module Quox.Whnf.Main import Quox.Whnf.Interface import Quox.Whnf.ComputeElimType import Quox.Whnf.TypeCase import Quox.Whnf.Coercion import Quox.Displace import Data.SnocVect %default total export covering CanWhnf Term Interface.isRedexT export covering CanWhnf Elim Interface.isRedexE covering CanWhnf Elim Interface.isRedexE where whnf defs ctx (F x u loc) with (lookupElim x defs) proof eq _ | Just y = whnf defs ctx $ setLoc loc $ displace u y _ | Nothing = pure $ Element (F x u loc) $ rewrite eq in Ah whnf _ _ (B i loc) = pure $ nred $ B i loc -- ((λ x ⇒ t) ∷ (π.x : A) → B) s ⇝ t[s∷A/x] ∷ B[s∷A/x] whnf defs ctx (App f s appLoc) = do Element f fnf <- whnf defs ctx f case nchoose $ isLamHead f of Left _ => case f of Ann (Lam {body, _}) (Pi {arg, res, _}) floc => let s = Ann s arg s.loc in whnf defs ctx $ Ann (sub1 body s) (sub1 res s) appLoc 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] whnf defs ctx (CasePair pi pair ret body caseLoc) = do Element pair pairnf <- whnf defs ctx pair case nchoose $ isPairHead pair of Left _ => case pair of Ann (Pair {fst, snd, _}) (Sig {fst = tfst, snd = tsnd, _}) pairLoc => let fst = Ann fst tfst fst.loc snd = Ann snd (sub1 tsnd fst) snd.loc in whnf defs ctx $ Ann (subN body [< fst, snd]) (sub1 ret pair) caseLoc Coe ty p q val _ => do sigCoe defs ctx pi ty p q val ret body caseLoc Right np => pure $ Element (CasePair pi pair ret body caseLoc) $ pairnf `orNo` np -- case 'a ∷ {a,…} return p ⇒ C of { 'a ⇒ u } ⇝ -- u ∷ C['a∷{a,…}/p] whnf defs ctx (CaseEnum pi tag ret arms caseLoc) = do Element tag tagnf <- whnf defs ctx tag case nchoose $ isTagHead tag of Left _ => case tag of Ann (Tag t _) (Enum ts _) _ => let ty = sub1 ret tag in case lookup t arms of Just arm => whnf defs ctx $ Ann arm ty arm.loc Nothing => throw $ MissingEnumArm caseLoc t (keys arms) Coe ty p q val _ => -- there is nowhere an equality can be hiding inside an enum type whnf defs ctx $ CaseEnum pi (Ann val (dsub1 ty q) val.loc) ret arms caseLoc Right nt => pure $ Element (CaseEnum pi tag ret arms caseLoc) $ tagnf `orNo` nt -- case zero ∷ ℕ return p ⇒ C of { zero ⇒ u; … } ⇝ -- u ∷ C[zero∷ℕ/p] -- -- case succ n ∷ ℕ return p ⇒ C of { succ n', π.ih ⇒ u; … } ⇝ -- u[n∷ℕ/n', (case n ∷ ℕ ⋯)/ih] ∷ C[succ n ∷ ℕ/p] whnf defs ctx (CaseNat pi piIH nat ret zer suc caseLoc) = do Element nat natnf <- whnf defs ctx nat case nchoose $ isNatHead nat of Left _ => let ty = sub1 ret nat in case nat of Ann (Zero _) (Nat _) _ => whnf defs ctx $ Ann zer ty zer.loc Ann (Succ n succLoc) (Nat natLoc) _ => let nn = Ann n (Nat natLoc) succLoc tm = subN suc [< nn, CaseNat pi piIH nn ret zer suc caseLoc] in whnf defs ctx $ Ann tm ty caseLoc Coe ty p q val _ => -- same deal as Enum whnf defs ctx $ CaseNat pi piIH (Ann val (dsub1 ty q) val.loc) ret zer suc caseLoc Right nn => pure $ Element (CaseNat pi piIH nat ret zer suc caseLoc) (natnf `orNo` nn) -- case [t] ∷ [π.A] return p ⇒ C of { [x] ⇒ u } ⇝ -- u[t∷A/x] ∷ C[[t] ∷ [π.A]/p] whnf defs ctx (CaseBox pi box ret body caseLoc) = do Element box boxnf <- whnf defs ctx box case nchoose $ isBoxHead box of Left _ => case box of Ann (Box val boxLoc) (BOX q bty tyLoc) _ => let ty = sub1 ret box in whnf defs ctx $ Ann (sub1 body (Ann val bty val.loc)) ty caseLoc Coe ty p q val _ => boxCoe defs ctx pi ty p q val ret body caseLoc Right nb => pure $ Element (CaseBox pi box ret body caseLoc) (boxnf `orNo` nb) -- e : Eq (𝑗 ⇒ A) t u ⊢ e @0 ⇝ t ∷ A‹0/𝑗› -- e : Eq (𝑗 ⇒ A) t u ⊢ e @1 ⇝ u ∷ A‹1/𝑗› -- -- ((δ 𝑖 ⇒ s) ∷ Eq (𝑗 ⇒ A) t u) @𝑘 ⇝ s‹𝑘/𝑖› ∷ A‹𝑘/𝑗› whnf defs ctx (DApp f p appLoc) = do Element f fnf <- whnf defs ctx f case nchoose $ isDLamHead f of Left _ => case f of Ann (DLam {body, _}) (Eq {ty, l, r, _}) _ => whnf defs ctx $ Ann (endsOr (setLoc appLoc l) (setLoc appLoc r) (dsub1 body p) p) (dsub1 ty p) appLoc Coe ty p' q' val _ => eqCoe defs ctx ty p' q' val p appLoc Right ndlh => case p of K e _ => do Eq {l, r, ty, _} <- whnf0 defs ctx =<< computeElimType defs ctx f | ty => throw $ ExpectedEq ty.loc ctx.names ty whnf defs ctx $ ends (Ann (setLoc appLoc l) ty.zero appLoc) (Ann (setLoc appLoc r) ty.one appLoc) e B {} => pure $ Element (DApp f p appLoc) (fnf `orNo` ndlh `orNo` Ah) -- e ∷ A ⇝ e whnf defs ctx (Ann s a annLoc) = do Element s snf <- whnf defs ctx s case nchoose $ isE s of Left _ => let E e = s in pure $ Element e $ noOr2 snf Right ne => do Element a anf <- whnf defs ctx a pure $ Element (Ann s a annLoc) (ne `orNo` snf `orNo` anf) whnf defs ctx (Coe ty p q val coeLoc) = -- 𝑖 ∉ fv(A) -- ------------------------------- -- coe (𝑖 ⇒ A) @p @q s ⇝ s ∷ A -- -- [fixme] needs a real equality check between ty.zero and ty.one case dsqueezed ty of Right ty => whnf defs ctx $ Ann val ty coeLoc Left ([< i], ty) => case p `decEqv` q of -- coe (𝑖 ⇒ A) @p @p s ⇝ (s ∷ A‹p/𝑖›) Yes _ => whnf defs ctx $ Ann val (ty // one p) coeLoc No npq => do Element ty tynf <- whnf defs (extendDim i ctx) ty case nchoose $ canPushCoe ty val of Left pc => pushCoe defs ctx i ty p q val coeLoc Right npc => pure $ Element (Coe (SY [< i] ty) p q val coeLoc) (tynf `orNo` npc `orNo` notYesNo npq) whnf defs ctx (Comp ty p q val r zero one compLoc) = case p `decEqv` q of -- comp [A] @p @p s @r { ⋯ } ⇝ s ∷ A Yes y => whnf defs ctx $ Ann val ty compLoc No npq => case r of -- comp [A] @p @q s @0 { 0 𝑗 ⇒ t₀; ⋯ } ⇝ t₀‹q/𝑗› ∷ A K Zero _ => whnf defs ctx $ Ann (dsub1 zero q) ty compLoc -- comp [A] @p @q s @1 { 1 𝑗 ⇒ t₁; ⋯ } ⇝ t₁‹q/𝑗› ∷ A K One _ => whnf defs ctx $ Ann (dsub1 one q) ty compLoc B {} => pure $ Element (Comp ty p q val r zero one compLoc) (notYesNo npq `orNo` Ah) whnf defs ctx (TypeCase ty ret arms def tcLoc) = do Element ty tynf <- whnf defs ctx ty Element ret retnf <- whnf defs ctx ret case nchoose $ isAnnTyCon ty of Left y => let Ann ty (TYPE u _) _ = ty in reduceTypeCase defs ctx ty u ret arms def tcLoc Right nt => pure $ Element (TypeCase ty ret arms def tcLoc) (tynf `orNo` retnf `orNo` nt) whnf defs ctx (CloE (Sub el th)) = whnf defs ctx $ pushSubstsWith' id th el whnf defs ctx (DCloE (Sub el th)) = whnf defs ctx $ pushSubstsWith' th id el covering CanWhnf Term Interface.isRedexT where whnf _ _ t@(TYPE {}) = pure $ nred t whnf _ _ t@(Pi {}) = pure $ nred t whnf _ _ t@(Lam {}) = pure $ nred t whnf _ _ t@(Sig {}) = pure $ nred t whnf _ _ t@(Pair {}) = pure $ nred t whnf _ _ t@(Enum {}) = pure $ nred t whnf _ _ t@(Tag {}) = pure $ nred t whnf _ _ t@(Eq {}) = pure $ nred t whnf _ _ t@(DLam {}) = pure $ nred t whnf _ _ t@(Nat {}) = pure $ nred t whnf _ _ t@(Zero {}) = pure $ nred t whnf _ _ t@(Succ {}) = pure $ nred t whnf _ _ t@(BOX {}) = pure $ nred t whnf _ _ t@(Box {}) = pure $ nred t -- s ∷ A ⇝ s (in term context) whnf defs ctx (E e) = do Element e enf <- whnf defs ctx e case nchoose $ isAnn e of Left _ => let Ann {tm, _} = e in pure $ Element tm $ noOr1 $ noOr2 enf Right na => pure $ Element (E e) $ na `orNo` enf whnf defs ctx (CloT (Sub tm th)) = whnf defs ctx $ pushSubstsWith' id th tm whnf defs ctx (DCloT (Sub tm th)) = whnf defs ctx $ pushSubstsWith' th id tm