term isRedexT : RedexTest Term
isRedexT _ (CloT {}) = True isRedexT _ (CloT {}) = True
isRedexT _ (DCloT {}) = True isRedexT _ (DCloT {}) = True
isRedexT defs (E e) = isAnn e || isRedexE defs e isRedexT defs (E e) = isAnn e || isRedexE defs e
isRedexT _ _ = False 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 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 export covering
Whnf Elim Reduce.isRedexE WhnfError where Whnf Elim Reduce.isRedexE where
whnf defs (F x) with (lookupElim x defs) proof eq whnf defs ctx (F x) with (lookupElim x defs) proof eq
_ | Just y = whnf defs y _ | Just y = whnf defs ctx y
_ | Nothing = pure $ Element (F x) $ rewrite eq in Ah _ | 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] -- ((λ x ⇒ t) ∷ (π.x : A) → B) s ⇝ t[s∷A/x] ∷ B[s∷A/x]
whnf defs (f :@ s) = do whnf defs ctx (f :@ s) = do
Element f fnf <- whnf defs f Element f fnf <- whnf defs ctx f
case nchoose $ isLamHead f of case nchoose $ isLamHead f of
Left _ => Left _ => case f of
let Lam body :# Pi {arg, res, _} = f Lam body :# Pi {arg, res, _} =>
s = s :# arg let s = s :# arg in
in whnf defs ctx $ sub1 body s :# sub1 res s
whnf defs $ 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 Right nlh => pure $ Element (f :@ s) $ fnf `orNo` nlh
-- case (s, t) ∷ (x : A) × B return p ⇒ C of { (a, b) ⇒ u } ⇝ -- 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] -- u[s∷A/a, t∷B[s∷A/x]] ∷ C[(s, t)∷((x : A) × B)/p]
whnf defs (CasePair pi pair ret body) = do whnf defs ctx (CasePair pi pair ret body) = do
Element pair pairnf <- whnf defs pair Element pair pairnf <- whnf defs ctx pair
case nchoose $ isPairHead pair of case nchoose $ isPairHead pair of
Left _ => Left _ => case pair of
let Pair {fst, snd} :# Sig {fst = tfst, snd = tsnd, _} = pair Pair {fst, snd} :# Sig {fst = tfst, snd = tsnd, _} =>
fst = fst :# tfst let fst = fst :# tfst
snd = snd :# sub1 tsnd fst snd = snd :# sub1 tsnd fst
in in
whnf defs $ subN body [< fst, snd] :# sub1 ret pair 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 => Right np =>
pure $ Element (CasePair pi pair ret body) pure $ Element (CasePair pi pair ret body) $ pairnf `orNo` np
(pairnf `orNo` np)
-- case 'a ∷ {a,…} return p ⇒ C of { 'a ⇒ u } ⇝ -- case 'a ∷ {a,…} return p ⇒ C of { 'a ⇒ u } ⇝
-- u ∷ C['a∷{a,…}/p] -- u ∷ C['a∷{a,…}/p]
whnf defs (CaseEnum pi tag ret arms) = do whnf defs ctx (CaseEnum pi tag ret arms) = do
Element tag tagnf <- whnf defs tag Element tag tagnf <- whnf defs ctx tag
case nchoose $ isTagHead tag of case nchoose $ isTagHead tag of
Left t => Left t => case tag of
let Tag t :# Enum ts = tag Tag t :# Enum ts =>
ty = sub1 ret tag let ty = sub1 ret tag in
in case lookup t arms of
case lookup t arms of Just arm => whnf defs ctx $ arm :# ty
Just arm => whnf defs $ arm :# ty Nothing => Left $ MissingEnumArm t (keys arms)
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 => Right nt =>
pure $ Element (CaseEnum pi tag ret arms) $ tagnf `orNo` nt pure $ Element (CaseEnum pi tag ret arms) $ tagnf `orNo` nt
-- case zero ∷ ℕ return p ⇒ C of { zero ⇒ u; … } ⇝ -- case zero ∷ ℕ return p ⇒ C of { zero ⇒ u; … } ⇝
-- u ∷ C[zero∷ℕ/p] -- 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] -- u[n∷ℕ/n', (case n ∷ ℕ ⋯)/ih] ∷ C[succ n ∷ ℕ/p]
whnf defs (CaseNat pi piIH nat ret zer suc) = do whnf defs ctx (CaseNat pi piIH nat ret zer suc) = do
Element nat natnf <- whnf defs nat Element nat natnf <- whnf defs ctx nat
case nchoose $ isNatHead nat of case nchoose $ isNatHead nat of
Left _ => Left _ =>
let ty = sub1 ret nat in let ty = sub1 ret nat in
case nat of case nat of
Zero :# Nat => whnf defs (zer :# ty) Zero :# Nat => whnf defs ctx (zer :# ty)
Succ n :# Nat => Succ n :# Nat =>
let nn = n :# Nat let nn = n :# Nat
tm = subN suc [< nn, CaseNat pi piIH nn ret zer suc] tm = subN suc [< nn, CaseNat pi piIH nn ret zer suc]
in 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 => Right nn =>
pure $ Element (CaseNat pi piIH nat ret zer suc) $ natnf `orNo` nn pure $ Element (CaseNat pi piIH nat ret zer suc) $ natnf `orNo` nn
-- case [t] ∷ [π.A] return p ⇒ C of { [x] ⇒ u } ⇝ -- case [t] ∷ [π.A] return p ⇒ C of { [x] ⇒ u } ⇝
-- u[t∷A/x] ∷ C[[t] ∷ [π.A]/p] -- u[t∷A/x] ∷ C[[t] ∷ [π.A]/p]
whnf defs (CaseBox pi box ret body) = do whnf defs ctx (CaseBox pi box ret body) = do
Element box boxnf <- whnf defs box Element box boxnf <- whnf defs ctx box
case nchoose $ isBoxHead box of case nchoose $ isBoxHead box of
Left _ => Left _ => case box of
let Box val :# BOX q bty = box Box val :# BOX q bty =>
ty = sub1 ret box let ty = sub1 ret box in
in whnf defs ctx $ sub1 body (val :# bty) :# ty
whnf defs $ sub1 body (val :# bty) :# ty Coe ty p q val =>
boxCoe defs ctx pi ty p q val ret body
Right nb => Right nb =>
pure $ Element (CaseBox pi box ret body) $ boxnf `orNo` 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) @1 ⇝ u ∷ A‹1/𝑗›
-- ((δ 𝑖 ⇒ s) ∷ Eq [𝑗 ⇒ A] t u) @𝑘 ⇝ s‹𝑘/𝑖› ∷ A‹𝑘/𝑗› -- ((δ 𝑖 ⇒ s) ∷ Eq [𝑗 ⇒ A] t u) @𝑘 ⇝ s‹𝑘/𝑖› ∷ A‹𝑘/𝑗›
-- (if 𝑘 is a variable) -- (if 𝑘 is a variable)
whnf defs (f :% p) = do whnf defs ctx (f :% p) = do
Element f fnf <- whnf defs f Element f fnf <- whnf defs ctx f
case nchoose $ isDLamHead f of case nchoose $ isDLamHead f of
Left _ => Left _ => case f of
let DLam body :# Eq {ty = ty, l, r, _} = f DLam body :# Eq {ty = ty, l, r, _} =>
body = endsOr l r (dsub1 body p) p let body = endsOr l r (dsub1 body p) p in
in whnf defs ctx $ body :# dsub1 ty p
whnf defs $ body :# dsub1 ty p Coe ty p' q' val =>
Right ndlh => eqCoe defs ctx ty p' q' val p
pure $ Element (f :% p) $ fnf `orNo` ndlh 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 -- e ∷ A ⇝ e
whnf defs (s :# a) = do whnf defs ctx (s :# a) = do
Element s snf <- whnf defs s Element s snf <- whnf defs ctx s
case nchoose $ isE s of case nchoose $ isE s of
Left _ => let E e = s in pure $ Element e $ noOr2 snf Left _ => let E e = s in pure $ Element e $ noOr2 snf
Right ne => do 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 pure $ Element (s :# a) $ ne `orNo` snf `orNo` anf
-- (type-case ★ᵢ ∷ _ return Q of { ★ ⇒ s; ⋯ }) ⇝ s ∷ Q whnf defs ctx (Coe (S _ (N ty)) _ _ val) =
-- whnf defs ctx $ val :# ty
-- (type-case π.(x : A) → B ∷ ★ᵢ return Q of { (a → b) ⇒ s; ⋯ }) ⇝ whnf defs ctx (Coe (S [< i] ty) p q val) = do
-- s[(A ∷ ★ᵢ)/a, ((λ x ⇒ B) ∷ 0.A → ★ᵢ)/b] ∷ ★ᵢ Element ty tynf <- whnf defs (extendDim i ctx) ty.term
-- Element val valnf <- whnf defs ctx val
-- (type-case (x : A) × B ∷ ★ᵢ return Q of { (a × b) ⇒ s; ⋯ }) ⇝ pushCoe defs ctx i ty p q val
-- s[(A ∷ ★ᵢ)/a, ((λ x ⇒ B) ∷ 0.A → ★ᵢ)/b] ∷ ★ᵢ
-- whnf defs ctx (Comp ty p q val r zero one) =
-- (type-case {⋯} ∷ _ return Q of { {} ⇒ s; ⋯ }) ⇝ s ∷ Q -- comp [A] @p @p s { ⋯ } ⇝ s ∷ A
-- if p == q then whnf defs ctx $ val :# ty else
-- (type-case Eq [i ⇒ A] L R ∷ ★ᵢ return Q of { case nchoose (isK r) of
-- Eq a₀ a₁ a l r ⇒ s; ⋯ }) ⇝ -- comp [A] @p @q s { (0=0) j ⇒ t; ⋯ } ⇝ t‹q/j› ∷ A
-- s[(A‹0/i› ∷ ★ᵢ)/a₀, (A‹1/i› ∷ ★ᵢ)/a₁, -- comp [A] @p @q s { (1=1) j ⇒ t; ⋯ } ⇝ t‹q/j› ∷ A
-- ((δ i ⇒ A) ∷ Eq [★ᵢ] A‹0/i› A‹1/i›)/a, Left y => case r of
-- (L ∷ A‹0/i›)/l, (R ∷ A‹1/i›)/r] ∷ Q K Zero => whnf defs ctx $ dsub1 zero q :# ty
-- K One => whnf defs ctx $ dsub1 one q :# ty
-- (type-case ℕ ∷ _ return Q of { ℕ ⇒ s; ⋯ }) ⇝ s ∷ Q Right nk => do
-- Element ty tynf <- whnf defs ctx ty
-- (type-case [π.A] ∷ ★ᵢ return Q of { [a] ⇒ s; ⋯ }) ⇝ s[(A ∷ ★ᵢ)/a] ∷ Q pure $ Element (Comp ty p q val r zero one) $ tynf `orNo` nk
whnf defs (TypeCase {ty, ret, univ, pi, sig, enum, eq, nat, box}) = do -- [todo] anything other than just the boundaries??
Element ty tynf <- whnf defs ty
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 case nchoose $ isAnnTyCon ty of
Left y => Left y => let ty :# TYPE u = ty in
let ty :# TYPE u = ty in reduceTypeCase defs ctx ty u ret arms def
case ty of Right nt => pure $ Element (TypeCase ty ret arms def) $
TYPE _ => tynf `orNo` retnf `orNo` nt
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
toDLam : {s : Nat} -> DScopeTermN s d n -> Term d n whnf defs ctx (CloE el th) = whnf defs ctx $ pushSubstsWith' id th el
toDLam (S names body) = names :\\% body.term whnf defs ctx (DCloE el th) = whnf defs ctx $ pushSubstsWith' th id el
whnf defs (CloE el th) = whnf defs $ pushSubstsWith' id th el
whnf defs (DCloE el th) = whnf defs $ pushSubstsWith' th id el
export covering export covering
Whnf Term Reduce.isRedexT WhnfError where Whnf Term Reduce.isRedexT where
whnf _ t@(TYPE {}) = pure $ nred t whnf _ _ t@(TYPE {}) = pure $ nred t
whnf _ t@(Pi {}) = pure $ nred t whnf _ _ t@(Pi {}) = pure $ nred t
whnf _ t@(Lam {}) = pure $ nred t whnf _ _ t@(Lam {}) = pure $ nred t
whnf _ t@(Sig {}) = pure $ nred t whnf _ _ t@(Sig {}) = pure $ nred t
whnf _ t@(Pair {}) = pure $ nred t whnf _ _ t@(Pair {}) = pure $ nred t
whnf _ t@(Enum {}) = pure $ nred t whnf _ _ t@(Enum {}) = pure $ nred t
whnf _ t@(Tag {}) = pure $ nred t whnf _ _ t@(Tag {}) = pure $ nred t
whnf _ t@(Eq {}) = pure $ nred t whnf _ _ t@(Eq {}) = pure $ nred t
whnf _ t@(DLam {}) = pure $ nred t whnf _ _ t@(DLam {}) = pure $ nred t
whnf _ Nat = pure $ nred Nat whnf _ _ Nat = pure $ nred Nat
whnf _ Zero = pure $ nred Zero whnf _ _ Zero = pure $ nred Zero
whnf _ t@(Succ {}) = pure $ nred t whnf _ _ t@(Succ {}) = pure $ nred t
whnf _ t@(BOX {}) = pure $ nred t whnf _ _ t@(BOX {}) = pure $ nred t
whnf _ t@(Box {}) = pure $ nred t whnf _ _ t@(Box {}) = pure $ nred t
-- s ∷ A ⇝ s (in term context) -- s ∷ A ⇝ s (in term context)
whnf defs (E e) = do whnf defs ctx (E e) = do
Element e enf <- whnf defs e Element e enf <- whnf defs ctx e
case nchoose $ isAnn e of case nchoose $ isAnn e of
Left _ => let tm :# _ = e in pure $ Element tm $ noOr1 $ noOr2 enf Left _ => let tm :# _ = e in pure $ Element tm $ noOr1 $ noOr2 enf
Right na => pure $ Element (E e) $ na `orNo` enf Right na => pure $ Element (E e) $ na `orNo` enf
whnf defs (CloT tm th) = whnf defs $ pushSubstsWith' id th tm whnf defs ctx (CloT tm th) = whnf defs ctx $ pushSubstsWith' id th tm
whnf defs (DCloT tm th) = whnf defs $ pushSubstsWith' th id 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`. ||| `ends l r e` returns `l` if `e` is `Zero`, or `r` if it is `One`.
public export public export
ends : a -> a -> DimConst -> a ends : Lazy a -> Lazy a -> DimConst -> a
ends l r Zero = l ends l r Zero = l
ends l r One = r ends l r One = r
@ -130,5 +130,5 @@ BV i = B $ V i
export export
weakD : {default 1 by : Nat} -> Dim d -> Dim (by + d) weakD : (by : Nat) -> Dim d -> Dim (by + d)
weakD p = p // shift by 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 ZeroIsOne act = pure Nothing
ifConsistent (C _) act = Just <$> act ifConsistent (C _) act = Just <$> act
public export
toMaybe : IfConsistent eqs a -> Maybe a
toMaybe Nothing = Nothing
toMaybe (Just x) = Just x
export export
fromGround' : Context' DimConst d -> DimEq' d fromGround' : Context' DimConst d -> DimEq' d
@ -245,7 +250,7 @@ PrettyHL (DimEq' d) where
go [<] = pure [<] go [<] = pure [<]
go (eqs :< Nothing) = local {dnames $= tail} $ go eqs go (eqs :< Nothing) = local {dnames $= tail} $ go eqs
go (eqs :< Just p) = do 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 eqs <- local {dnames $= tail} $ go eqs
pure $ eqs :< eq 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.Subst
import public Quox.Syntax.Qty import public Quox.Syntax.Qty
import public Quox.Syntax.Dim import public Quox.Syntax.Dim
import public Quox.Syntax.Term.TyConKind
import public Quox.Name import public Quox.Name
import public Quox.Context import public Quox.Context
@ -17,33 +18,35 @@ import Data.Nat
import public Data.So import public Data.So
import Data.String import Data.String
import public Data.SortedMap import public Data.SortedMap
import public Data.SortedMap.Dependent
import public Data.SortedSet import public Data.SortedSet
%default total %default total
public export public export
0 TermLike : Type TermLike : Type
TermLike = Nat -> Nat -> Type TermLike = Nat -> Nat -> Type
public export public export
0 TSubstLike : Type TSubstLike : Type
TSubstLike = Nat -> Nat -> Nat -> Type TSubstLike = Nat -> Nat -> Nat -> Type
public export public export
0 Universe : Type Universe : Type
Universe = Nat Universe = Nat
public export public export
0 TagVal : Type TagVal : Type
TagVal = String TagVal = String
infixl 8 :# infixl 8 :#
infixl 9 :@, :% infixl 9 :@, :%
mutual mutual
public export public export
0 TSubst : TSubstLike TSubst : TSubstLike
TSubst d = Subst $ Elim d TSubst d = Subst $ \n => Elim d n
||| first argument `d` is dimension scope size; ||| first argument `d` is dimension scope size;
||| second `n` is term scope size ||| second `n` is term scope size
@ -138,16 +141,19 @@ mutual
||| type-annotated term ||| type-annotated term
(:#) : (tm, ty : Term d n) -> Elim d n (:#) : (tm, ty : Term d n) -> Elim d n
||| match on types (needed for coercions :mario_flop:) ||| coerce a value along a type equality, or show its coherence
TypeCase : (ty : Elim d n) -> ||| [@xtt; §2.1.1]
(ret : Term d n) -> Coe : (ty : DScopeTerm d n) -> (p, q : Dim d) ->
(univ : Term d n) -> (val : Term d n) -> Elim d n
(pi : ScopeTermN 2 d n) ->
(sig : ScopeTermN 2 d n) -> ||| "generalised composition" [@xtt; §2.1.2]
(enum : Term d n) -> Comp : (ty : Term d n) -> (p, q : Dim d) ->
(eq : ScopeTermN 5 d n) -> (val : Term d n) -> (r : Dim d) ->
(nat : Term d n) -> (zero, one : DScopeTerm d n) -> Elim d n
(box : ScopeTerm 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 Elim d n
||| term closure/suspended substitution ||| term closure/suspended substitution
@ -158,9 +164,22 @@ mutual
Elim dto n Elim dto n
public export public export
0 CaseEnumArms : TermLike CaseEnumArms : TermLike
CaseEnumArms d n = SortedMap TagVal (Term d n) 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 ||| a scoped term with names
public export public export
record Scoped (s : Nat) (f : Nat -> Type) (n : Nat) where record Scoped (s : Nat) (f : Nat -> Type) (n : Nat) where
@ -174,15 +193,16 @@ mutual
N : (body : f n) -> ScopedBody s f n N : (body : f n) -> ScopedBody s f n
public export public export
0 ScopeTermN, DScopeTermN : Nat -> TermLike ScopeTermN, DScopeTermN : Nat -> TermLike
ScopeTermN s d n = Scoped s (Term d) n ScopeTermN s d n = Scoped s (Term d) n
DScopeTermN s d n = Scoped s (\d => Term d n) d DScopeTermN s d n = Scoped s (\d => Term d n) d
public export public export
0 ScopeTerm, DScopeTerm : TermLike ScopeTerm, DScopeTerm : TermLike
ScopeTerm = ScopeTermN 1 ScopeTerm = ScopeTermN 1
DScopeTerm = DScopeTermN 1 DScopeTerm = DScopeTermN 1
%name Term s, t, r %name Term s, t, r
%name Elim e, f %name Elim e, f
%name Scoped body %name Scoped body
@ -260,6 +280,19 @@ makeNat : Nat -> Term d n
makeNat 0 = Zero makeNat 0 = Zero
makeNat (S k) = Succ $ makeNat k makeNat (S k) = Succ $ makeNat k
public export public export %inline
enum : List TagVal -> Term d n enum : List TagVal -> Term d n
enum = Enum . SortedSet.fromList 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 : typeD, arrowD, darrowD, timesD, lamD, eqndD, dlamD, annD, natD :
Pretty.HasEnv m => m (Doc HL) Pretty.HasEnv m => m (Doc HL)
typeD = hlF Syntax $ ifUnicode "★" "Type" typeD = hlF Syntax $ ifUnicode "★" "Type"
arrowD = hlF Syntax $ ifUnicode "→" "->" arrowD = hlF Delim $ ifUnicode "→" "->"
darrowD = hlF Syntax $ ifUnicode "⇒" "=>" darrowD = hlF Delim $ ifUnicode "⇒" "=>"
timesD = hlF Syntax $ ifUnicode "×" "**" timesD = hlF Delim $ ifUnicode "×" "**"
lamD = hlF Syntax $ ifUnicode "λ" "fun" lamD = hlF Syntax $ ifUnicode "λ" "fun"
eqndD = hlF Syntax $ ifUnicode "≡" "==" eqndD = hlF Delim $ ifUnicode "≡" "=="
dlamD = hlF Syntax $ ifUnicode "δ" "dfun" dlamD = hlF Syntax $ ifUnicode "δ" "dfun"
annD = hlF Syntax $ ifUnicode "∷" "::" annD = hlF Delim $ ifUnicode "∷" "::"
natD = hlF Syntax $ ifUnicode "ℕ" "Nat" natD = hlF Syntax $ ifUnicode "ℕ" "Nat"
export %inline export %inline
eqD, colonD, commaD, semiD, caseD, typecaseD, returnD, 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" eqD = hl Syntax "Eq"
colonD = hl Syntax ":" colonD = hl Delim ":"
commaD = hl Syntax "," commaD = hl Delim ","
semiD = hl Syntax ";" semiD = hl Delim ";"
caseD = hl Syntax "case" caseD = hl Syntax "case"
typecaseD = hl Syntax "type-case" typecaseD = hl Syntax "type-case"
ofD = hl Syntax "of" ofD = hl Syntax "of"
@ -38,6 +38,8 @@ returnD = hl Syntax "return"
dotD = hl Delim "." dotD = hl Delim "."
zeroD = hl Syntax "zero" zeroD = hl Syntax "zero"
succD = hl Syntax "succ" succD = hl Syntax "succ"
coeD = hl Syntax "coe"
compD = hl Syntax "compD"
export export
@ -138,10 +140,10 @@ prettyTuple = map (parens . align . separate commaD) . traverse prettyM
export export
prettyArms : PrettyHL a => Pretty.HasEnv m => prettyArms : PrettyHL a => Pretty.HasEnv m =>
List (SnocList BaseName, Doc HL, a) -> m (Doc HL) BinderSort -> List (SnocList BaseName, Doc HL, a) -> m (Doc HL)
prettyArms = prettyArms s =
map (braces . aseparate semiD) . map (braces . aseparate semiD) .
traverse (\(xs, l, r) => prettyArm T xs l r) traverse (\(xs, l, r) => prettyArm s xs l r)
export export
prettyCase' : (PrettyHL a, PrettyHL b, PrettyHL c, Pretty.HasEnv m) => 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 ret <- case r of
Unused => pretty0M ret Unused => pretty0M ret
_ => prettyLams Nothing T [< r] ret _ => prettyLams Nothing T [< r] ret
arms <- prettyArms arms arms <- prettyArms T arms
pure $ asep [intro <++> elim, returnD <++> ret, ofD <++> arms] pure $ asep [intro <++> elim, returnD <++> ret, ofD <++> arms]
export export
@ -192,6 +194,12 @@ export
prettyBoxVal : PrettyHL a => Pretty.HasEnv m => a -> m (Doc HL) prettyBoxVal : PrettyHL a => Pretty.HasEnv m => a -> m (Doc HL)
prettyBoxVal val = bracks <$> pretty0M val prettyBoxVal val = bracks <$> 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 export
toNatLit : Term d n -> Maybe Nat toNatLit : Term d n -> Maybe Nat
toNatLit Zero = Just 0 toNatLit Zero = Just 0
@ -210,58 +218,77 @@ parameters (showSubsts : Bool)
where where
prettyM (TYPE l) = prettyM (TYPE l) =
parensIfM App $ !typeD <+> hl Syntax !(prettyUnivSuffix l) parensIfM App $ !typeD <+> hl Syntax !(prettyUnivSuffix l)
prettyM (Pi qty s (S _ (N t))) = do prettyM (Pi qty s (S _ (N t))) = do
dom <- pretty0M $ MkWithQty qty s dom <- pretty0M $ MkWithQty qty s
cod <- withPrec AnnR $ prettyM t cod <- withPrec AnnR $ prettyM t
parensIfM AnnR $ asep [dom <++> !arrowD, cod] parensIfM AnnR $ asep [dom <++> !arrowD, cod]
prettyM (Pi qty s (S [< x] (Y t))) = prettyM (Pi qty s (S [< x] (Y t))) =
prettyBindType (Just qty) x s !arrowD t prettyBindType (Just qty) x s !arrowD t
prettyM (Lam (S x t)) = prettyM (Lam (S x t)) =
let GotLams {names, body, _} = getLams' x t.term Refl in let GotLams {names, body, _} = getLams' x t.term Refl in
prettyLams (Just !lamD) T (toSnocList' names) body prettyLams (Just !lamD) T (toSnocList' names) body
prettyM (Sig s (S _ (N t))) = do prettyM (Sig s (S _ (N t))) = do
s <- withPrec InTimes $ prettyM s s <- withPrec InTimes $ prettyM s
t <- withPrec Times $ prettyM t t <- withPrec Times $ prettyM t
parensIfM Times $ asep [s <++> !timesD, t] parensIfM Times $ asep [s <++> !timesD, t]
prettyM (Sig s (S [< x] (Y t))) = prettyM (Sig s (S [< x] (Y t))) =
prettyBindType Nothing x s !timesD t prettyBindType Nothing x s !timesD t
prettyM (Pair s t) = prettyM (Pair s t) =
let GotPairs {init, last, _} = getPairs' [< s] t in let GotPairs {init, last, _} = getPairs' [< s] t in
prettyTuple $ toList $ init :< last prettyTuple $ toList $ init :< last
prettyM (Enum tags) = prettyM (Enum tags) =
pure $ delims "{" "}" . aseparate comma $ map prettyTagBare $ pure $ delims "{" "}" . aseparate comma $ map prettyTagBare $
Prelude.toList tags Prelude.toList tags
prettyM (Tag t) = prettyM (Tag t) =
pure $ prettyTag t pure $ prettyTag t
prettyM (Eq (S _ (N ty)) l r) = do prettyM (Eq (S _ (N ty)) l r) = do
l <- withPrec InEq $ prettyM l l <- withPrec InEq $ prettyM l
r <- withPrec InEq $ prettyM r r <- withPrec InEq $ prettyM r
ty <- withPrec InEq $ prettyM ty ty <- withPrec InEq $ prettyM ty
parensIfM Eq $ asep [l <++> !eqndD, r <++> colonD, ty] parensIfM Eq $ asep [l <++> !eqndD, r <++> colonD, ty]
prettyM (Eq (S [< i] (Y ty)) l r) = do prettyM (Eq (S [< i] (Y ty)) l r) = do
prettyApps Nothing (L eqD) prettyApps Nothing (L eqD)
[epretty $ MkTypeLine i ty, epretty l, epretty r] [epretty $ MkTypeLine i ty, epretty l, epretty r]
prettyM (DLam (S i t)) = prettyM (DLam (S i t)) =
let GotDLams {names, body, _} = getDLams' i t.term Refl in let GotDLams {names, body, _} = getDLams' i t.term Refl in
prettyLams (Just !dlamD) D (toSnocList' names) body prettyLams (Just !dlamD) D (toSnocList' names) body
prettyM Nat = natD prettyM Nat = natD
prettyM Zero = pure $ hl Syntax "0" prettyM Zero = pure $ hl Syntax "0"
prettyM (Succ n) = prettyM (Succ n) =
case toNatLit n of case toNatLit n of
Just n => pure $ hl Syntax $ pretty $ S n Just n => pure $ hl Syntax $ pretty $ S n
Nothing => prettyApps Nothing (L succD) [n] Nothing => prettyApps Nothing (L succD) [n]
prettyM (BOX pi ty) = do prettyM (BOX pi ty) = do
pi <- pretty0M pi pi <- pretty0M pi
ty <- pretty0M ty ty <- pretty0M ty
pure $ bracks $ hcat [pi, dotD, align ty] pure $ bracks $ hcat [pi, dotD, align ty]
prettyM (Box val) = prettyBoxVal val prettyM (Box val) = prettyBoxVal val
prettyM (E e) = prettyM e prettyM (E e) = prettyM e
prettyM (CloT s th) = prettyM (CloT s th) =
if showSubsts then if showSubsts then
parensIfM SApp . hang 2 =<< parensIfM SApp . hang 2 =<<
[|withPrec SApp (prettyM s) <%> prettyTSubst th|] [|withPrec SApp (prettyM s) <%> prettyTSubst th|]
else else
prettyM $ pushSubstsWith' id th s prettyM $ pushSubstsWith' id th s
prettyM (DCloT s th) = prettyM (DCloT s th) =
if showSubsts then if showSubsts then
parensIfM SApp . hang 2 =<< parensIfM SApp . hang 2 =<<
@ -274,61 +301,97 @@ parameters (showSubsts : Bool)
where where
prettyM (F x) = prettyM (F x) =
hl' Free <$> prettyM x hl' Free <$> prettyM x
prettyM (B i) = prettyM (B i) =
prettyVar TVar TVarErr (!ask).tnames i prettyVar TVar TVarErr (!ask).tnames i
prettyM (e :@ s) = prettyM (e :@ s) =
let GotArgs {fun, args, _} = getArgs' e [s] in let GotArgs {fun, args, _} = getArgs' e [s] in
prettyApps Nothing fun args prettyApps Nothing fun args
prettyM (CasePair pi p (S [< r] ret) (S [< x, y] body)) = do prettyM (CasePair pi p (S [< r] ret) (S [< x, y] body)) = do
pat <- parens . separate commaD <$> traverse (hlF TVar . prettyM) [x, y] pat <- parens . separate commaD <$> traverse (hlF TVar . prettyM) [x, y]
prettyCase pi p r ret.term [([< x, y], pat, body.term)] prettyCase pi p r ret.term [([< x, y], pat, body.term)]
prettyM (CaseEnum pi t (S [< r] ret) arms) = prettyM (CaseEnum pi t (S [< r] ret) arms) =
prettyCase pi t r ret.term prettyCase pi t r ret.term
[([<], prettyTag t, b) | (t, b) <- SortedMap.toList arms] [([<], prettyTag t, b) | (t, b) <- SortedMap.toList arms]
prettyM (CaseNat pi pi' nat (S [< r] ret) zer (S [< s, ih] suc)) = prettyM (CaseNat pi pi' nat (S [< r] ret) zer (S [< s, ih] suc)) =
prettyCase pi nat r ret.term prettyCase pi nat r ret.term
[([<], zeroD, eterm zer), [([<], zeroD, eterm zer),
([< s, ih], !succPat, eterm suc.term)] ([< s, ih], !succPat, eterm suc.term)]
where where
succPat : m (Doc HL) succPat : m (Doc HL)
succPat = case (ih, pi') of succPat = case (ih, pi') of
(Unused, Zero) => pure $ succD <++> !(pretty0M s) (Unused, Zero) => pure $ succD <++> !(pretty0M s)
_ => pure $ asep [succD <++> !(pretty0M s) <+> comma, _ => pure $ asep [succD <++> !(pretty0M s) <+> comma,
!(pretty0M $ MkWithQty pi' ih)] !(pretty0M $ MkWithQty pi' ih)]
prettyM (CaseBox pi box (S [< r] ret) (S [< u] body)) = prettyM (CaseBox pi box (S [< r] ret) (S [< u] body)) =
prettyCase pi box r ret.term prettyCase pi box r ret.term
[([< u], !(prettyBoxVal $ TV u), body.term)] [([< u], !(prettyBoxVal $ TV u), body.term)]
prettyM (e :% d) = prettyM (e :% d) =
let GotDArgs {fun, args, _} = getDArgs' e [d] in let GotDArgs {fun, args, _} = getDArgs' e [d] in
prettyApps (Just "@") fun args prettyApps (Just "@") fun args
prettyM (s :# a) = do prettyM (s :# a) = do
s <- withPrec AnnL $ prettyM s s <- withPrec AnnL $ prettyM s
a <- withPrec AnnR $ prettyM a a <- withPrec AnnR $ prettyM a
parensIfM AnnR $ hang 2 $ s <++> !annD <%%> a parensIfM AnnR $ hang 2 $ s <++> !annD <%%> a
prettyM (TypeCase ty ret univ
(S [< piA, piB] pi) (S [< sigA, sigB] sig) enum prettyM (Coe (S [< i] ty) p q val) =
(S [< eqA0, eqA1, eqA, eqL, eqR] eq) let ty = case ty of
nat (S [< boxA] box)) = do Y ty => epretty $ MkTypeLine i ty
let v : BaseName -> Doc HL := pretty0 True . TV N ty => epretty ty
pipat <- pure $ parens $ hsep [v piA, !arrowD, v piB] in
sigpat <- pure $ parens $ hsep [v sigA, !timesD, v sigB] prettyApps' (L coeD)
eqpat <- prettyApps Nothing (L eqD) [(Nothing, ty),
[TV eqA0, TV eqA1, TV eqA, TV eqL, TV eqR] (Just "@", epretty p),
boxpat <- pure $ bracks $ v boxA (Just "@", epretty q),
prettyCase' typecaseD ty Unused ret (Nothing, epretty val)]
[([<], !typeD, eterm univ),
([< piA, piB], pipat, eterm pi.term), prettyM (Comp ty p q val r (S [< z] zero) (S [< o] one)) = do
([< sigA, sigB], sigpat, eterm sig.term), apps <- prettyApps' (L compD)
([<], hl Syntax "{}", eterm enum), [(Nothing, epretty ty),
([< eqA0, eqA1, eqA, eqL, eqR], eqpat, eterm eq.term), (Just "@", epretty p),
([<], !natD, eterm nat), (Just "@", epretty q),
([< boxA], boxpat, eterm box.term)] (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) = prettyM (CloE e th) =
if showSubsts then if showSubsts then
parensIfM SApp . hang 2 =<< parensIfM SApp . hang 2 =<<
[|withPrec SApp (prettyM e) <%> prettyTSubst th|] [|withPrec SApp (prettyM e) <%> prettyTSubst th|]
else else
prettyM $ pushSubstsWith' id th e prettyM $ pushSubstsWith' id th e
prettyM (DCloE e th) = prettyM (DCloE e th) =
if showSubsts then if showSubsts then
parensIfM SApp . hang 2 =<< 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 public export %inline
dweakT : {by : Nat} -> Term d n -> Term (by + d) n dweakT : (by : Nat) -> Term d n -> Term (by + d) n
dweakT t = t // shift by dweakT by t = t // shift by
public export %inline public export %inline
dweakE : {by : Nat} -> Elim d n -> Elim (by + d) n dweakE : (by : Nat) -> Elim d n -> Elim (by + d) n
dweakE t = t // shift by dweakE by t = t // shift by
public export %inline public export %inline
weakT : {default 1 by : Nat} -> Term d n -> Term d (by + n) weakT : (by : Nat) -> Term d n -> Term d (by + n)
weakT t = t // shift by weakT by t = t // shift by
public export %inline public export %inline
weakE : {default 1 by : Nat} -> Elim d n -> Elim d (by + n) weakE : (by : Nat) -> Elim d n -> Elim d (by + n)
weakE t = t // shift by weakE by t = t // shift by
parameters {s : Nat} parameters {s : Nat}
@ -152,7 +152,7 @@ parameters {s : Nat}
export %inline export %inline
(.term) : ScopedBody s (Term d) n -> Term d (s + n) (.term) : ScopedBody s (Term d) n -> Term d (s + n)
(Y b).term = b (Y b).term = b
(N b).term = weakT b {by = s} (N b).term = weakT s b
namespace ScopeTermN namespace ScopeTermN
export %inline export %inline
@ -163,7 +163,7 @@ parameters {s : Nat}
export %inline export %inline
(.term) : ScopedBody s (\d => Term d n) d -> Term (s + d) n (.term) : ScopedBody s (\d => Term d n) d -> Term (s + d) n
(Y b).term = b (Y b).term = b
(N b).term = dweakT b {by = s} (N b).term = dweakT s b
namespace DScopeTermN namespace DScopeTermN
export %inline export %inline
@ -305,13 +305,37 @@ mutual
nclo $ (f // th // ph) :% (d // th) nclo $ (f // th // ph) :% (d // th)
pushSubstsWith th ph (s :# a) = pushSubstsWith th ph (s :# a) =
nclo $ (s // th // ph) :# (a // th // ph) nclo $ (s // th // ph) :# (a // th // ph)
pushSubstsWith th ph (TypeCase ty ret univ pi sig enum eq nat box) = pushSubstsWith th ph (Coe ty p q val) =
nclo $ TypeCase (ty // th // ph) (ret // th // ph) nclo $ Coe (ty // th // ph) (p // th) (q // th) (val // th // ph)
(univ // th // ph) (pi // th // ph) pushSubstsWith th ph (Comp ty p q val r zero one) =
(sig // th // ph) (enum // th // ph) nclo $ Comp (ty // th // ph) (p // th) (q // th)
(eq // th // ph) (nat // th // ph) (val // th // ph) (r // th)
(box // th // ph) (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 ph (CloE e ps) =
pushSubstsWith th (comp th ps ph) e pushSubstsWith th (comp th ps ph) e
pushSubstsWith th ph (DCloE e ps) = pushSubstsWith th ph (DCloE e ps) =
pushSubstsWith (ps . th) ph e 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 [<] [<] = [<]
addNames0 (ts :< t) (xs :< x) = addNames0 ts xs :< (Zero, x, t) 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 mutual
||| "Ψ | Γ ⊢ σ · s ⇐ A ⊳ Σ" ||| "Ψ | Γ ⊢ σ · s ⇐ A ⊳ Σ"
@ -291,7 +305,7 @@ mutual
ScopeTermN s d n -> Term d n -> TC () ScopeTermN s d n -> Term d n -> TC ()
check0ScopeN ctx ext (S _ (N body)) ty = check0 ctx body ty check0ScopeN ctx ext (S _ (N body)) ty = check0 ctx body ty
check0ScopeN ctx ext (S names (Y 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 private covering
check0Scope : TyContext d n -> Term d n -> check0Scope : TyContext d n -> Term d n ->
@ -332,11 +346,11 @@ mutual
pure $ lookupBound sg.fst i ctx.tctx pure $ lookupBound sg.fst i ctx.tctx
where where
lookupBound : forall n. Qty -> Var n -> TContext d n -> InferResult' d n lookupBound : forall n. Qty -> Var n -> TContext d n -> InferResult' d n
lookupBound pi VZ (ctx :< ty) = lookupBound pi VZ (ctx :< type) =
InfRes {type = weakT ty, qout = zeroFor ctx :< pi} InfRes {type = weakT 1 type, qout = zeroFor ctx :< pi}
lookupBound pi (VS i) (ctx :< _) = lookupBound pi (VS i) (ctx :< _) =
let InfRes {type, qout} = lookupBound pi i ctx in 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 infer' ctx sg (fun :@ arg) = do
-- if Ψ | Γ ⊢ σ · f ⇒ (π·x : A) → B ⊳ Σ₁ -- 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 bodyctx = extendTyN [< (pisg, x, tfst), (pisg, y, tsnd.term)] ctx
bodyty = substCasePairRet pairres.type ret bodyty = substCasePairRet pairres.type ret
bodyout <- checkC bodyctx sg body.term bodyty >>= popQs [< pisg, pisg] 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 { pure $ InfRes {
type = sub1 ret pair, type = sub1 ret pair,
qout = pi * pairres.qout + bodyout qout = pi * pairres.qout + bodyout
@ -390,7 +404,7 @@ mutual
armres <- for arms $ \(a, s) => armres <- for arms $ \(a, s) =>
checkC ctx sg s (sub1 ret (Tag a :# tres.type)) checkC ctx sg s (sub1 ret (Tag a :# tres.type))
let Just armout = lubs ctx armres let Just armout = lubs ctx armres
| _ => throw $ BadCaseQtys ctx $ | _ => throw $ BadQtys "case arms" ctx $
zipWith (\qs, (t, rhs) => (qs, Tag t)) armres arms zipWith (\qs, (t, rhs) => (qs, Tag t)) armres arms
pure $ InfRes { pure $ InfRes {
type = sub1 ret t, type = sub1 ret t,
@ -417,7 +431,7 @@ mutual
expectCompatQ qih (pi' * sg.fst) expectCompatQ qih (pi' * sg.fst)
-- [fixme] better error here -- [fixme] better error here
expectCompatQ (qp + qih) pisg expectCompatQ (qp + qih) pisg
-- then Ψ | Γ ⊢ case ⋯ ⇒ A[n] ⊳ πΣn + Σz + ωΣs -- then Ψ | Γ ⊢ caseπ ⋯ ⇒ A[n] ⊳ πΣn + Σz + ωΣs
pure $ InfRes { pure $ InfRes {
type = sub1 ret n, type = sub1 ret n,
qout = pi * nres.qout + zerout + Any * sucout qout = pi * nres.qout + zerout + Any * sucout
@ -435,7 +449,7 @@ mutual
bodyCtx = extendTy qpisg body.name ty ctx bodyCtx = extendTy qpisg body.name ty ctx
bodyType = substCaseBoxRet ty ret bodyType = substCaseBoxRet ty ret
bodyout <- checkC bodyCtx sg body.term bodyType >>= popQ qpisg 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 { pure $ InfRes {
type = sub1 ret box, type = sub1 ret box,
qout = boxres.qout + bodyout qout = boxres.qout + bodyout
@ -448,23 +462,43 @@ mutual
-- then Ψ | Γ ⊢ σ · f p ⇒ A‹p/𝑖› ⊳ Σ -- then Ψ | Γ ⊢ σ · f p ⇒ A‹p/𝑖› ⊳ Σ
pure $ InfRes {type = dsub1 ty dim, qout} 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 -- if σ = 0
expectEqualQ Zero sg.fst expectEqualQ Zero sg.fst
-- if Ψ, Γ ⊢₀ e ⇒ Type u -- if Ψ, Γ ⊢₀ e ⇒ Type u
u <- expectTYPE !ask ctx . type =<< inferC ctx szero ty u <- expectTYPE !ask ctx . type =<< inferC ctx szero ty
-- if Ψ, Γ ⊢₀ C ⇐ Type -- if Ψ, Γ ⊢₀ C ⇐ Type (non-dependent return type)
-- (non-dependent return type)
checkTypeC ctx ret Nothing checkTypeC ctx ret Nothing
-- if all the cases have type C -- if Ψ, Γ' ⊢₀ A ⇐ C for each rhs A
check0 ctx univ ret for_ allKinds $ \k =>
check0ScopeN ctx [< TYPE u, Arr Zero (BVT 0) (TYPE u)] pi ret for_ (lookupPrecise k arms) $ \(S names t) =>
check0ScopeN ctx [< TYPE u, Arr Zero (BVT 0) (TYPE u)] sig ret check0 (extendTyN (addNames0 (typecaseTel k u) names) ctx)
check0 ctx enum ret t.term (weakT (arity k) 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
-- then Ψ, Γ ⊢₀ type-case ⋯ ⇒ C -- then Ψ, Γ ⊢₀ type-case ⋯ ⇒ C
pure $ InfRes {type = ret, qout = zeroFor ctx} 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.Definition
import public Quox.Reduce import public Quox.Reduce
import Language.Reflection
import Control.Eff import Control.Eff
%default total %default total
%language ElabReflection
private TTName : Type
TTName = TT.Name
%hide TT.Name
public export public export
@ -50,146 +56,94 @@ substCaseSuccRet retty = retty.term // (Succ (BVT 1) :# Nat ::: shift 2)
public export public export
substCaseBoxRet : Term d n -> ScopeTerm d n -> Term d (S n) substCaseBoxRet : Term d n -> ScopeTerm d n -> Term d (S n)
substCaseBoxRet dty retty = 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} parameters (defs : Definitions) {auto _ : Has ErrorEff fs}
export covering %inline namespace TyContext
whnfT : {0 isRedex : RedexTest tm} -> Whnf tm isRedex WhnfError => parameters (ctx : TyContext d n)
{d, n : Nat} -> tm d n -> Eff fs (NonRedex tm d n defs) export covering
whnfT = either (throw . WhnfError) pure . whnf defs 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)) private covering %macro
(th : Lazy (DSubst d2 d1)) expect : (forall d, n. NameContexts d n -> Term d n -> Error) ->
export covering %inline TTImp -> TTImp -> Elab (Term d n -> Eff fs a)
expectTYPE_ : Term d2 n -> Eff fs Universe expect k l r = do
expectTYPE_ s = case fst !(whnfT s) of f <- check `(\case ~(l) => Just ~(r); _ => Nothing)
TYPE l => pure l pure $ \t => maybe (throw $ k ctx.names t) pure . f . fst =<< whnf t
_ => throw $ ExpectedTYPE ctx (s // th)
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 export covering %inline
expectTYPE : Term d n -> Eff fs Universe expectTYPE : Term d n -> Eff fs Universe
expectTYPE = expectTYPE = expect ExpectedTYPE `(TYPE l) `(l)
let Val d = ctx.dimLen; Val n = ctx.termLen in
expectTYPE_ ctx id
export covering %inline export covering %inline
expectPi : Term d n -> Eff fs (Qty, Term d n, ScopeTerm d n) expectPi : Term d n -> Eff fs (Qty, Term d n, ScopeTerm d n)
expectPi = expectPi = expect ExpectedPi `(Pi {qty, arg, res}) `((qty, arg, res))
let Val d = ctx.dimLen; Val n = ctx.termLen in
expectPi_ ctx id
export covering %inline export covering %inline
expectSig : Term d n -> Eff fs (Term d n, ScopeTerm d n) expectSig : Term d n -> Eff fs (Term d n, ScopeTerm d n)
expectSig = expectSig = expect ExpectedSig `(Sig {fst, snd}) `((fst, snd))
let Val d = ctx.dimLen; Val n = ctx.termLen in
expectSig_ ctx id
export covering %inline export covering %inline
expectEnum : Term d n -> Eff fs (SortedSet TagVal) expectEnum : Term d n -> Eff fs (SortedSet TagVal)
expectEnum = expectEnum = expect ExpectedEnum `(Enum ts) `(ts)
let Val d = ctx.dimLen; Val n = ctx.termLen in
expectEnum_ ctx id
export covering %inline export covering %inline
expectEq : Term d n -> Eff fs (DScopeTerm d n, Term d n, Term d n) expectEq : Term d n -> Eff fs (DScopeTerm d n, Term d n, Term d n)
expectEq = expectEq = expect ExpectedEq `(Eq {ty, l, r}) `((ty, l, r))
let Val d = ctx.dimLen; Val n = ctx.termLen in
expectEq_ ctx id
export covering %inline export covering %inline
expectNat : Term d n -> Eff fs () expectNat : Term d n -> Eff fs ()
expectNat = expectNat = expect ExpectedNat `(Nat) `(())
let Val d = ctx.dimLen; Val n = ctx.termLen in
expectNat_ ctx id
export covering %inline export covering %inline
expectBOX : Term d n -> Eff fs (Qty, Term d n) expectBOX : Term d n -> Eff fs (Qty, Term d n)
expectBOX = expectBOX = expect ExpectedBOX `(BOX {qty, ty}) `((qty, ty))
let Val d = ctx.dimLen; Val n = ctx.termLen in
expectBOX_ ctx id
parameters (ctx : EqContext n) namespace EqContext
export covering %inline parameters (ctx : EqContext n)
expectTYPEE : Term 0 n -> Eff fs Universe export covering
expectTYPEE t = whnf : {0 isRedex : RedexTest tm} -> Whnf tm isRedex =>
let Val n = ctx.termLen in tm 0 n -> Eff fs (NonRedex tm 0 n defs)
expectTYPE_ (toTyContext ctx) (shift0 ctx.dimLen) t 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 export covering %inline
expectPiE : Term 0 n -> Eff fs (Qty, Term 0 n, ScopeTerm 0 n) expectTYPE : Term 0 n -> Eff fs Universe
expectPiE t = expectTYPE = expect ExpectedTYPE `(TYPE l) `(l)
let Val n = ctx.termLen in
expectPi_ (toTyContext ctx) (shift0 ctx.dimLen) t
export covering %inline export covering %inline
expectSigE : Term 0 n -> Eff fs (Term 0 n, ScopeTerm 0 n) expectPi : Term 0 n -> Eff fs (Qty, Term 0 n, ScopeTerm 0 n)
expectSigE t = expectPi = expect ExpectedPi `(Pi {qty, arg, res}) `((qty, arg, res))
let Val n = ctx.termLen in
expectSig_ (toTyContext ctx) (shift0 ctx.dimLen) t
export covering %inline export covering %inline
expectEnumE : Term 0 n -> Eff fs (SortedSet TagVal) expectSig : Term 0 n -> Eff fs (Term 0 n, ScopeTerm 0 n)
expectEnumE t = expectSig = expect ExpectedSig `(Sig {fst, snd}) `((fst, snd))
let Val n = ctx.termLen in
expectEnum_ (toTyContext ctx) (shift0 ctx.dimLen) t
export covering %inline export covering %inline
expectEqE : Term 0 n -> Eff fs (DScopeTerm 0 n, Term 0 n, Term 0 n) expectEnum : Term 0 n -> Eff fs (SortedSet TagVal)
expectEqE t = expectEnum = expect ExpectedEnum `(Enum ts) `(ts)
let Val n = ctx.termLen in
expectEq_ (toTyContext ctx) (shift0 ctx.dimLen) t
export covering %inline export covering %inline
expectNatE : Term 0 n -> Eff fs () expectEq : Term 0 n -> Eff fs (DScopeTerm 0 n, Term 0 n, Term 0 n)
expectNatE t = expectEq = expect ExpectedEq `(Eq {ty, l, r}) `((ty, l, r))
let Val n = ctx.termLen in
expectNat_ (toTyContext ctx) (shift0 ctx.dimLen) t
export covering %inline export covering %inline
expectBOXE : Term 0 n -> Eff fs (Qty, Term 0 n) expectNat : Term 0 n -> Eff fs ()
expectBOXE t = expectNat = expect ExpectedNat `(Nat) `(())
let Val n = ctx.termLen in
expectBOX_ (toTyContext ctx) (shift0 ctx.dimLen) t 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 %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 namespace TContext
export %inline export %inline
pushD : TContext d n -> TContext (S d) n 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 : Dim d -> Dim d -> TyContext d n -> TyContext d n
eqDim p q = {dctx $= set p q, dimLen $= id, termLen $= id} eqDim p q = {dctx $= set p q, dimLen $= id, termLen $= id}
export
toWhnfContext : TyContext d n -> WhnfContext d n
toWhnfContext (MkTyContext {dnames, tnames, tctx, _}) =
MkWhnfContext {dnames, tnames, tctx}
namespace QOutput namespace QOutput
export %inline export %inline
@ -190,6 +203,30 @@ namespace EqContext
dnames, tnames, qtys dnames, tnames, qtys
} }
export
toWhnfContext : (ectx : EqContext n) -> WhnfContext 0 n
toWhnfContext (MkEqContext {tnames, tctx, _}) =
MkWhnfContext {dnames = [<], tnames, tctx}
namespace WhnfContext
public export %inline
empty : WhnfContext 0 0
empty = MkWhnfContext [<] [<] [<]
export
extendDimN : {s : Nat} -> NContext s -> WhnfContext d n ->
WhnfContext (s + d) n
extendDimN ns (MkWhnfContext {dnames, tnames, tctx}) =
MkWhnfContext {
dnames = dnames ++ toSnocVect' ns,
tctx = dweakT s <$> tctx,
tnames
}
export
extendDim : BaseName -> WhnfContext d n -> WhnfContext (S d) n
extendDim i = extendDimN [< i]
private private
data CtxBinder a = MkCtxBinder BaseName a data CtxBinder a = MkCtxBinder BaseName a

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

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

3
lib/quox-lib.ipkg
View file

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

47
tests/TermImpls.idr
View file

@ -25,14 +25,14 @@ mutual
TYPE _ == _ = False TYPE _ == _ = False
Pi qty1 arg1 res1 == Pi qty2 arg2 res2 = Pi qty1 arg1 res1 == Pi qty2 arg2 res2 =
qty1 == qty2 && arg1 == arg2 && res1.term == res2.term qty1 == qty2 && arg1 == arg2 && res1 == res2
Pi {} == _ = False Pi {} == _ = False
Lam body1 == Lam body2 = body1.term == body2.term Lam body1 == Lam body2 = body1 == body2
Lam {} == _ = False Lam {} == _ = False
Sig fst1 snd1 == Sig fst2 snd2 = Sig fst1 snd1 == Sig fst2 snd2 =
fst1 == fst2 && snd1.term == snd2.term fst1 == fst2 && snd1 == snd2
Sig {} == _ = False Sig {} == _ = False
Pair fst1 snd1 == Pair fst2 snd2 = fst1 == fst2 && snd1 == snd2 Pair fst1 snd1 == Pair fst2 snd2 = fst1 == fst2 && snd1 == snd2
@ -45,10 +45,10 @@ mutual
Tag _ == _ = False Tag _ == _ = False
Eq ty1 l1 r1 == Eq ty2 l2 r2 = Eq ty1 l1 r1 == Eq ty2 l2 r2 =
ty1.term == ty2.term && l1 == l2 && r1 == r2 ty1 == ty2 && l1 == l2 && r1 == r2
Eq {} == _ = False Eq {} == _ = False
DLam body1 == DLam body2 = body1.term == body2.term DLam body1 == DLam body2 = body1 == body2
DLam {} == _ = False DLam {} == _ = False
Nat == Nat = True Nat == Nat = True
@ -93,20 +93,20 @@ mutual
(_ :@ _) == _ = False (_ :@ _) == _ = False
CasePair q1 p1 r1 b1 == CasePair q2 p2 r2 b2 = 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 CasePair {} == _ = False
CaseEnum q1 t1 r1 a1 == CaseEnum q2 t2 r2 a2 = 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 CaseEnum {} == _ = False
CaseNat q1 q1' n1 r1 z1 s1 == CaseNat q2 q2' n2 r2 z2 s2 = CaseNat q1 q1' n1 r1 z1 s1 == CaseNat q2 q2' n2 r2 z2 s2 =
q1 == q2 && q1' == q2' && n1 == n2 && q1 == q2 && q1' == q2' && n1 == n2 &&
r1.term == r2.term && z1 == z2 && s1.term == s2.term r1 == r2 && z1 == z2 && s1 == s2
CaseNat {} == _ = False CaseNat {} == _ = False
CaseBox q1 x1 r1 b1 == CaseBox q2 x2 r2 b2 = 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 CaseBox {} == _ = False
(fun1 :% dim1) == (fun2 :% dim2) = fun1 == fun2 && dim1 == dim2 (fun1 :% dim1) == (fun2 :% dim2) = fun1 == fun2 && dim1 == dim2
@ -115,17 +115,18 @@ mutual
(tm1 :# ty1) == (tm2 :# ty2) = tm1 == tm2 && ty1 == ty2 (tm1 :# ty1) == (tm2 :# ty2) = tm1 == tm2 && ty1 == ty2
(_ :# _) == _ = False (_ :# _) == _ = False
TypeCase ty1 ret1 univ1 pi1 sig1 enum1 eq1 nat1 box1 Coe ty1 p1 q1 val1 == Coe ty2 p2 q2 val2 =
== ty1 == ty2 && p1 == p2 && q1 == q2 && val1 == val2
TypeCase ty2 ret2 univ2 pi2 sig2 enum2 eq2 nat2 box2 = Coe {} == _ = False
ty1 == ty2 && ret1 == ret2 &&
pi1.term == pi2.term &&
sig1.term == sig2.term &&
enum1 == enum2 &&
eq1.term == eq2.term &&
nat1 == nat2 &&
box1.term == box2.term
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 TypeCase {} == _ = False
CloE el1 th1 == CloE el2 th2 = CloE el1 th1 == CloE el2 th2 =
@ -140,6 +141,14 @@ mutual
Nothing => False Nothing => False
DCloE {} == _ = 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 export covering
Show (Term d n) where Show (Term d n) where
showPrec d t = showParens (d /= Open) $ prettyStr True t 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" :- [ "type-case" :- [
testPrettyE [<] [<] testPrettyE [<] [<]
{label = "type-case ℕ ∷ ★₀ return ★₀ of { ⋯ }"} {label = "type-case ℕ ∷ ★₀ return ★₀ of { ⋯ }"}
(TypeCase (Nat :# TYPE 0) (TYPE 0) Nat (SN Nat) (SN Nat) Nat (TypeCase (Nat :# TYPE 0) (TYPE 0) empty Nat)
(SN Nat) Nat (SN Nat)) "type-case ℕ ∷ ★₀ return ★₀ of { _ ⇒ ℕ }"
""" "type-case Nat :: Type0 return Type0 of { _ => 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
}
"""
], ],
"annotations" :- [ "annotations" :- [

79
tests/Tests/Reduce.idr
View file

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

9
tests/TypingImpls.idr
View file

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