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WIP: 𝕎 #25

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rhi wants to merge 8 commits from 𝕎 into 🐉
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5
lib/Quox/Displace.idr
View file

@ -19,6 +19,9 @@ parameters (k : Universe)
doDisplace (Lam body loc) = Lam (doDisplaceS body) loc
doDisplace (Sig fst snd loc) = Sig (doDisplace fst) (doDisplaceS snd) loc
doDisplace (Pair fst snd loc) = Pair (doDisplace fst) (doDisplace snd) loc
doDisplace (W shape body loc) =
W (doDisplace shape) (doDisplaceS body) loc
doDisplace (Sup root sub loc) = Sup (doDisplace root) (doDisplace sub) loc
doDisplace (Enum cases loc) = Enum cases loc
doDisplace (Tag tag loc) = Tag tag loc
doDisplace (Eq ty l r loc) =
@ -47,6 +50,8 @@ parameters (k : Universe)
doDisplace (App fun arg loc) = App (doDisplace fun) (doDisplace arg) loc
doDisplace (CasePair qty pair ret body loc) =
CasePair qty (doDisplace pair) (doDisplaceS ret) (doDisplaceS body) loc
doDisplace (CaseW qty qtyIH tree ret body loc) =
CaseW qty qtyIH (doDisplace tree) (doDisplaceS ret) (doDisplaceS body) loc
doDisplace (CaseEnum qty tag ret arms loc) =
CaseEnum qty (doDisplace tag) (doDisplaceS ret) (map doDisplace arms) loc
doDisplace (CaseNat qty qtyIH nat ret zero succ loc) =

20
lib/Quox/EffExtra.idr
View file

@ -26,6 +26,26 @@ local_ : Has (State s) fs => s -> Eff fs a -> Eff fs a
local_ = localAt_ ()
public export
record StateRes s a where
constructor SR
state : s
result : a
export
stateAt : (0 lbl : tag) -> Has (StateL lbl s) fs =>
(s -> StateRes s a) -> Eff fs a
stateAt lbl f = do
s <- getAt lbl
let out = f s
putAt lbl out.state
pure out.result
export %inline
state : Has (State s) fs => (s -> StateRes s a) -> Eff fs a
state = stateAt ()
export
hasDrop : (0 neq : Not (a = b)) ->
(ha : Has a fs) => (hb : Has b fs) =>

91
lib/Quox/Equal.idr
View file

@ -79,6 +79,8 @@ sameTyCon (Pi {}) (Pi {}) = True
sameTyCon (Pi {}) _ = False
sameTyCon (Sig {}) (Sig {}) = True
sameTyCon (Sig {}) _ = False
sameTyCon (W {}) (W {}) = True
sameTyCon (W {}) _ = False
sameTyCon (Enum {}) (Enum {}) = True
sameTyCon (Enum {}) _ = False
sameTyCon (Eq {}) (Eq {}) = True
@ -111,6 +113,7 @@ isSubSing defs ctx ty0 = do
Sig {fst, snd, _} =>
isSubSing defs ctx fst `andM`
isSubSing defs (extendTy Zero snd.name fst ctx) snd.term
W {} => pure False
Enum {cases, _} =>
pure $ length (SortedSet.toList cases) <= 1
Eq {} => pure True
@ -120,6 +123,7 @@ isSubSing defs ctx ty0 = do
E _ => pure False
Lam {} => pure False
Pair {} => pure False
Sup {} => pure False
Tag {} => pure False
DLam {} => pure False
Zero {} => pure False
@ -209,9 +213,9 @@ parameters (defs : Definitions)
case (s, t) of
-- Γ ⊢ s₁ = t₁ : A Γ ⊢ s₂ = t₂ : B{s₁/x}
-- --------------------------------------------
-- Γ ⊢ (s₁, t₁) = (s₂,t₂) : (x : A) × B
-- Γ ⊢ (s₁, t₁) = (s₂, t₂) : (x : A) × B
--
-- [todo] η for π ≥ 0 maybe
-- [todo] η for π ≰ 1 maybe
(Pair sFst sSnd {}, Pair tFst tSnd {}) => do
compare0 ctx fst sFst tFst
compare0 ctx (sub1 snd (Ann sFst fst fst.loc)) sSnd tSnd
@ -225,6 +229,27 @@ parameters (defs : Definitions)
(E _, t) => wrongType t.loc ctx ty t
(s, _) => wrongType s.loc ctx ty s
compare0' ctx ty@(W {shape, body, _}) s t =
case (s, t) of
-- Γ ⊢ s₁ = t₁ : A
-- Γ ⊢ s₂ = t₂ : 1.B[s₁∷A/x] → (x : A) ⊲ B
-- -----------------------------------------
-- Γ ⊢ s₁⋄s₂ = t₁⋄t₂ : (x : A) ⊲ B
(Sup sRoot sSub {}, Sup tRoot tSub {}) => do
compare0 ctx shape sRoot tRoot
let arg = sub1 body (Ann sRoot shape sRoot.loc)
subTy = Arr One arg ty ty.loc
compare0 ctx subTy sSub tSub
(E e, E f) => Elim.compare0 ctx e f
(Sup {}, E {}) => clashT s.loc ctx ty s t
(E {}, Sup {}) => clashT s.loc ctx ty s t
(Sup {}, t) => wrongType t.loc ctx ty t
(E {}, t) => wrongType t.loc ctx ty t
(s, _) => wrongType s.loc ctx ty s
compare0' ctx ty@(Enum {}) s t = local_ Equal $
case (s, t) of
-- --------------------
@ -322,12 +347,16 @@ parameters (defs : Definitions)
-- Γ ⊢ Type 𝓀 <: Type ℓ
expectModeU a.loc !mode k l
compareType' ctx a@(Pi {qty = sQty, arg = sArg, res = sRes, _})
compareType' ctx (Pi {qty = sQty, arg = sArg, res = sRes, loc})
(Pi {qty = tQty, arg = tArg, res = tRes, _}) = do
-- Γ ⊢ A₁ :> A₂ Γ, x : A₁ ⊢ B₁ <: B₂
-- ----------------------------------------
-- Γ ⊢ (π·x : A₁) → B₁ <: (π·x : A₂) → B₂
expectEqualQ a.loc sQty tQty
-- Γ ⊢ π.(x : A₁) → B₁ <: π.(x : A₂) → B₂
--
-- no quantity subtyping since that would need a runtime coercion
-- e.g. if ⌊0.A → B⌋ ⇝ ⌊B⌋, then the promotion to ω.A → B would need
-- to re-add the abstraction
expectEqualQ loc sQty tQty
local flip $ compareType ctx sArg tArg -- contra
compareType (extendTy Zero sRes.name sArg ctx) sRes.term tRes.term
@ -339,12 +368,20 @@ parameters (defs : Definitions)
compareType ctx sFst tFst
compareType (extendTy Zero sSnd.name sFst ctx) sSnd.term tSnd.term
compareType' ctx (W {shape = sShape, body = sBody, loc})
(W {shape = tShape, body = tBody, _}) = do
-- Γ ⊢ A₁ <: A₂ Γ, x : A₁ ⊢ B₁ <: B₂
-- --------------------------------------
-- Γ ⊢ (x : A₁) ⊲ B₁ <: (x : A₂) ⊲ B₂
compareType ctx sShape tShape
compareType (extendTy Zero sBody.name sShape ctx) sBody.term tBody.term
compareType' ctx (Eq {ty = sTy, l = sl, r = sr, _})
(Eq {ty = tTy, l = tl, r = tr, _}) = do
-- Γ ⊢ A₁‹ε/i› <: A₂‹ε/i›
-- Γ ⊢ l₁ = l₂ : A₁‹𝟎/i› Γ ⊢ r₁ = r₂ : A₁‹𝟏/i›
-- Γ ⊢ l₁ = l₂ : A₁‹0/i› Γ ⊢ r₁ = r₂ : A₁‹1/i›
-- ------------------------------------------------
-- Γ ⊢ Eq [i ⇒ A₁] l₁ r₂ <: Eq [i ⇒ A₂] l₂ r₂
-- Γ ⊢ Eq (i ⇒ A₁) l₁ r₂ <: Eq (i ⇒ A₂) l₂ r₂
compareType (extendDim sTy.name Zero ctx) sTy.zero tTy.zero
compareType (extendDim sTy.name One ctx) sTy.one tTy.one
let ty = case !mode of Super => sTy; _ => tTy
@ -366,6 +403,9 @@ parameters (defs : Definitions)
pure ()
compareType' ctx (BOX pi a loc) (BOX rh b {}) = do
-- Γ ⊢ A <: B
-- --------------------
-- Γ ⊢ [π.A] <: [π.B]
expectEqualQ loc pi rh
compareType ctx a b
@ -439,6 +479,36 @@ parameters (defs : Definitions)
expectEqualQ e.loc epi fpi
compare0' ctx e@(CasePair {}) f _ _ = clashE e.loc ctx e f
-- Ψ | Γ ⊢ e = f ⇒ (x : A) ⊲ B
-- Ψ | Γ, p : (x : A) ⊲ B ⊢ Q = R ⇐ Type
-- Ψ | Γ, x : A, y : 1.B → (x : A) ⊲ B, ih : 1.(z : B) → Q[y z/p]
-- ⊢ s = t ⇐ Q[(x⋄y ∷ (x : A) ⊲ B)/p]
-- ----------------------------------------------------------------
-- Ψ | Γ ⊢ caseπ e return Q of { x ⋄ y, ς.ih ⇒ s }
-- = caseπ f return R of { x ⋄ y, ς.ih ⇒ t } ⇒ Q[e/p]
compare0' ctx (CaseW epi epi' e eret ebody eloc)
(CaseW fpi fpi' f fret fbody floc) ne nf =
local_ Equal $ do
compare0 ctx e f
ety <- computeElimTypeE defs ctx e @{noOr1 ne}
compareType (extendTy Zero eret.name ety ctx) eret.term fret.term
(shape, tbody) <- expectW defs ctx eloc ety
let [< x, y, ih] = ebody.names
z <- mnb "z" ih.loc
let xbind = (epi, x, shape)
ybind = (epi, y, Arr One tbody.term (weakT 1 ety) y.loc)
ihbind = (epi', ih,
PiY One z
(sub1 (weakS 2 tbody) (BV 1 x.loc))
(sub1 (weakS 3 eret) (App (BV 1 y.loc) (BVT 0 z.loc) ih.loc))
ih.loc)
ctx' = extendTyN [< xbind, ybind, ihbind] ctx
Term.compare0 ctx' (substCaseWRet ebody.names ety eret)
ebody.term fbody.term
expectEqualQ e.loc epi fpi
expectEqualQ e.loc epi' fpi'
compare0' ctx e@(CaseW {}) f _ _ = clashE e.loc ctx e f
-- Ψ | Γ ⊢ e = f ⇒ {𝐚s}
-- Ψ | Γ, x : {𝐚s} ⊢ Q = R
-- Ψ | Γ ⊢ sᵢ = tᵢ ⇐ Q[𝐚ᵢ∷{𝐚s}]
@ -598,6 +668,13 @@ parameters (defs : Definitions)
(Zero, b, Arr Zero (BVT 0 b.loc) (TYPE u b.loc) b.loc)] ctx
compare0 ctx (weakT 2 ret) b1.term b2.term
compareArm_ ctx KW ret u b1 b2 = do
let [< a, b] = b1.names
ctx = extendTyN
[< (Zero, a, TYPE u a.loc),
(Zero, b, Arr Zero (BVT 0 b.loc) (TYPE u b.loc) b.loc)] ctx
compare0 ctx (weakT 2 ret) b1.term b2.term
compareArm_ ctx KEnum ret u b1 b2 =
compare0 ctx ret b1.term b2.term

25
lib/Quox/Name.idr
View file

@ -4,7 +4,7 @@ import Quox.Loc
import Quox.CharExtra
import public Data.SnocList
import Data.List
import Control.Eff
import Quox.EffExtra
import Text.Lexer
import Derive.Prelude
@ -178,23 +178,22 @@ export
runNameGen : Has NameGen fs => Eff fs a -> Eff (fs - NameGen) a
runNameGen = map fst . runNameGenWith 0
export
gen : Has NameGen fs => Eff fs Nat
gen = stateAt GEN $ \i => SR {result = i, state = S i}
||| generate a fresh name with the given base
export
mn : Has NameGen fs => PBaseName -> Eff fs BaseName
mn base = do
i <- getAt GEN
modifyAt GEN S
pure $ MN base i
mn base = MN base <$> gen
||| generate a fresh binding name with the given base and
||| (optionally) location `loc`
||| generate a fresh binding name with the given base and location `loc`
export
mnb : Has NameGen fs =>
PBaseName -> {default noLoc loc : Loc} -> Eff fs BindName
mnb base = pure $ BN !(mn base) loc
mnb : Has NameGen fs => PBaseName -> Loc -> Eff fs BindName
mnb base loc = pure $ BN !(mn base) loc
export
fresh : Has NameGen fs => BindName -> Eff fs BindName
fresh (BN (UN str) loc) = mnb str {loc}
fresh (BN (MN str k) loc) = mnb str {loc}
fresh (BN Unused loc) = mnb "x" {loc}
fresh (BN (UN str) loc) = mnb str loc
fresh (BN (MN str k) loc) = mnb str loc
fresh (BN Unused loc) = mnb "x" loc

14
lib/Quox/Pretty.idr
View file

@ -24,9 +24,13 @@ data PPrec
= Outer
| Times -- "_ × _"
| InTimes -- arguments of ×
| W -- "_ ⊲ _"
| InW -- arguments of ⊲
| AnnL -- left of "∷"
| Eq -- "_ ≡ _ : _"
| InEq -- arguments of ≡
| Sup -- "_ ⋄ _"
| InSup -- arguments of ⋄
-- ...
| App -- term/dimension application
| Arg -- argument to nonfix function
@ -229,10 +233,10 @@ prettyDBind = hl DVar . prettyBind'
export %inline
typeD, arrowD, darrowD, timesD, lamD, eqndD, dlamD, annD, natD,
eqD, colonD, commaD, semiD, caseD, typecaseD, returnD,
ofD, dotD, zeroD, succD, coeD, compD, undD, cstD, pipeD :
{opts : _} -> Eff Pretty (Doc opts)
typeD, arrowD, darrowD, timesD, lamD, eqndD, dlamD, annD, natD, triD, diamondD,
eqD, colonD, commaD, semiD, caseD, typecaseD, returnD, ofD, dotD, zeroD, succD,
coeD, compD, undD, cstD, pipeD :
{opts : LayoutOpts} -> Eff Pretty (Doc opts)
typeD = hl Syntax . text =<< ifUnicode "★" "Type"
arrowD = hl Delim . text =<< ifUnicode "→" "->"
darrowD = hl Delim . text =<< ifUnicode "⇒" "=>"
@ -242,6 +246,8 @@ eqndD = hl Delim . text =<< ifUnicode "≡" "=="
dlamD = hl Syntax . text =<< ifUnicode "δ" "dfun"
annD = hl Delim . text =<< ifUnicode "∷" "::"
natD = hl Syntax . text =<< ifUnicode "ℕ" "Nat"
triD = hl Syntax . text =<< ifUnicode "⊲" "<|"
diamondD = hl Syntax . text =<< ifUnicode "⋄" "<>"
eqD = hl Syntax $ text "Eq"
colonD = hl Delim $ text ":"
commaD = hl Delim $ text ","

250
lib/Quox/Reduce.idr
View file

@ -78,6 +78,12 @@ isPairHead (Ann (Pair {}) (Sig {}) _) = True
isPairHead (Coe {}) = True
isPairHead _ = False
public export %inline
isWHead : Elim {} -> Bool
isWHead (Ann (Sup {}) (W {}) _) = True
isWHead (Coe {}) = True
isWHead _ = False
public export %inline
isTagHead : Elim {} -> Bool
isTagHead (Ann (Tag {}) (Enum {}) _) = True
@ -113,6 +119,8 @@ isTyCon : Term {} -> Bool
isTyCon (TYPE {}) = True
isTyCon (Pi {}) = True
isTyCon (Lam {}) = False
isTyCon (W {}) = True
isTyCon (Sup {}) = False
isTyCon (Sig {}) = True
isTyCon (Pair {}) = False
isTyCon (Enum {}) = True
@ -155,6 +163,8 @@ mutual
isRedexE defs fun || isLamHead fun
isRedexE defs (CasePair {pair, _}) =
isRedexE defs pair || isPairHead pair
isRedexE defs (CaseW {tree, _}) =
isRedexE defs tree || isWHead tree
isRedexE defs (CaseEnum {tag, _}) =
isRedexE defs tag || isTagHead tag
isRedexE defs (CaseNat {nat, _}) =
@ -204,16 +214,36 @@ tycaseRhsDef0 : Term d n -> (k : TyConKind) -> TypeCaseArms d n ->
tycaseRhsDef0 def k arms = fromMaybe def $ tycaseRhs0 k arms
export
weakAtT : CanTSubst f => (by, at : Nat) ->
f d (at + n) -> f d (at + (by + n))
weakAtT by at t = t `CanTSubst.(//)` pushN at (shift by)
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
export
weakAtD : CanDSubst f => (by, at : Nat) ->
f (at + d) n -> f (at + (by + d)) n
weakAtD by at t = t `CanDSubst.(//)` pushN at (shift by)
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
parameters {s : Nat}
export
weakS : (by : Nat) -> ScopeTermN s d n -> ScopeTermN s d (by + n)
weakS by (S names (Y body)) = S names $ Y $ weakAtT by s body
weakS by (S names (N body)) = S names $ N $ weakT by body
export
weakDS : (by : Nat) -> DScopeTermN s d n -> DScopeTermN s 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
export
dweakS : (by : Nat) -> ScopeTermN s d n -> ScopeTermN s (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
export
dweakDS : (by : Nat) -> DScopeTermN s d n -> DScopeTermN s (by + d) n
dweakDS by (S names (Y body)) = S names $ Y $ weakAtD by s body
dweakDS by (S names (N body)) = S names $ N $ dweakT by body
private
coeScoped : {s : Nat} -> DScopeTerm d n -> Dim d -> Dim d -> Loc ->
@ -246,6 +276,7 @@ parameters {d, n : Nat} (defs : Definitions) (ctx : WhnfContext d n)
| t => throw $ ExpectedPi loc ctx.names t
pure $ sub1 res $ Ann s arg loc
computeElimType (CasePair {pair, ret, _}) = pure $ sub1 ret pair
computeElimType (CaseW {tree, ret, _}) = pure $ sub1 ret tree
computeElimType (CaseEnum {tag, ret, _}) = pure $ sub1 ret tag
computeElimType (CaseNat {nat, ret, _}) = pure $ sub1 ret nat
computeElimType (CaseBox {box, ret, _}) = pure $ sub1 ret box
@ -269,7 +300,7 @@ parameters {d, n : Nat} (defs : Definitions) (ctx : WhnfContext (S d) n)
tycasePi (E e) {tnf} = do
ty <- computeElimType defs ctx e @{noOr2 tnf}
let loc = e.loc
narg = mnb "Arg"; nret = mnb "Ret"
narg = mnb "Arg" loc; nret = mnb "Ret" loc
arg = E $ typeCase1Y e ty KPi [< !narg, !nret] (BVT 1 loc) loc
res' = typeCase1Y e (Arr Zero arg ty loc) KPi [< !narg, !nret]
(BVT 0 loc) loc
@ -287,7 +318,7 @@ parameters {d, n : Nat} (defs : Definitions) (ctx : WhnfContext (S d) n)
tycaseSig (E e) {tnf} = do
ty <- computeElimType defs ctx e @{noOr2 tnf}
let loc = e.loc
nfst = mnb "Fst"; nsnd = mnb "Snd"
nfst = mnb "Fst" loc; nsnd = mnb "Snd" loc
fst = E $ typeCase1Y e ty KSig [< !nfst, !nsnd] (BVT 1 loc) loc
snd' = typeCase1Y e (Arr Zero fst ty loc) KSig [< !nfst, !nsnd]
(BVT 0 loc) loc
@ -295,6 +326,24 @@ parameters {d, n : Nat} (defs : Definitions) (ctx : WhnfContext (S d) n)
pure (fst, snd)
tycaseSig t = throw $ ExpectedSig t.loc 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
tycaseW : (t : Term (S d) n) -> (0 tnf : No (isRedexT defs t)) =>
Eff Whnf (Term (S d) n, ScopeTerm (S d) n)
tycaseW (W {shape, body, _}) = pure (shape, body)
tycaseW (E e) {tnf} = do
ty <- computeElimType defs ctx e @{noOr2 tnf}
let loc = e.loc
nshape = mnb "Shape" loc; nbody = mnb "Body" loc
shape = E $ typeCase1Y e ty KW [< !nshape, !nbody] (BVT 1 loc) loc
body' = typeCase1Y e (Arr Zero shape ty loc) KW [< !nshape, !nbody]
(BVT 0 loc) loc
body = ST [< !nshape] $ E $ App (weakE 1 body') (BVT 0 loc) loc
pure (shape, body)
tycaseW t = throw $ ExpectedW t.loc 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
@ -303,8 +352,9 @@ parameters {d, n : Nat} (defs : Definitions) (ctx : WhnfContext (S d) n)
Eff Whnf (Term (S d) n)
tycaseBOX (BOX {ty, _}) = pure ty
tycaseBOX (E e) {tnf} = do
let loc = e.loc
ty <- computeElimType defs ctx e @{noOr2 tnf}
pure $ E $ typeCase1Y e ty KBOX [< !(mnb "Ty")] (BVT 0 e.loc) e.loc
pure $ E $ typeCase1Y e ty KBOX [< !(mnb "Ty" loc)] (BVT 0 loc) loc
tycaseBOX t = throw $ ExpectedBOX t.loc ctx.names t
||| for Eq [i ⇒ A] l r, returns (A‹0/i›, A‹1/i›, A, l, r);
@ -318,11 +368,11 @@ parameters {d, n : Nat} (defs : Definitions) (ctx : WhnfContext (S d) n)
tycaseEq (E e) {tnf} = do
ty <- computeElimType defs ctx e @{noOr2 tnf}
let loc = e.loc
names = traverse' (\x => mnb x) [< "A0", "A1", "A", "L", "R"]
names = traverse' (\x => mnb x loc) [< "A0", "A1", "A", "l", "r"]
a0 = E $ typeCase1Y e ty KEq !names (BVT 4 loc) loc
a1 = E $ typeCase1Y e ty KEq !names (BVT 3 loc) loc
a' = typeCase1Y e (Eq0 ty a0 a1 loc) KEq !names (BVT 2 loc) loc
a = DST [< !(mnb "i")] $ E $ DApp (dweakE 1 a') (B VZ loc) loc
a = DST [< !(mnb "i" loc)] $ E $ DApp (dweakE 1 a') (B VZ loc) loc
l = E $ typeCase1Y e a0 KEq !names (BVT 1 loc) loc
r = E $ typeCase1Y e a1 KEq !names (BVT 0 loc) loc
pure (a0, a1, a, l, r)
@ -337,9 +387,12 @@ parameters {d, n : Nat} (defs : Definitions) (ctx : WhnfContext d n)
(val, s : Term d n) -> Loc ->
Eff Whnf (Subset (Elim d n) (No . isRedexE defs))
piCoe sty@(S [< i] ty) p q val s loc = 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
-- 𝒮‹𝑘› ≔ π.(x : A‹𝑘/𝑖›) → B‹𝑘/𝑖›
-- 𝓈‹𝑘› ≔ coe [𝑖 ⇒ A] @q @𝑘 s
-- -------------------------------------------------------
-- (coe [𝑖 ⇒ 𝒮‹𝑖›] @p @q t) s
-- ⇝
-- coe [i ⇒ B[𝓈‹i›/x] @p @q ((t ∷ 𝒮‹p›) 𝓈‹p›)
--
-- type-case is used to expose A,B if the type is neutral
let ctx1 = extendDim i ctx
@ -358,11 +411,11 @@ parameters {d, n : Nat} (defs : Definitions) (ctx : WhnfContext d n)
(ret : ScopeTerm d n) -> (body : ScopeTermN 2 d n) -> Loc ->
Eff Whnf (Subset (Elim d n) (No . isRedexE defs))
sigCoe qty sty@(S [< i] ty) p q val ret body loc = do
-- caseπ (coe [i ⇒ (x : A) × B] @p @q s) return z ⇒ C of { (a, b) ⇒ e }
-- caseπ (coe [i ⇒ (x : A) × B] @p @q s) return z ⇒ C of { (a, b) ⇒ u }
-- ⇝
-- caseπ s ∷ ((x : A) × B)‹p/i› return z ⇒ C
-- of { (a, b) ⇒
-- e[(coe [i ⇒ A] @p @q a)/a,
-- u[(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
@ -370,14 +423,58 @@ parameters {d, n : Nat} (defs : Definitions) (ctx : WhnfContext d n)
Element ty tynf <- whnf defs ctx1 ty.term
(tfst, tsnd) <- tycaseSig defs ctx1 ty
let [< x, y] = body.names
a' = CoeT i (weakT 2 tfst) p q (BVT 1 noLoc) x.loc
a' = CoeT i (weakT 2 tfst) p q (BVT 1 x.loc) x.loc
tsnd' = tsnd.term //
(CoeT i (weakT 2 $ tfst // (B VZ noLoc ::: shift 2))
(weakD 1 p) (B VZ noLoc) (BVT 1 noLoc) y.loc ::: shift 2)
b' = CoeT i tsnd' p q (BVT 0 noLoc) y.loc
whnf defs ctx $ CasePair qty (Ann val (ty // one p) val.loc) ret
(CoeT !(fresh i) (weakT 2 $ tfst // (B VZ i.loc ::: shift 2))
(weakD 1 p) (B VZ i.loc) (BVT 1 x.loc) y.loc ::: shift 2)
b' = CoeT i tsnd' p q (BVT 0 y.loc) y.loc
whnf defs ctx $ CasePair qty (Ann val (dsub1 sty p) val.loc) ret
(ST body.names $ body.term // (a' ::: b' ::: shift 2)) loc
||| reduce a w elimination `CaseW pi piIH (Coe ty p q val) ret body loc`
private covering
wCoe : (qty, qtyIH : Qty) ->
(ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) ->
(ret : ScopeTerm d n) -> (body : ScopeTermN 3 d n) -> Loc ->
Eff Whnf (Subset (Elim d n) (No . isRedexE defs))
wCoe qty qtyIH sty@(S [< i] ty) p q val ret body loc = do
-- 𝒮‹𝑘› ≔ ((x : A) ⊲ B)‹𝑘/𝑖›
-- 𝒶‹𝑘› ≔ coe [𝑖 ⇒ A] @p @𝑘 a
-- : A‹𝑘/𝑖›
-- 𝒷‹𝑘› ≔ coe [𝑖 ⇒ 1.B[𝒶‹𝑖›/x] → 𝒮‹𝑖›] @p @𝑘 b
-- : 1.B‹𝑘/𝑖›[𝒶‹𝑘›/x] → 𝒮‹𝑘›
-- 𝒾𝒽 ≔ coe [𝑖 ⇒ π.(z : B[𝒶‹𝑖›/x]) → C[𝒷‹𝑖› z/p]] @p @q ih
-- : π.(z : B‹q/𝑖›[𝒶‹q›/x]) → C[𝒷‹q› z/p]
-- --------------------------------------------------------------------
-- caseπ (coe [𝑖 ⇒ 𝒮‹𝑖›] @p @q s) return z ⇒ C of { a ⋄ b, ς.ih ⇒ u }
-- ⇝
-- caseπ s ∷ 𝒮‹p› return z ⇒ C
-- of { a ⋄ b, ς.ih ⇒ u[𝒶‹q›/a, 𝒷‹q›/b, 𝒾𝒽/ih] }
let ctx1 = extendDim i ctx
Element ty tynf <- whnf defs ctx1 ty.term
(shape, tbody) <- tycaseW defs ctx1 ty
let [< a, b, ih] = body.names
ai <- fresh i; bi <- fresh i; ihi <- fresh i; z <- mnb "z" ih.loc
let a', b' : forall d'. (by : Shift d d') => Dim d' -> Elim d' (3 + n)
a' k =
let shape' = shape // Shift (weak 1 by) // shift 3 in
CoeT ai shape' (p // by) k (BVT 2 a.loc) a.loc
b' k =
let tbody' = tbody.term // Shift (weak 1 by)
// (a' (BV 0 bi.loc) ::: shift 3)
ty' = ty // Shift (weak 1 by) // shift 3
in
CoeT bi (Arr One tbody' ty' b.loc) (p // by) k (BVT 1 b.loc) b.loc
ih' : Elim d (3 + n) :=
let tbody' = tbody.term // (a' (BV 0 ihi.loc) ::: shift 3)
ret' = sub1 (weakS 4 $ dweakS 1 ret) $
App (weakE 1 $ b' (BV 0 ihi.loc)) (BVT 0 z.loc) ih.loc
ty = PiY qty z tbody' ret' ih.loc
in
CoeT ihi ty p q (BVT 0 ih.loc) ih.loc
whnf defs ctx $ CaseW qty qtyIH (Ann val (dsub1 sty p) val.loc) ret
(ST body.names $ body.term // (a' q ::: b' q ::: ih' ::: shift 3)) loc
||| reduce a dimension application `DApp (Coe ty p q val) r loc`
private covering
eqCoe : (ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) ->
@ -392,7 +489,7 @@ parameters {d, n : Nat} (defs : Definitions) (ctx : WhnfContext d n)
Element ty tynf <- whnf defs ctx1 ty.term
(a0, a1, a, s, t) <- tycaseEq defs ctx1 ty
let a' = dsub1 a (weakD 1 r)
val' = E $ DApp (Ann val (ty // one p) val.loc) r loc
val' = E $ DApp (Ann val (dsub1 sty p) val.loc) r loc
whnf defs ctx $ CompH j a' p q val' r j s j t loc
||| reduce a pair elimination `CaseBox pi (Coe ty p q val) ret body`
@ -409,8 +506,8 @@ parameters {d, n : Nat} (defs : Definitions) (ctx : WhnfContext d n)
let ctx1 = extendDim i ctx
Element ty tynf <- whnf defs ctx1 ty.term
ta <- tycaseBOX defs ctx1 ty
let a' = CoeT i (weakT 1 ta) p q (BVT 0 noLoc) body.name.loc
whnf defs ctx $ CaseBox qty (Ann val (ty // one p) val.loc) ret
let a' = CoeT i (weakT 1 ta) p q (BVT 0 body.name.loc) body.name.loc
whnf defs ctx $ CaseBox qty (Ann val (dsub1 sty p) val.loc) ret
(ST body.names $ body.term // (a' ::: shift 1)) loc
@ -429,19 +526,29 @@ reduceTypeCase defs ctx ty u ret arms def loc = case ty of
-- (type-case π.(x : A) → B ∷ ★ᵢ return Q of { (a → b) ⇒ s; ⋯ }) ⇝
-- s[(A ∷ ★ᵢ)/a, ((λ x ⇒ B) ∷ 0.A → ★ᵢ)/b] ∷ Q
Pi {arg, res, loc = piLoc, _} =>
let arg' = Ann arg (TYPE u noLoc) arg.loc
let arg' = Ann arg (TYPE u arg.loc) arg.loc
res' = Ann (Lam res res.loc)
(Arr Zero arg (TYPE u noLoc) arg.loc) res.loc
(Arr Zero arg (TYPE u arg.loc) arg.loc) res.loc
in
whnf defs ctx $
Ann (subN (tycaseRhsDef def KPi arms) [< arg', res']) ret loc
-- (type-case (x : A) ⊲ π.B ∷ ★ᵢ return Q of { (a ⊲ b) ⇒ s; ⋯ }) ⇝
-- s[(A ∷ ★ᵢ)/a, ((λ x ⇒ B) ∷ 0.A → ★ᵢ)/b] ∷ Q
W {shape, body, loc = wLoc, _} =>
let shape' = Ann shape (TYPE u shape.loc) shape.loc
body' = Ann (Lam body body.loc)
(Arr Zero shape (TYPE u shape.loc) shape.loc) body.loc
in
whnf defs ctx $
Ann (subN (tycaseRhsDef def KW arms) [< shape', body']) ret loc
-- (type-case (x : A) × B ∷ ★ᵢ return Q of { (a × b) ⇒ s; ⋯ }) ⇝
-- s[(A ∷ ★ᵢ)/a, ((λ x ⇒ B) ∷ 0.A → ★ᵢ)/b] ∷ Q
Sig {fst, snd, loc = sigLoc, _} =>
let fst' = Ann fst (TYPE u noLoc) fst.loc
let fst' = Ann fst (TYPE u fst.loc) fst.loc
snd' = Ann (Lam snd snd.loc)
(Arr Zero fst (TYPE u noLoc) fst.loc) snd.loc
(Arr Zero fst (TYPE u fst.loc) fst.loc) snd.loc
in
whnf defs ctx $
Ann (subN (tycaseRhsDef def KSig arms) [< fst', snd']) ret loc
@ -459,8 +566,8 @@ reduceTypeCase defs ctx ty u ret arms def loc = case ty of
let a0 = a.zero; a1 = a.one in
whnf defs ctx $ Ann
(subN (tycaseRhsDef def KEq arms)
[< Ann a0 (TYPE u noLoc) a.loc, Ann a1 (TYPE u noLoc) a.loc,
Ann (DLam a a.loc) (Eq0 (TYPE u noLoc) a0 a1 a.loc) a.loc,
[< Ann a0 (TYPE u a.loc) a.loc, Ann a1 (TYPE u a.loc) a.loc,
Ann (DLam a a.loc) (Eq0 (TYPE u a.loc) a0 a1 a.loc) a.loc,
Ann l a0 l.loc, Ann r a1 r.loc])
ret loc
@ -471,7 +578,7 @@ reduceTypeCase defs ctx ty u ret arms def loc = case ty of
-- (type-case [π.A] ∷ ★ᵢ return Q of { [a] ⇒ s; ⋯ }) ⇝ s[(A ∷ ★ᵢ)/a] ∷ Q
BOX {ty = a, loc = boxLoc, _} =>
whnf defs ctx $ Ann
(sub1 (tycaseRhsDef def KBOX arms) (Ann a (TYPE u noLoc) a.loc))
(sub1 (tycaseRhsDef def KBOX arms) (Ann a (TYPE u a.loc) a.loc))
ret loc
@ -489,6 +596,7 @@ pushCoe defs ctx i ty p q s loc =
-- (coe [_ ⇒ ★ᵢ] @_ @_ ty) ⇝ (ty ∷ ★ᵢ)
TYPE {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
Pi {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
W {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
Sig {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
Enum {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
Eq {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
@ -503,7 +611,7 @@ pushCoe defs ctx i ty p q s loc =
lam@(Lam {body, _}) => do
let lam' = CoeT i ty p q lam loc
term' = LamY !(fresh body.name)
(E $ App (weakE 1 lam') (BVT 0 noLoc) loc) loc
(E $ App (weakE 1 lam') (BVT 0 loc) loc) loc
type' = ty // one q
whnf defs ctx $ Ann term' type' loc
@ -517,23 +625,40 @@ pushCoe defs ctx i ty p q s loc =
let Sig {fst = tfst, snd = tsnd, loc = sigLoc} = ty
| _ => throw $ ExpectedSig ty.loc (extendDim i ctx.names) ty
let fst' = E $ CoeT i tfst p q fst fst.loc
tfst' = tfst // (B VZ noLoc ::: shift 2)
tfst' = tfst // (B VZ i.loc ::: shift 2)
tsnd' = sub1 tsnd $
CoeT !(fresh i) tfst' (weakD 1 p) (B VZ noLoc)
(dweakT 1 fst) fst.loc
CoeT !(fresh i) tfst' (weakD 1 p) (B VZ snd.loc)
(dweakT 1 fst) snd.loc
snd' = E $ CoeT i tsnd' p q snd snd.loc
pure $
Element (Ann (Pair fst' snd' pairLoc)
(Sig (tfst // one q) (tsnd // one q) sigLoc) loc) Ah
-- (coe [i ⇒ (x : A) ⊲ π.B] @p @q (s ⋄ t) ⇝
-- (coe [i ⇒ A] @p @q s ⋄
-- coe [i ⇒ 1.B[coe [j ⇒ A‹j/i›] @p @i s/x] → (x : A) ⊲ B] t)
-- ∷ ((x : A) ⊲ B)‹q/i›
Sup {root, sub, loc = supLoc} => do
let W {shape, body, loc = wLoc} = ty
| _ => throw $ ExpectedW ty.loc (extendDim i ctx.names) ty
let root' = E $ CoeT i shape p q root root.loc
tsub' = sub1 body $
CoeT !(fresh i) (shape // (B VZ root.loc ::: shift 2))
(weakD 1 p) (BV 0 sub.loc)
(dweakT 1 sub) sub.loc
sub' = E $ CoeT i tsub' p q sub sub.loc
pure $
Element (Ann (Sup root' sub' supLoc)
(W (shape // one q) (body // one q) wLoc) loc) Ah
-- η expand, like for Lam
--
-- (coe [i ⇒ A] @p @q (δ j ⇒ s)) ⇝
-- (δ k ⇒ (coe [i ⇒ A] @p @q (δ j ⇒ s)) @k) ∷ A‹q/i› ⇝ ⋯
dlam@(DLam {body, _}) => do
let dlam' = CoeT i ty p q dlam loc
term' = DLamY !(mnb "j")
(E $ DApp (dweakE 1 dlam') (B VZ noLoc) loc) loc
term' = DLamY !(mnb "j" loc)
(E $ DApp (dweakE 1 dlam') (B VZ loc) loc) loc
type' = ty // one q
whnf defs ctx $ Ann term' type' loc
@ -585,8 +710,12 @@ CanWhnf Elim Reduce.isRedexE where
Coe ty p q val _ => piCoe defs ctx ty p q val s appLoc
Right nlh => pure $ Element (App f s appLoc) $ fnf `orNo` nlh
-- case (s, t) ∷ (x : A) × B return p ⇒ C of { (a, b) ⇒ u } ⇝
-- u[s∷A/a, t∷B[s∷A/x]] ∷ C[(s, t)∷((x : A) × B)/p]
-- s' ≔ s ∷ A
-- t' ≔ t ∷ B[s'/x]
-- st' ≔ (s, t) ∷ (x : A) × B
-- C' ≔ C[st'/p]
-- ---------------------------------------------------------------
-- case st' return p ⇒ C of { (a, b) ⇒ u } ⇝ u[s'/a, t'/x]] ∷ C'
whnf defs ctx (CasePair pi pair ret body caseLoc) = do
Element pair pairnf <- whnf defs ctx pair
case nchoose $ isPairHead pair of
@ -601,6 +730,43 @@ CanWhnf Elim Reduce.isRedexE where
Right np =>
pure $ Element (CasePair pi pair ret body caseLoc) $ pairnf `orNo` np
-- s' ≔ s ∷ A
-- t' ≔ t ∷ 1.B[s'/x] → (x : A) ⊲ B
-- ih' ≔ (λ x ⇒ caseπ t x return p ⇒ C of { (a ⋄ b), ς.ih ⇒ u }) ∷
-- π.(y : B[s'/x]) → C[t' y/p]
-- st' ≔ s ⋄ t ∷ (x : A) ⊲ B
-- C' ≔ C[st'/p]
-- --------------------------------------------------------------------
-- caseπ st' return p ⇒ C of { a ⋄ b, ς.ih ⇒ u }
-- ⇝
-- u[s'/a, t'/b, ih'/ih] ∷ C'
whnf defs ctx (CaseW qty qtyIH tree ret body caseLoc) = do
Element tree treenf <- whnf defs ctx tree
case nchoose $ isWHead tree of
Left _ => case tree of
Ann (Sup {root, sub, _})
w@(W {shape, body = wbody, _}) treeLoc =>
let root = Ann root shape root.loc
wbody' = sub1 wbody root
tsub = Arr One wbody' w sub.loc
sub = Ann sub tsub sub.loc
ih' = LamY !(mnb "y" caseLoc) -- [todo] better name
(E $ CaseW qty qtyIH
(App (weakE 1 sub) (BVT 0 sub.loc) sub.loc)
(weakS 1 ret) (weakS 1 body) caseLoc) sub.loc
ihret = sub1 (weakS 1 ret)
(App (weakE 1 sub) (BVT 0 sub.loc) caseLoc)
tih = PiY qty !(mnb "y" caseLoc)
wbody' ihret caseLoc
ih = Ann ih' tih caseLoc
in
whnf defs ctx $
Ann (subN body [< root, sub, ih]) (sub1 ret tree) tree.loc
Coe ty p q val _ => do
wCoe defs ctx qty qtyIH ty p q val ret body caseLoc
Right nw => pure $
Element (CaseW qty qtyIH tree ret body caseLoc) $ treenf `orNo` nw
-- case 'a ∷ {a,…} return p ⇒ C of { 'a ⇒ u } ⇝
-- u ∷ C['a∷{a,…}/p]
whnf defs ctx (CaseEnum pi tag ret arms caseLoc) = do
@ -730,6 +896,8 @@ CanWhnf Term Reduce.isRedexT where
whnf _ _ t@(Lam {}) = pure $ nred t
whnf _ _ t@(Sig {}) = pure $ nred t
whnf _ _ t@(Pair {}) = pure $ nred t
whnf _ _ t@(W {}) = pure $ nred t
whnf _ _ t@(Sup {}) = pure $ nred t
whnf _ _ t@(Enum {}) = pure $ nred t
whnf _ _ t@(Tag {}) = pure $ nred t
whnf _ _ t@(Eq {}) = pure $ nred t

24
lib/Quox/Syntax/Term/Base.idr
View file

@ -102,6 +102,16 @@ mutual
||| pair value
Pair : (fst, snd : Term d n) -> (loc : Loc) -> Term d n
||| inductive (w) type `(x : A) ⊲ B`
W : (shape : Term d n) ->
(body : ScopeTerm d n) -> (loc : Loc) -> Term d n
||| subterms for `(x : A) ⊲ B` are:
||| 1. `x : A`
||| (the "constructor" and non-recursive fields)
||| 2. `f : 1.(B x) → (x : A) ⊲ B`
||| (the recursive fields, one for each element of B x)
Sup : (root, sub : Term d n) -> (loc : Loc) -> Term d n
||| enumeration type
Enum : (cases : SortedSet TagVal) -> (loc : Loc) -> Term d n
||| enumeration value
@ -155,6 +165,13 @@ mutual
(loc : Loc) ->
Elim d n
||| recursion
CaseW : (qty, qtyIH : Qty) -> (tree : Elim d n) ->
(ret : ScopeTerm d n) ->
(body : ScopeTermN 3 d n) ->
(loc : Loc) ->
Elim d n
||| enum matching
CaseEnum : (qty : Qty) -> (tag : Elim d n) ->
(ret : ScopeTerm d n) ->
@ -364,6 +381,7 @@ Located (Elim d n) where
(B _ loc).loc = loc
(App _ _ loc).loc = loc
(CasePair _ _ _ _ loc).loc = loc
(CaseW _ _ _ _ _ loc).loc = loc
(CaseEnum _ _ _ _ loc).loc = loc
(CaseNat _ _ _ _ _ _ loc).loc = loc
(CaseBox _ _ _ _ loc).loc = loc
@ -382,6 +400,8 @@ Located (Term d n) where
(Lam _ loc).loc = loc
(Sig _ _ loc).loc = loc
(Pair _ _ loc).loc = loc
(W _ _ loc).loc = loc
(Sup _ _ loc).loc = loc
(Enum _ loc).loc = loc
(Tag _ loc).loc = loc
(Eq _ _ _ loc).loc = loc
@ -412,6 +432,8 @@ Relocatable (Elim d n) where
setLoc loc (App fun arg _) = App fun arg loc
setLoc loc (CasePair qty pair ret body _) =
CasePair qty pair ret body loc
setLoc loc (CaseW qty qtyIH tree ret body _) =
CaseW qty qtyIH tree ret body loc
setLoc loc (CaseEnum qty tag ret arms _) =
CaseEnum qty tag ret arms loc
setLoc loc (CaseNat qty qtyIH nat ret zero succ _) =
@ -440,6 +462,8 @@ Relocatable (Term d n) where
setLoc loc (Lam body _) = Lam body loc
setLoc loc (Sig fst snd _) = Sig fst snd loc
setLoc loc (Pair fst snd _) = Pair fst snd loc
setLoc loc (W shape body _) = W shape body loc
setLoc loc (Sup root sub _) = Sup root sub loc
setLoc loc (Enum cases _) = Enum cases loc
setLoc loc (Tag tag _) = Tag tag loc
setLoc loc (Eq ty l r _) = Eq ty l r loc

52
lib/Quox/Syntax/Term/Pretty.idr
View file

@ -346,6 +346,8 @@ prettyTyCasePat KPi [< a, b] =
parens . hsep =<< sequence [prettyTBind a, arrowD, prettyTBind b]
prettyTyCasePat KSig [< a, b] =
parens . hsep =<< sequence [prettyTBind a, timesD, prettyTBind b]
prettyTyCasePat KW [< a, b] =
parens . hsep =<< sequence [prettyTBind a, triD, prettyTBind b]
prettyTyCasePat KEnum [<] = hl Syntax $ text "{}"
prettyTyCasePat KEq [< a0, a1, a, l, r] =
hsep <$> sequence (eqD :: map prettyTBind [a0, a1, a, l, r])
@ -420,6 +422,21 @@ prettyTerm dnames tnames p@(Pair fst snd _) =
withPrec Outer $ prettyTerm dnames tnames $ assert_smaller p t
pure $ separateTight !commaD lines
prettyTerm dnames tnames (W a b _) = do
parensIfM W =<< do
left <- prettySigBind1 b.name dnames tnames a
right <- withPrec InW $
prettyTerm dnames (tnames :< b.name) (assert_smaller b b.term)
pure $ sep [hsep [left, !triD], right]
prettyTerm dnames tnames (Sup root sub _) = do
parensIfM Sup =<< do
left <- withPrec InSup $ prettyTerm dnames tnames root
right <- withPrec InSup $ prettyTerm dnames tnames sub
pure $
hsep [left, !diamondD, right] <|>
vsep [hsep [left, !diamondD], !(indentD right)]
prettyTerm dnames tnames (Enum cases _) =
prettyEnum $ SortedSet.toList cases
@ -446,17 +463,22 @@ prettyTerm dnames tnames s@(DLam {}) =
prettyTerm dnames tnames (Nat _) = natD
prettyTerm dnames tnames (Zero _) = hl Syntax "0"
prettyTerm dnames tnames (Succ p _) = do
succD <- succD
let succ : Doc opts -> Eff Pretty (Doc opts)
succ t = prettyAppD succD [t]
toNat : Term d n -> Eff Pretty (Either (Doc opts) Nat)
toNat s with (pushSubsts' s)
s <- succD
either (succ s) prettyNat =<< tryToNat s p
where
succ : Doc opts -> Doc opts -> Eff Pretty (Doc opts)
succ s t = prettyAppD s [t]
tryToNat : Doc opts -> Term d n -> Eff Pretty (Either (Doc opts) Nat)
tryToNat s t with (pushSubsts' t)
_ | Zero _ = pure $ Right 0
_ | Succ d _ = bitraverse succ (pure . S) =<<
toNat (assert_smaller s d)
_ | s' = map Left . withPrec Arg $
prettyTerm dnames tnames $ assert_smaller s s'
either succ (hl Syntax . text . show . S) =<< toNat p
_ | Succ d _ = bitraverse (succ s) (pure . S) =<<
tryToNat s (assert_smaller t d)
_ | t' = map Left . withPrec Arg $
prettyTerm dnames tnames $ assert_smaller t t'
prettyNat : Nat -> Eff Pretty (Doc opts)
prettyNat = hl Syntax . text . show . S
prettyTerm dnames tnames (BOX qty ty _) =
bracks . hcat =<<
@ -493,6 +515,16 @@ prettyElim dnames tnames (CasePair qty pair ret body _) = do
prettyCase dnames tnames qty pair ret
[MkCaseArm pat [<] [< x, y] body.term]
prettyElim dnames tnames (CaseW qty qtyIH tree ret body _) = do
let [< t, r, ih] = body.names
pat0 <- hsep <$> sequence [prettyTBind t, diamondD, prettyTBind r]
ihpat <- map hcat $ sequence [prettyQty qtyIH, dotD, prettyTBind ih]
pat <- if ih.name == Unused
then pure pat0
else pure $ hsep [pat0 <+> !commaD, ihpat]
let arm = MkCaseArm pat [<] [< t, r, ih] body.term
prettyCase dnames tnames qty tree ret [arm]
prettyElim dnames tnames (CaseEnum qty tag ret arms _) = do
arms <- for (SortedMap.toList arms) $ \(tag, body) =>
pure $ MkCaseArm !(prettyTag tag) [<] [<] body

6
lib/Quox/Syntax/Term/Subst.idr
View file

@ -261,6 +261,10 @@ mutual
nclo $ Sig (a // th // ph) (b // th // ph) loc
pushSubstsWith th ph (Pair s t loc) =
nclo $ Pair (s // th // ph) (t // th // ph) loc
pushSubstsWith th ph (W a b loc) =
nclo $ W (a // th // ph) (b // th // ph) loc
pushSubstsWith th ph (Sup s t loc) =
nclo $ Sup (s // th // ph) (t // th // ph) loc
pushSubstsWith th ph (Enum tags loc) =
nclo $ Enum tags loc
pushSubstsWith th ph (Tag tag loc) =
@ -299,6 +303,8 @@ mutual
nclo $ App (f // th // ph) (s // th // ph) loc
pushSubstsWith th ph (CasePair pi p r b loc) =
nclo $ CasePair pi (p // th // ph) (r // th // ph) (b // th // ph) loc
pushSubstsWith th ph (CaseW pi pi' e r b loc) =
nclo $ CaseW pi pi' (e // th // ph) (r // th // ph) (b // th // ph) loc
pushSubstsWith th ph (CaseEnum pi t r arms loc) =
nclo $ CaseEnum pi (t // th // ph) (r // th // ph)
(map (\b => b // th // ph) arms) loc

20
lib/Quox/Syntax/Term/Tighten.idr
View file

@ -52,6 +52,10 @@ mutual
Sig <$> tightenT p fst <*> tightenS p snd <*> pure loc
tightenT' p (Pair fst snd loc) =
Pair <$> tightenT p fst <*> tightenT p snd <*> pure loc
tightenT' p (W shape body loc) =
W <$> tightenT p shape <*> tightenS p body <*> pure loc
tightenT' p (Sup root sub loc) =
Sup <$> tightenT p root <*> tightenT p sub <*> pure loc
tightenT' p (Enum cases loc) =
pure $ Enum cases loc
tightenT' p (Tag tag loc) =
@ -87,6 +91,12 @@ mutual
<*> tightenS p ret
<*> tightenS p body
<*> pure loc
tightenE' p (CaseW qty qtyIH tree ret body loc) =
CaseW qty qtyIH
<$> tightenE p tree
<*> tightenS p ret
<*> tightenS p body
<*> pure loc
tightenE' p (CaseEnum qty tag ret arms loc) =
CaseEnum qty <$> tightenE p tag
<*> tightenS p ret
@ -167,6 +177,10 @@ mutual
Sig <$> dtightenT p fst <*> dtightenS p snd <*> pure loc
dtightenT' p (Pair fst snd loc) =
Pair <$> dtightenT p fst <*> dtightenT p snd <*> pure loc
dtightenT' p (W shape body loc) =
W <$> dtightenT p shape <*> dtightenS p body <*> pure loc
dtightenT' p (Sup root sub loc) =
Sup <$> dtightenT p root <*> dtightenT p sub <*> pure loc
dtightenT' p (Enum cases loc) =
pure $ Enum cases loc
dtightenT' p (Tag tag loc) =
@ -202,6 +216,12 @@ mutual
<*> dtightenS p ret
<*> dtightenS p body
<*> pure loc
dtightenE' p (CaseW qty qtyIH tree ret body loc) =
CaseW qty qtyIH
<$> dtightenE p tree
<*> dtightenS p ret
<*> dtightenS p body
<*> pure loc
dtightenE' p (CaseEnum qty tag ret arms loc) =
CaseEnum qty <$> dtightenE p tag
<*> dtightenS p ret

3
lib/Quox/Syntax/Term/TyConKind.idr
View file

@ -9,7 +9,7 @@ import Generics.Derive
public export
data TyConKind = KTYPE | KPi | KSig | KEnum | KEq | KNat | KBOX
data TyConKind = KTYPE | KPi | KSig | KW | KEnum | KEq | KNat | KBOX
%name TyConKind k
%runElab derive "TyConKind" [Eq.Eq, Ord.Ord, Show.Show, Generic, Meta, DecEq]
@ -28,6 +28,7 @@ arity : TyConKind -> Nat
arity KTYPE = 0
arity KPi = 2
arity KSig = 2
arity KW = 2
arity KEnum = 0
arity KEq = 5
arity KNat = 0

100
lib/Quox/Typechecker.idr
View file

@ -57,27 +57,40 @@ typecaseTel : (k : TyConKind) -> BContext (arity k) -> Universe ->
CtxExtension d n (arity k + n)
typecaseTel k xs u = case k of
KTYPE => [<]
-- A : ★ᵤ, B : 0.A → ★ᵤ
KPi =>
let [< a, b] = xs in
[< (Zero, a, TYPE u a.loc),
(Zero, b, Arr Zero (BVT 0 b.loc) (TYPE u b.loc) b.loc)]
KSig =>
let [< a, b] = xs in
[< (Zero, a, TYPE u a.loc),
(Zero, b, Arr Zero (BVT 0 b.loc) (TYPE u b.loc) b.loc)]
KPi => binaryTyCon xs
KSig => binaryTyCon xs
KW => binaryTyCon xs
KEnum => [<]
-- A₀ : ★ᵤ, A₁ : ★ᵤ, A : (A₀ ≡ A₁ : ★ᵤ), L : A₀, R : A₀
KEq =>
let [< a0, a1, a, l, r] = xs in
KEq => eqCon xs
KNat => [<]
KBOX => unaryTyCon xs
where
-- 0.A : ★ᵤ
unaryTyCon : BContext 1 -> CtxExtension d n (S n)
unaryTyCon [< a] = [< (Zero, a, TYPE u a.loc)]
-- 0.A : ★ᵤ, 0.B : 0.A → ★ᵤ
binaryTyCon : BContext 2 -> CtxExtension d n (2 + n)
binaryTyCon [< a, b] =
[< (Zero, a, TYPE u a.loc),
(Zero, b, Arr Zero (BVT 0 b.loc) (TYPE u b.loc) b.loc)]
-- 0.A₀ : ★ᵤ, 0.A₁ : ★ᵤ, 0.A : (A₀ ≡ A₁ : ★ᵤ), 0.L : A₀, 0.R : A₁
eqCon : BContext 5 -> CtxExtension d n (5 + n)
eqCon [< a0, a1, a, l, r] =
[< (Zero, a0, TYPE u a0.loc),
(Zero, a1, TYPE u a1.loc),
(Zero, a, Eq0 (TYPE u a.loc) (BVT 1 a.loc) (BVT 0 a.loc) a.loc),
(Zero, l, BVT 2 l.loc),
(Zero, r, BVT 2 r.loc)]
KNat => [<]
-- A : ★ᵤ
KBOX => let [< a] = xs in [< (Zero, a, TYPE u a.loc)]
||| if a ⋄ b : (x : A) ⊲ B, then b : `supSubTy a A B _`
||| i.e. 1.B[a∷A/x] → ((x : A) ⊲ B)
export
supSubTy : (root, rootTy : Term d n) ->
(body : ScopeTerm d n) -> Loc -> Term d n
supSubTy root rootTy body loc =
Arr One (sub1 body (Ann root rootTy root.loc)) (W rootTy body loc) loc
mutual
@ -188,6 +201,17 @@ mutual
check' ctx sg t@(Sig {}) ty = toCheckType ctx sg t ty
check' ctx sg t@(W {}) ty = toCheckType ctx sg t ty
check' ctx sg (Sup root sub loc) ty = do
(shape, body) <- expectW !(askAt DEFS) ctx ty.loc ty
-- if Ψ | Γ ⊢ σ · a ⇐ A ⊳ Σ₁
qroot <- checkC ctx sg root shape
-- if Ψ | Γ ⊢ σ · b ⇐ 1.B[a∷A/x] → ((x : A) ⊲ B) ⊳ Σ₂
qsub <- checkC ctx sg sub (supSubTy root shape body sub.loc)
-- then Ψ | Γ ⊢ σ · (a ⋄ b) ⇐ ((x : A) ⊲ B) ⊳ Σ₁+Σ₂
pure $ qroot + qsub
check' ctx sg (Pair fst snd loc) ty = do
(tfst, tsnd) <- expectSig !(askAt DEFS) ctx ty.loc ty
-- if Ψ | Γ ⊢ σ · s ⇐ A ⊳ Σ₁
@ -281,6 +305,16 @@ mutual
checkType' ctx t@(Pair {}) u =
throw $ NotType t.loc ctx t
checkType' ctx (W shape body _) u = do
-- if Ψ | Γ ⊢₀ A ⇐ Type ℓ
checkTypeC ctx shape u
-- if Ψ | Γ, x : A ⊢₀ B ⇐ Type ℓ
checkTypeScope ctx shape body u
-- then Ψ | Γ ⊢₀ (x : A) ⊲ π.B ⇐ Type ℓ
checkType' ctx t@(Sup {}) u =
throw $ NotType t.loc ctx t
checkType' ctx (Enum {}) u = pure ()
-- Ψ | Γ ⊢₀ {ts} ⇐ Type ℓ
@ -388,6 +422,42 @@ mutual
qout = pi * pairres.qout + bodyout
}
infer' ctx sg (CaseW pi si tree ret body loc) = do
-- if 1 ≤ π
expectCompatQ loc One pi
-- if Ψ | Γ ⊢ σ · e ⇒ ((x : A) ⊲ B) ⊳ Σ₁
InfRes {type = w, qout = qtree} <- inferC ctx sg tree
-- if Ψ | Γ, p : (x : A) ⊲ B ⊢₀ C ⇐ Type
checkTypeC (extendTy Zero ret.name w ctx) ret.term Nothing
(shape, tbody) <- expectW !(askAt DEFS) ctx tree.loc w
-- if Ψ | Γ, x : A, y : 1.B → (x : A) ⊲ B,
-- ih : π.(z : B) → C[y z/p]
-- ⊢ σ · u ⇐ C[((x ⋄ y) ∷ (x : A) ⊲ B)/p]
-- ⊳ Σ₂, π'.x, ς₁.y, ς₂.ih
-- with π' ≤ σπ, ς₂ ≤ σς, ς₁+ς₂ ≤ σπ
let [< x, y, ih] = body.names
-- 1.B → (x : A) ⊲ B
tsub = Arr One tbody.term (weakT 1 w) y.loc
-- y z
ihret = App (BV 1 y.loc) (BVT 0 ih.loc) y.loc
-- π.(z : B) → C[y z/p]
tih = PiY pi !(mnb "z" ih.loc)
(tbody.term // (BV 1 x.loc ::: shift 2))
(ret.term // (ihret ::: shift 3)) ih.loc
sp = sg.fst * pi; ss = sg.fst * si
ctx' = extendTyN [< (sp, x, shape), (sp, y, tsub), (ss, ih, tih)] ctx
qbody' <- checkC ctx' sg body.term $ substCaseWRet body.names w ret
let qbody :< qx :< qy :< qih = qbody'
expectCompatQ x.loc qx sp
expectCompatQ (ih.loc `or` loc) qih ss
expectCompatQ y.loc (qy + qih) sp -- [todo] better error message
-- then Ψ | Γ ⊢ σ · caseπ e return p ⇒ C of { x ⋄ y, ς.ih ⇒ u }
-- ⇒ C[e/p] ⊳ Σ₁+Σ₂
pure $ InfRes {
type = sub1 ret tree,
qout = qtree + qbody
}
infer' ctx sg (CaseEnum pi t ret arms loc) {d, n} = do
-- if Ψ | Γ ⊢ σ · t ⇒ {ts} ⊳ Σ₁
tres <- inferC ctx sg t

18
lib/Quox/Typing.idr
View file

@ -47,10 +47,18 @@ public export
substCasePairRet : BContext 2 -> Term d n -> ScopeTerm d n -> Term d (2 + n)
substCasePairRet [< x, y] dty retty =
let tm = Pair (BVT 1 x.loc) (BVT 0 y.loc) $ x.loc `extendL` y.loc
arg = Ann tm (dty // fromNat 2) tm.loc
arg = Ann tm (dty // shift 2) tm.loc
in
retty.term // (arg ::: shift 2)
public export
substCaseWRet : BContext 3 -> Term d n -> ScopeTerm d n -> Term d (3 + n)
substCaseWRet [< x, y, ih] dty retty =
let tm = Sup (BVT 2 x.loc) (BVT 1 y.loc) $ x.loc `extendL` y.loc
arg = Ann tm (dty // shift 3) tm.loc
in
sub1 (weakS 3 retty) arg
public export
substCaseSuccRet : BContext 2 -> ScopeTerm d n -> Term d (2 + n)
substCaseSuccRet [< p, ih] retty =
@ -95,6 +103,10 @@ parameters (defs : Definitions) {auto _ : (Has ErrorEff fs, Has NameGen fs)}
expectSig : Term d n -> Eff fs (Term d n, ScopeTerm d n)
expectSig = expect ExpectedSig `(Sig {fst, snd, _}) `((fst, snd))
export covering %inline
expectW : Term d n -> Eff fs (Term d n, ScopeTerm d n)
expectW = expect ExpectedW `(W {shape, body, _}) `((shape, body))
export covering %inline
expectEnum : Term d n -> Eff fs (SortedSet TagVal)
expectEnum = expect ExpectedEnum `(Enum {cases, _}) `(cases)
@ -143,6 +155,10 @@ parameters (defs : Definitions) {auto _ : (Has ErrorEff fs, Has NameGen fs)}
expectSig : Term 0 n -> Eff fs (Term 0 n, ScopeTerm 0 n)
expectSig = expect ExpectedSig `(Sig {fst, snd, _}) `((fst, snd))
export covering %inline
expectW : Term 0 n -> Eff fs (Term 0 n, ScopeTerm 0 n)
expectW = expect ExpectedW `(W {shape, body, _}) `((shape, body))
export covering %inline
expectEnum : Term 0 n -> Eff fs (SortedSet TagVal)
expectEnum = expect ExpectedEnum `(Enum {cases, _}) `(cases)

6
lib/Quox/Typing/Error.idr
View file

@ -58,6 +58,7 @@ data Error
= ExpectedTYPE Loc (NameContexts d n) (Term d n)
| ExpectedPi Loc (NameContexts d n) (Term d n)
| ExpectedSig Loc (NameContexts d n) (Term d n)
| ExpectedW Loc (NameContexts d n) (Term d n)
| ExpectedEnum Loc (NameContexts d n) (Term d n)
| ExpectedEq Loc (NameContexts d n) (Term d n)
| ExpectedNat Loc (NameContexts d n) (Term d n)
@ -116,6 +117,7 @@ Located Error where
(ExpectedTYPE loc _ _).loc = loc
(ExpectedPi loc _ _).loc = loc
(ExpectedSig loc _ _).loc = loc
(ExpectedW loc _ _).loc = loc
(ExpectedEnum loc _ _).loc = loc
(ExpectedEq loc _ _).loc = loc
(ExpectedNat loc _ _).loc = loc
@ -256,6 +258,10 @@ prettyErrorNoLoc showContext = \case
hangDSingle "expected a pair type, but got"
!(prettyTerm ctx.dnames ctx.tnames s)
ExpectedW _ ctx s =>
hangDSingle "expected an inductive (W) type, but got"
!(prettyTerm ctx.dnames ctx.tnames s)
ExpectedEnum _ ctx s =>
hangDSingle "expected an enumeration type, but got"
!(prettyTerm ctx.dnames ctx.tnames s)