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 sg (F x u loc) with (lookupElim x u defs) proof eq _ | Just y = whnf defs ctx sg $ setLoc loc 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 sg (App f s appLoc) = do Element f fnf <- whnf defs ctx sg 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 sg $ Ann (sub1 body s) (sub1 res s) appLoc Coe ty p q val _ => piCoe defs ctx sg 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] -- -- 0 · case e return p ⇒ C of { (a, b) ⇒ u } ⇝ -- u[fst e/a, snd e/b] ∷ C[e/p] whnf defs ctx sg (CasePair pi pair ret body caseLoc) = do Element pair pairnf <- whnf defs ctx sg 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 sg $ Ann (subN body [< fst, snd]) (sub1 ret pair) caseLoc Coe ty p q val _ => do sigCoe defs ctx sg pi ty p q val ret body caseLoc Right np => case sg `decEq` SZero of Yes Refl => whnf defs ctx SZero $ Ann (subN body [< Fst pair caseLoc, Snd pair caseLoc]) (sub1 ret pair) caseLoc No n0 => pure $ Element (CasePair pi pair ret body caseLoc) (pairnf `orNo` np `orNo` notYesNo n0) -- fst ((s, t) ∷ (x : A) × B) ⇝ s ∷ A whnf defs ctx sg (Fst pair fstLoc) = do Element pair pairnf <- whnf defs ctx sg pair case nchoose $ isPairHead pair of Left _ => case pair of Ann (Pair {fst, snd, _}) (Sig {fst = tfst, snd = tsnd, _}) pairLoc => whnf defs ctx sg $ Ann fst tfst pairLoc Coe ty p q val _ => do fstCoe defs ctx sg ty p q val fstLoc Right np => pure $ Element (Fst pair fstLoc) (pairnf `orNo` np) -- snd ((s, t) ∷ (x : A) × B) ⇝ t ∷ B[(s ∷ A)/x] whnf defs ctx sg (Snd pair sndLoc) = do Element pair pairnf <- whnf defs ctx sg pair case nchoose $ isPairHead pair of Left _ => case pair of Ann (Pair {fst, snd, _}) (Sig {fst = tfst, snd = tsnd, _}) pairLoc => whnf defs ctx sg $ Ann snd (sub1 tsnd (Ann fst tfst fst.loc)) sndLoc Coe ty p q val _ => do sndCoe defs ctx sg ty p q val sndLoc Right np => pure $ Element (Snd pair sndLoc) (pairnf `orNo` np) -- case 'a ∷ {a,…} return p ⇒ C of { 'a ⇒ u } ⇝ -- u ∷ C['a∷{a,…}/p] whnf defs ctx sg (CaseEnum pi tag ret arms caseLoc) = do Element tag tagnf <- whnf defs ctx sg 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 sg $ 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 sg $ 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 sg (CaseNat pi piIH nat ret zer suc caseLoc) = do Element nat natnf <- whnf defs ctx sg nat case nchoose $ isNatHead nat of Left _ => let ty = sub1 ret nat in case nat of Ann (Zero _) (Nat _) _ => whnf defs ctx sg $ 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 sg $ Ann tm ty caseLoc Coe ty p q val _ => -- same deal as Enum whnf defs ctx sg $ 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 sg (CaseBox pi box ret body caseLoc) = do Element box boxnf <- whnf defs ctx sg 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 sg $ Ann (sub1 body (Ann val bty val.loc)) ty caseLoc Coe ty p q val _ => boxCoe defs ctx sg 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 sg (DApp f p appLoc) = do Element f fnf <- whnf defs ctx sg f case nchoose $ isDLamHead f of Left _ => case f of Ann (DLam {body, _}) (Eq {ty, l, r, _}) _ => whnf defs ctx sg $ Ann (endsOr (setLoc appLoc l) (setLoc appLoc r) (dsub1 body p) p) (dsub1 ty p) appLoc Coe ty p' q' val _ => eqCoe defs ctx sg ty p' q' val p appLoc Right ndlh => case p of K e _ => do Eq {l, r, ty, _} <- computeWhnfElimType0 defs ctx sg f | ty => throw $ ExpectedEq ty.loc ctx.names ty whnf defs ctx sg $ 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 sg (Ann s a annLoc) = do Element s snf <- whnf defs ctx sg 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 SZero a pure $ Element (Ann s a annLoc) (ne `orNo` snf `orNo` anf) whnf defs ctx sg (Coe sty p q val coeLoc) = -- 𝑖 ∉ fv(A) -- ------------------------------- -- coe (𝑖 ⇒ A) @p @q s ⇝ s ∷ A -- -- [fixme] needs a real equality check between A‹0/𝑖› and A‹1/𝑖› case dsqueeze sty {f = Term} of ([< i], Left ty) => case p `decEqv` q of -- coe (𝑖 ⇒ A) @p @p s ⇝ (s ∷ A‹p/𝑖›) Yes _ => whnf defs ctx sg $ Ann val (dsub1 sty p) coeLoc No npq => do Element ty tynf <- whnf defs (extendDim i ctx) SZero ty case nchoose $ canPushCoe sg ty val of Left pc => pushCoe defs ctx sg i ty p q val coeLoc Right npc => pure $ Element (Coe (SY [< i] ty) p q val coeLoc) (tynf `orNo` npc `orNo` notYesNo npq) (_, Right ty) => whnf defs ctx sg $ Ann val ty coeLoc whnf defs ctx sg (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 sg $ 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 sg $ Ann (dsub1 zero q) ty compLoc -- comp [A] @p @q s @1 { 1 𝑗 ⇒ t₁; ⋯ } ⇝ t₁‹q/𝑗› ∷ A K One _ => whnf defs ctx sg $ 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 sg (TypeCase ty ret arms def tcLoc) = case sg `decEq` SZero of Yes Refl => do Element ty tynf <- whnf defs ctx SZero ty Element ret retnf <- whnf defs ctx SZero 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) No _ => throw $ ClashQ tcLoc sg.qty Zero whnf defs ctx sg (CloE (Sub el th)) = whnf defs ctx sg $ pushSubstsWith' id th el whnf defs ctx sg (DCloE (Sub el th)) = whnf defs ctx sg $ 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 sg (E e) = do Element e enf <- whnf defs ctx sg 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 sg (CloT (Sub tm th)) = whnf defs ctx sg $ pushSubstsWith' id th tm whnf defs ctx sg (DCloT (Sub tm th)) = whnf defs ctx sg $ pushSubstsWith' th id tm