module Quox.Equal import Quox.BoolExtra import public Quox.Typing import Data.Maybe import Quox.EffExtra %default total public export EqModeState : Type -> Type EqModeState = State EqMode public export Equal : Type -> Type Equal = Eff [ErrorEff, DefsReader, NameGen] public export Equal_ : Type -> Type Equal_ = Eff [ErrorEff, NameGen, EqModeState] export runEqualWith_ : EqMode -> NameSuf -> Equal_ a -> (Either Error a, NameSuf) runEqualWith_ mode suf act = extract $ runNameGenWith suf $ runExcept $ evalState mode act export runEqual_ : EqMode -> Equal_ a -> Either Error a runEqual_ mode act = fst $ runEqualWith_ mode 0 act export runEqualWith : NameSuf -> Definitions -> Equal a -> (Either Error a, NameSuf) runEqualWith suf defs act = extract $ runStateAt GEN suf $ runReaderAt DEFS defs $ runExcept act export runEqual : Definitions -> Equal a -> Either Error a runEqual defs act = fst $ runEqualWith 0 defs act export %inline mode : Has EqModeState fs => Eff fs EqMode mode = get parameters (loc : Loc) (ctx : EqContext n) private %inline clashT : Term 0 n -> Term 0 n -> Term 0 n -> Equal_ a clashT ty s t = throw $ ClashT loc ctx !mode ty s t private %inline clashTy : Term 0 n -> Term 0 n -> Equal_ a clashTy s t = throw $ ClashTy loc ctx !mode s t private %inline clashE : Elim 0 n -> Elim 0 n -> Equal_ a clashE e f = throw $ ClashE loc ctx !mode e f private %inline wrongType : Term 0 n -> Term 0 n -> Equal_ a wrongType ty s = throw $ WrongType loc ctx ty s public export %inline sameTyCon : (s, t : Term d n) -> (0 ts : So (isTyConE s)) => (0 tt : So (isTyConE t)) => Bool sameTyCon (TYPE {}) (TYPE {}) = True sameTyCon (TYPE {}) _ = False sameTyCon (Pi {}) (Pi {}) = True sameTyCon (Pi {}) _ = False sameTyCon (Sig {}) (Sig {}) = True sameTyCon (Sig {}) _ = False sameTyCon (Enum {}) (Enum {}) = True sameTyCon (Enum {}) _ = False sameTyCon (Eq {}) (Eq {}) = True sameTyCon (Eq {}) _ = False sameTyCon (Nat {}) (Nat {}) = True sameTyCon (Nat {}) _ = False sameTyCon (BOX {}) (BOX {}) = True sameTyCon (BOX {}) _ = False sameTyCon (E {}) (E {}) = True sameTyCon (E {}) _ = False ||| true if a type is known to be a subsingleton purely by its form. ||| a subsingleton is a type with only zero or one possible values. ||| equality/subtyping accepts immediately on values of subsingleton types. ||| ||| * a function type is a subsingleton if its codomain is. ||| * a pair type is a subsingleton if both its elements are. ||| * equality types are subsingletons because of uip. ||| * an enum type is a subsingleton if it has zero or one tags. ||| * a box type is a subsingleton if its content is public export covering isSubSing : {n : Nat} -> Definitions -> EqContext n -> Term 0 n -> Equal_ Bool isSubSing defs ctx ty0 = do Element ty0 nc <- whnf defs ctx ty0.loc ty0 case ty0 of TYPE {} => pure False Pi {arg, res, _} => isSubSing defs (extendTy Zero res.name arg ctx) res.term Sig {fst, snd, _} => isSubSing defs ctx fst `andM` isSubSing defs (extendTy Zero snd.name fst ctx) snd.term Enum {cases, _} => pure $ length (SortedSet.toList cases) <= 1 Eq {} => pure True Nat {} => pure False BOX {ty, _} => isSubSing defs ctx ty E (Ann {tm, _}) => isSubSing defs ctx tm E _ => pure False Lam {} => pure False Pair {} => pure False Tag {} => pure False DLam {} => pure False Zero {} => pure False Succ {} => pure False Box {} => pure False export ensureTyCon : Has ErrorEff fs => (loc : Loc) -> (ctx : EqContext n) -> (t : Term 0 n) -> Eff fs (So (isTyConE t)) ensureTyCon loc ctx t = case nchoose $ isTyConE t of Left y => pure y Right n => throw $ NotType loc (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 lift $ computeElimType defs (toWhnfContext ectx) e parameters (defs : Definitions) mutual namespace Term ||| `compare0 ctx ty s t` compares `s` and `t` at type `ty`, according to ||| the current variance `mode`. ||| ||| ⚠ **assumes that `s`, `t` have already been checked against `ty`**. ⚠ export covering %inline compare0 : EqContext n -> (ty, s, t : Term 0 n) -> Equal_ () compare0 ctx ty s t = wrapErr (WhileComparingT ctx !mode ty s t) $ do let Val n = ctx.termLen Element ty' _ <- whnf defs ctx ty.loc ty Element s' _ <- whnf defs ctx s.loc s Element t' _ <- whnf defs ctx t.loc t tty <- ensureTyCon ty.loc ctx ty' compare0' ctx ty' s' t' ||| converts an elim "Γ ⊢ e" to "Γ, x ⊢ e x", for comparing with ||| a lambda "Γ ⊢ λx ⇒ t" that has been converted to "Γ, x ⊢ t". private %inline toLamBody : Elim d n -> Term d (S n) toLamBody e = E $ App (weakE 1 e) (BVT 0 e.loc) e.loc private covering compare0' : EqContext n -> (ty, s, t : Term 0 n) -> (0 _ : NotRedex defs ty) => (0 _ : So (isTyConE ty)) => (0 _ : NotRedex defs s) => (0 _ : NotRedex defs t) => Equal_ () compare0' ctx (TYPE {}) s t = compareType ctx s t compare0' ctx ty@(Pi {qty, arg, res, _}) s t {n} = local_ Equal $ case (s, t) of -- Γ, x : A ⊢ s = t : B -- ------------------------------------------- -- Γ ⊢ (λ x ⇒ s) = (λ x ⇒ t) : (π·x : A) → B (Lam b1 {}, Lam b2 {}) => compare0 ctx' res.term b1.term b2.term -- Γ, x : A ⊢ s = e x : B -- ----------------------------------- -- Γ ⊢ (λ x ⇒ s) = e : (π·x : A) → B (E e, Lam b {}) => eta s.loc e b (Lam b {}, E e) => eta s.loc e b (E e, E f) => Elim.compare0 ctx e f (Lam {}, t) => wrongType t.loc ctx ty t (E _, t) => wrongType t.loc ctx ty t (s, _) => wrongType s.loc ctx ty s where ctx' : EqContext (S n) ctx' = extendTy qty res.name arg ctx eta : Loc -> Elim 0 n -> ScopeTerm 0 n -> Equal_ () eta _ e (S _ (Y b)) = compare0 ctx' res.term (toLamBody e) b eta loc e (S _ (N _)) = clashT loc ctx ty s t compare0' ctx ty@(Sig {fst, snd, _}) s t = local_ Equal $ case (s, t) of -- Γ ⊢ s₁ = t₁ : A Γ ⊢ s₂ = t₂ : B{s₁/x} -- -------------------------------------------- -- Γ ⊢ (s₁, t₁) = (s₂,t₂) : (x : A) × B -- -- [todo] η for π ≥ 0 maybe (Pair sFst sSnd {}, Pair tFst tSnd {}) => do compare0 ctx fst sFst tFst compare0 ctx (sub1 snd (Ann sFst fst fst.loc)) sSnd tSnd (E e, E f) => Elim.compare0 ctx e f (Pair {}, E _) => clashT s.loc ctx ty s t (E _, Pair {}) => clashT s.loc ctx ty s t (Pair {}, 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 -- -------------------- -- Γ ⊢ `t = `t : {ts} -- -- t ∈ ts is in the typechecker, not here, ofc (Tag t1 {}, Tag t2 {}) => unless (t1 == t2) $ clashT s.loc ctx ty s t (E e, E f) => Elim.compare0 ctx e f (Tag {}, E _) => clashT s.loc ctx ty s t (E _, Tag {}) => clashT s.loc ctx ty s t (Tag {}, t) => wrongType t.loc ctx ty t (E _, t) => wrongType t.loc ctx ty t (s, _) => wrongType s.loc ctx ty s compare0' _ (Eq {}) _ _ = -- ✨ uip ✨ -- -- ---------------------------- -- Γ ⊢ e = f : Eq [i ⇒ A] s t pure () compare0' ctx nat@(Nat {}) s t = local_ Equal $ case (s, t) of -- --------------- -- Γ ⊢ 0 = 0 : ℕ (Zero {}, Zero {}) => pure () -- Γ ⊢ s = t : ℕ -- ------------------------- -- Γ ⊢ succ s = succ t : ℕ (Succ s' {}, Succ t' {}) => compare0 ctx nat s' t' (E e, E f) => Elim.compare0 ctx e f (Zero {}, Succ {}) => clashT s.loc ctx nat s t (Zero {}, E _) => clashT s.loc ctx nat s t (Succ {}, Zero {}) => clashT s.loc ctx nat s t (Succ {}, E _) => clashT s.loc ctx nat s t (E _, Zero {}) => clashT s.loc ctx nat s t (E _, Succ {}) => clashT s.loc ctx nat s t (Zero {}, t) => wrongType t.loc ctx nat t (Succ {}, t) => wrongType t.loc ctx nat t (E _, t) => wrongType t.loc ctx nat t (s, _) => wrongType s.loc ctx nat s compare0' ctx ty@(BOX q ty' {}) s t = local_ Equal $ case (s, t) of -- Γ ⊢ s = t : A -- ----------------------- -- Γ ⊢ [s] = [t] : [π.A] (Box s' {}, Box t' {}) => compare0 ctx ty' s' t' (E e, E f) => Elim.compare0 ctx e f (Box {}, 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@(E _) s t = do -- a neutral type can only be inhabited by neutral values -- e.g. an abstract value in an abstract type, bound variables, … let E e = s | _ => wrongType s.loc ctx ty s E f = t | _ => wrongType t.loc ctx ty t Elim.compare0 ctx e f ||| compares two types, using the current variance `mode` for universes. ||| fails if they are not types, even if they would happen to be equal. export covering %inline compareType : EqContext n -> (s, t : Term 0 n) -> Equal_ () compareType ctx s t = do let Val n = ctx.termLen Element s' _ <- whnf defs ctx s.loc s Element t' _ <- whnf defs ctx t.loc t ts <- ensureTyCon s.loc ctx s' tt <- ensureTyCon t.loc ctx t' st <- either pure (const $ clashTy s.loc ctx s' t') $ nchoose $ sameTyCon s' t' compareType' ctx s' t' private covering compareType' : EqContext n -> (s, t : Term 0 n) -> (0 _ : NotRedex defs s) => (0 _ : So (isTyConE s)) => (0 _ : NotRedex defs t) => (0 _ : So (isTyConE t)) => (0 _ : So (sameTyCon s t)) => Equal_ () -- equality is the same as subtyping, except with the -- "≤" in the TYPE rule being replaced with "=" compareType' ctx a@(TYPE k {}) (TYPE l {}) = -- 𝓀 ≤ ℓ -- ---------------------- -- Γ ⊢ Type 𝓀 <: Type ℓ expectModeU a.loc !mode k l compareType' ctx a@(Pi {qty = sQty, arg = sArg, res = sRes, _}) (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 local flip $ compareType ctx sArg tArg -- contra compareType (extendTy Zero sRes.name sArg ctx) sRes.term tRes.term compareType' ctx (Sig {fst = sFst, snd = sSnd, _}) (Sig {fst = tFst, snd = tSnd, _}) = do -- Γ ⊢ A₁ <: A₂ Γ, x : A₁ ⊢ B₁ <: B₂ -- -------------------------------------- -- Γ ⊢ (x : A₁) × B₁ <: (x : A₂) × B₂ compareType ctx sFst tFst compareType (extendTy Zero sSnd.name sFst ctx) sSnd.term tSnd.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 ⊢ 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 local_ Equal $ do Term.compare0 ctx ty.zero sl tl Term.compare0 ctx ty.one sr tr compareType' ctx s@(Enum tags1 {}) t@(Enum tags2 {}) = do -- ------------------ -- Γ ⊢ {ts} <: {ts} -- -- no subtyping based on tag subsets, since that would need -- a runtime coercion unless (tags1 == tags2) $ clashTy s.loc ctx s t compareType' ctx (Nat {}) (Nat {}) = -- ------------ -- Γ ⊢ ℕ <: ℕ pure () compareType' ctx (BOX pi a loc) (BOX rh b {}) = do expectEqualQ loc pi rh compareType ctx a b compareType' ctx (E e) (E f) = do -- no fanciness needed here cos anything other than a neutral -- has been inlined by whnf Elim.compare0 ctx e f namespace Elim -- [fixme] the following code ends up repeating a lot of work in the -- computeElimType calls. the results should be shared better ||| compare two eliminations according to the given variance `mode`. ||| ||| ⚠ **assumes that they have both been typechecked, and have ||| equal types.** ⚠ export covering %inline compare0 : EqContext n -> (e, f : Elim 0 n) -> Equal_ () compare0 ctx e f = wrapErr (WhileComparingE ctx !mode e f) $ do let Val n = ctx.termLen Element e' ne <- whnf defs ctx e.loc e Element f' nf <- whnf defs ctx f.loc f unless !(isSubSing defs ctx =<< computeElimTypeE defs ctx e') $ compare0' ctx e' f' ne nf private covering compare0' : EqContext n -> (e, f : Elim 0 n) -> (0 ne : NotRedex defs e) -> (0 nf : NotRedex defs f) -> Equal_ () compare0' ctx e@(F x u _) f@(F y v _) _ _ = unless (x == y && u == v) $ clashE e.loc ctx e f compare0' ctx e@(F {}) f _ _ = clashE e.loc ctx e f compare0' ctx e@(B i _) f@(B j _) _ _ = unless (i == j) $ clashE e.loc ctx e f compare0' ctx e@(B {}) f _ _ = clashE e.loc ctx e f -- Ψ | Γ ⊢ e = f ⇒ π.(x : A) → B -- Ψ | Γ ⊢ s = t ⇐ A -- ------------------------------- -- Ψ | Γ ⊢ e s = f t ⇒ B[s∷A/x] compare0' ctx (App e s eloc) (App f t floc) ne nf = local_ Equal $ do compare0 ctx e f (_, arg, _) <- expectPi defs ctx eloc =<< computeElimTypeE defs ctx e @{noOr1 ne} Term.compare0 ctx arg s t compare0' ctx e@(App {}) f _ _ = clashE e.loc ctx e f -- Ψ | Γ ⊢ e = f ⇒ (x : A) × B -- Ψ | Γ, 0.p : (x : A) × B ⊢ Q = R -- Ψ | Γ, x : A, y : B ⊢ s = t ⇐ Q[((x, y) ∷ (x : A) × B)/p] -- ----------------------------------------------------------- -- Ψ | Γ ⊢ caseπ e return Q of { (x, y) ⇒ s } -- = caseπ f return R of { (x, y) ⇒ t } ⇒ Q[e/p] compare0' ctx (CasePair epi e eret ebody eloc) (CasePair fpi f fret fbody {}) 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 (fst, snd) <- expectSig defs ctx eloc ety let [< x, y] = ebody.names Term.compare0 (extendTyN [< (epi, x, fst), (epi, y, snd.term)] ctx) (substCasePairRet ebody.names ety eret) ebody.term fbody.term expectEqualQ e.loc epi fpi compare0' ctx e@(CasePair {}) 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}] -- -------------------------------------------------- -- Ψ | Γ ⊢ caseπ e return Q of { '𝐚ᵢ ⇒ sᵢ } -- = caseπ f return R of { '𝐚ᵢ ⇒ tᵢ } ⇒ Q[e/x] compare0' ctx (CaseEnum epi e eret earms eloc) (CaseEnum fpi f fret farms 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 for_ !(expectEnum defs ctx eloc ety) $ \t => do l <- lookupArm eloc t earms r <- lookupArm floc t farms compare0 ctx (sub1 eret $ Ann (Tag t l.loc) ety l.loc) l r expectEqualQ eloc epi fpi where lookupArm : Loc -> TagVal -> CaseEnumArms d n -> Equal_ (Term d n) lookupArm loc t arms = case lookup t arms of Just arm => pure arm Nothing => throw $ TagNotIn loc t (fromList $ keys arms) compare0' ctx e@(CaseEnum {}) f _ _ = clashE e.loc ctx e f -- Ψ | Γ ⊢ e = f ⇒ ℕ -- Ψ | Γ, x : ℕ ⊢ Q = R -- Ψ | Γ ⊢ s₀ = t₀ ⇐ Q[(0 ∷ ℕ)/x] -- Ψ | Γ, x : ℕ, y : Q ⊢ s₁ = t₁ ⇐ Q[(succ x ∷ ℕ)/x] -- ----------------------------------------------------- -- Ψ | Γ ⊢ caseπ e return Q of { 0 ⇒ s₀; x, π.y ⇒ s₁ } -- = caseπ f return R of { 0 ⇒ t₀; x, π.y ⇒ t₁ } -- ⇒ Q[e/x] compare0' ctx (CaseNat epi epi' e eret ezer esuc eloc) (CaseNat fpi fpi' f fret fzer fsuc 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 compare0 ctx (sub1 eret (Ann (Zero ezer.loc) (Nat ezer.loc) ezer.loc)) ezer fzer let [< p, ih] = esuc.names compare0 (extendTyN [< (epi, p, Nat p.loc), (epi', ih, eret.term)] ctx) (substCaseSuccRet esuc.names eret) esuc.term fsuc.term expectEqualQ e.loc epi fpi expectEqualQ e.loc epi' fpi' compare0' ctx e@(CaseNat {}) f _ _ = clashE e.loc ctx e f -- Ψ | Γ ⊢ e = f ⇒ [ρ. A] -- Ψ | Γ, x : [ρ. A] ⊢ Q = R -- Ψ | Γ, x : A ⊢ s = t ⇐ Q[([x] ∷ [ρ. A])/x] -- -------------------------------------------------- -- Ψ | Γ ⊢ caseπ e return Q of { [x] ⇒ s } -- = caseπ f return R of { [x] ⇒ t } ⇒ Q[e/x] compare0' ctx (CaseBox epi e eret ebody eloc) (CaseBox 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 (q, ty) <- expectBOX defs ctx eloc ety compare0 (extendTy (epi * q) ebody.name ty ctx) (substCaseBoxRet ebody.name ety eret) ebody.term fbody.term expectEqualQ eloc epi fpi compare0' ctx e@(CaseBox {}) f _ _ = clashE e.loc ctx e f -- all dim apps replaced with ends by whnf compare0' _ (DApp _ (K {}) _) _ ne _ = void $ absurd $ noOr2 $ noOr2 ne compare0' _ _ (DApp _ (K {}) _) _ nf = void $ absurd $ noOr2 $ noOr2 nf -- Ψ | Γ ⊢ s <: t : B -- -------------------------------- -- Ψ | Γ ⊢ (s ∷ A) <: (t ∷ B) ⇒ B -- -- and similar for :> and A compare0' ctx (Ann s a _) (Ann t b _) _ _ = let ty = case !mode of Super => a; _ => b in Term.compare0 ctx ty s t -- Ψ | Γ ⊢ A‹p₁/𝑖› <: B‹p₂/𝑖› -- Ψ | Γ ⊢ A‹q₁/𝑖› <: B‹q₂/𝑖› -- Ψ | Γ ⊢ e <: f ⇒ _ -- (non-neutral forms have the coercion already pushed in) -- ----------------------------------------------------------- -- Ψ | Γ ⊢ coe [𝑖 ⇒ A] @p₁ @q₁ e -- <: coe [𝑖 ⇒ B] @p₂ @q₂ f ⇒ B‹q₂/𝑖› compare0' ctx (Coe ty1 p1 q1 (E val1) _) (Coe ty2 p2 q2 (E val2) _) ne nf = do compareType ctx (dsub1 ty1 p1) (dsub1 ty2 p2) compareType ctx (dsub1 ty1 q1) (dsub1 ty2 q2) compare0 ctx val1 val2 compare0' ctx e@(Coe {}) f _ _ = clashE e.loc ctx e f -- (no neutral compositions in a closed dctx) compare0' _ (Comp {r = K e _, _}) _ ne _ = void $ absurd $ noOr2 ne compare0' _ (Comp {r = B i _, _}) _ _ _ = absurd i compare0' _ _ (Comp {r = K _ _, _}) _ nf = void $ absurd $ noOr2 nf -- (type case equality purely structural) compare0' ctx (TypeCase ty1 ret1 arms1 def1 eloc) (TypeCase ty2 ret2 arms2 def2 floc) ne _ = local_ Equal $ do compare0 ctx ty1 ty2 u <- expectTYPE defs ctx eloc =<< computeElimTypeE defs ctx ty1 @{noOr1 ne} compareType ctx ret1 ret2 compareType ctx def1 def2 for_ allKinds $ \k => compareArm ctx k ret1 u (lookupPrecise k arms1) (lookupPrecise k arms2) def1 compare0' ctx e@(TypeCase {}) f _ _ = clashE e.loc ctx e f -- Ψ | Γ ⊢ s <: f ⇐ A -- -------------------------- -- Ψ | Γ ⊢ (s ∷ A) <: f ⇒ A -- -- and vice versa compare0' ctx (Ann s a _) f _ _ = Term.compare0 ctx a s (E f) compare0' ctx e (Ann t b _) _ _ = Term.compare0 ctx b (E e) t compare0' ctx e@(Ann {}) f _ _ = clashE e.loc 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 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 KSig 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 compareArm_ ctx KEq ret u b1 b2 = do let [< a0, a1, a, l, r] = b1.names ctx = extendTyN [< (Zero, a0, TYPE u a0.loc), (Zero, a1, TYPE u a1.loc), (Zero, a, Eq0 (TYPE u a.loc) (BVT 1 a0.loc) (BVT 0 a1.loc) a.loc), (Zero, l, BVT 2 a0.loc), (Zero, r, BVT 2 a1.loc)] 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 b1.name.loc) ctx compare0 ctx (weakT 1 ret) b1.term b1.term parameters (loc : Loc) (ctx : TyContext d n) -- [todo] only split on the dvars that are actually used anywhere in -- the calls to `splits` parameters (mode : EqMode) private fromEqual_ : Equal_ a -> Equal a fromEqual_ act = lift $ evalState mode act private eachFace : Applicative f => (EqContext n -> DSubst d 0 -> f ()) -> f () eachFace act = for_ (splits loc ctx.dctx) $ \th => act (makeEqContext ctx th) th private runCompare : (Definitions -> EqContext n -> DSubst d 0 -> Equal_ ()) -> Equal () runCompare act = fromEqual_ $ eachFace $ act !(askAt DEFS) namespace Term export covering compare : (ty, s, t : Term d n) -> Equal () compare ty s t = runCompare $ \defs, ectx, th => compare0 defs ectx (ty // th) (s // th) (t // th) export covering compareType : (s, t : Term d n) -> Equal () compareType s t = runCompare $ \defs, ectx, th => compareType defs ectx (s // th) (t // th) namespace Elim ||| you don't have to pass the type in but the arguments must still be ||| of the same type!! export covering compare : (e, f : Elim d n) -> Equal () compare e f = runCompare $ \defs, ectx, th => compare0 defs ectx (e // th) (f // th) namespace Term export covering %inline equal, sub, super : (ty, s, t : Term d n) -> Equal () equal = compare Equal sub = compare Sub super = compare Super export covering %inline equalType, subtype, supertype : (s, t : Term d n) -> Equal () equalType = compareType Equal subtype = compareType Sub supertype = compareType Super namespace Elim export covering %inline equal, sub, super : (e, f : Elim d n) -> Equal () equal = compare Equal sub = compare Sub super = compare Super