From 6b649aba925b6f7462da07599fe67ebb12a3460e Mon Sep 17 00:00:00 2001 From: Samuel Mimram Date: Wed, 28 Jul 2004 21:54:47 +0000 Subject: Imported Upstream version 8.0pl1 --- kernel/reduction.ml | 412 ++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 412 insertions(+) create mode 100644 kernel/reduction.ml (limited to 'kernel/reduction.ml') diff --git a/kernel/reduction.ml b/kernel/reduction.ml new file mode 100644 index 00000000..5428a40d --- /dev/null +++ b/kernel/reduction.ml @@ -0,0 +1,412 @@ +(************************************************************************) +(* v * The Coq Proof Assistant / The Coq Development Team *) +(* true + | Zupdate _::s -> is_empty_stack s + | Zshift _::s -> is_empty_stack s + | _ -> false + +(* Compute the lift to be performed on a term placed in a given stack *) +let el_stack el stk = + let n = + List.fold_left + (fun i z -> + match z with + Zshift n -> i+n + | _ -> i) + 0 + stk in + el_shft n el + +let compare_stack_shape stk1 stk2 = + let rec compare_rec bal stk1 stk2 = + match (stk1,stk2) with + ([],[]) -> bal=0 + | ((Zupdate _|Zshift _)::s1, _) -> compare_rec bal s1 stk2 + | (_, (Zupdate _|Zshift _)::s2) -> compare_rec bal stk1 s2 + | (Zapp l1::s1, _) -> compare_rec (bal+List.length l1) s1 stk2 + | (_, Zapp l2::s2) -> compare_rec (bal-List.length l2) stk1 s2 + | (Zcase(c1,_,_)::s1, Zcase(c2,_,_)::s2) -> + bal=0 (* && c1.ci_ind = c2.ci_ind *) && compare_rec 0 s1 s2 + | (Zfix(_,a1)::s1, Zfix(_,a2)::s2) -> + bal=0 && compare_rec 0 a1 a2 && compare_rec 0 s1 s2 + | (_,_) -> false in + compare_rec 0 stk1 stk2 + +let pure_stack lfts stk = + let rec pure_rec lfts stk = + match stk with + [] -> (lfts,[]) + | zi::s -> + (match (zi,pure_rec lfts s) with + (Zupdate _,lpstk) -> lpstk + | (Zshift n,(l,pstk)) -> (el_shft n l, pstk) + | (Zapp a1,(l,Zapp a2::pstk)) -> + (l,Zapp (List.map (fun t -> (l,t)) a1 @ a2)::pstk) + | (Zapp a, (l,pstk)) -> + (l,Zapp (List.map (fun t -> (l,t)) a)::pstk) + | (Zfix(fx,a),(l,pstk)) -> + let (lfx,pa) = pure_rec l a in + (l, Zfix((lfx,fx),pa)::pstk) + | (Zcase(ci,p,br),(l,pstk)) -> + (l,Zcase(ci,(l,p),Array.map (fun t -> (l,t)) br)::pstk)) in + snd (pure_rec lfts stk) + +(****************************************************************************) +(* Reduction Functions *) +(****************************************************************************) + +let nf_betaiota t = + norm_val (create_clos_infos betaiota empty_env) (inject t) + +let whd_betaiotazeta env x = + match kind_of_term x with + | (Sort _|Var _|Meta _|Evar _|Const _|Ind _|Construct _| + Prod _|Lambda _|Fix _|CoFix _) -> x + | _ -> whd_val (create_clos_infos betaiotazeta env) (inject x) + +let whd_betadeltaiota env t = + match kind_of_term t with + | (Sort _|Meta _|Evar _|Ind _|Construct _| + Prod _|Lambda _|Fix _|CoFix _) -> t + | _ -> whd_val (create_clos_infos betadeltaiota env) (inject t) + +let whd_betadeltaiota_nolet env t = + match kind_of_term t with + | (Sort _|Meta _|Evar _|Ind _|Construct _| + Prod _|Lambda _|Fix _|CoFix _|LetIn _) -> t + | _ -> whd_val (create_clos_infos betadeltaiotanolet env) (inject t) + +(* Beta *) + +let beta_appvect c v = + let rec stacklam env t stack = + match (decomp_stack stack,kind_of_term t) with + | Some (h,stacktl), Lambda (_,_,c) -> stacklam (h::env) c stacktl + | _ -> app_stack (substl env t, stack) in + stacklam [] c (append_stack v empty_stack) + +(********************************************************************) +(* Conversion *) +(********************************************************************) + +(* Conversion utility functions *) +type 'a conversion_function = env -> 'a -> 'a -> Univ.constraints + +exception NotConvertible +exception NotConvertibleVect of int + +let compare_stacks f fmind lft1 stk1 lft2 stk2 cuniv = + let rec cmp_rec pstk1 pstk2 cuniv = + match (pstk1,pstk2) with + | (z1::s1, z2::s2) -> + let c1 = cmp_rec s1 s2 cuniv in + (match (z1,z2) with + | (Zapp a1,Zapp a2) -> List.fold_right2 f a1 a2 c1 + | (Zfix(fx1,a1),Zfix(fx2,a2)) -> + let c2 = f fx1 fx2 c1 in + cmp_rec a1 a2 c2 + | (Zcase(ci1,p1,br1),Zcase(ci2,p2,br2)) -> + if not (fmind ci1.ci_ind ci2.ci_ind) then + raise NotConvertible; + let c2 = f p1 p2 c1 in + array_fold_right2 f br1 br2 c2 + | _ -> assert false) + | _ -> cuniv in + if compare_stack_shape stk1 stk2 then + cmp_rec (pure_stack lft1 stk1) (pure_stack lft2 stk2) cuniv + else raise NotConvertible + +(* Convertibility of sorts *) + +type conv_pb = + | CONV + | CUMUL + +let sort_cmp pb s0 s1 cuniv = + match (s0,s1) with + | (Prop c1, Prop c2) -> if c1 = c2 then cuniv else raise NotConvertible + | (Prop c1, Type u) -> + (match pb with + CUMUL -> cuniv + | _ -> raise NotConvertible) + | (Type u1, Type u2) -> + (match pb with + | CONV -> enforce_eq u1 u2 cuniv + | CUMUL -> enforce_geq u2 u1 cuniv) + | (_, _) -> raise NotConvertible + + +let conv_sort env s0 s1 = sort_cmp CONV s0 s1 Constraint.empty + +let conv_sort_leq env s0 s1 = sort_cmp CUMUL s0 s1 Constraint.empty + + +(* Conversion between [lft1]term1 and [lft2]term2 *) +let rec ccnv cv_pb infos lft1 lft2 term1 term2 cuniv = + Util.check_for_interrupt (); + eqappr cv_pb infos + (lft1, whd_stack infos term1 []) + (lft2, whd_stack infos term2 []) + cuniv + +(* Conversion between [lft1](hd1 v1) and [lft2](hd2 v2) *) +and eqappr cv_pb infos appr1 appr2 cuniv = + let (lft1,(hd1,v1)) = appr1 in + let (lft2,(hd2,v2)) = appr2 in + let el1 = el_stack lft1 v1 in + let el2 = el_stack lft2 v2 in + match (fterm_of hd1, fterm_of hd2) with + (* case of leaves *) + | (FAtom a1, FAtom a2) -> + (match kind_of_term a1, kind_of_term a2 with + | (Sort s1, Sort s2) -> + assert (is_empty_stack v1 && is_empty_stack v2); + sort_cmp cv_pb s1 s2 cuniv + | (Meta n, Meta m) -> + if n=m + then convert_stacks infos lft1 lft2 v1 v2 cuniv + else raise NotConvertible + | _ -> raise NotConvertible) + | (FEvar (ev1,args1), FEvar (ev2,args2)) -> + if ev1=ev2 then + let u1 = convert_stacks infos lft1 lft2 v1 v2 cuniv in + convert_vect infos el1 el2 args1 args2 u1 + else raise NotConvertible + + (* 2 index known to be bound to no constant *) + | (FRel n, FRel m) -> + if reloc_rel n el1 = reloc_rel m el2 + then convert_stacks infos lft1 lft2 v1 v2 cuniv + else raise NotConvertible + + (* 2 constants, 2 local defined vars or 2 defined rels *) + | (FFlex fl1, FFlex fl2) -> + (try (* try first intensional equality *) + if fl1 = fl2 + then convert_stacks infos lft1 lft2 v1 v2 cuniv + else raise NotConvertible + with NotConvertible -> + (* else the oracle tells which constant is to be expanded *) + let (app1,app2) = + if Conv_oracle.oracle_order fl1 fl2 then + match unfold_reference infos fl1 with + | Some def1 -> ((lft1, whd_stack infos def1 v1), appr2) + | None -> + (match unfold_reference infos fl2 with + | Some def2 -> (appr1, (lft2, whd_stack infos def2 v2)) + | None -> raise NotConvertible) + else + match unfold_reference infos fl2 with + | Some def2 -> (appr1, (lft2, whd_stack infos def2 v2)) + | None -> + (match unfold_reference infos fl1 with + | Some def1 -> ((lft1, whd_stack infos def1 v1), appr2) + | None -> raise NotConvertible) in + eqappr cv_pb infos app1 app2 cuniv) + + (* only one constant, defined var or defined rel *) + | (FFlex fl1, _) -> + (match unfold_reference infos fl1 with + | Some def1 -> + eqappr cv_pb infos (lft1, whd_stack infos def1 v1) appr2 cuniv + | None -> raise NotConvertible) + | (_, FFlex fl2) -> + (match unfold_reference infos fl2 with + | Some def2 -> + eqappr cv_pb infos appr1 (lft2, whd_stack infos def2 v2) cuniv + | None -> raise NotConvertible) + + (* other constructors *) + | (FLambda _, FLambda _) -> + let (_,ty1,bd1) = destFLambda mk_clos hd1 in + let (_,ty2,bd2) = destFLambda mk_clos hd2 in + let u1 = ccnv CONV infos el1 el2 ty1 ty2 cuniv in + ccnv CONV infos (el_lift el1) (el_lift el2) bd1 bd2 u1 + + | (FProd (_,c1,c2), FProd (_,c'1,c'2)) -> + assert (is_empty_stack v1 && is_empty_stack v2); + (* Luo's system *) + let u1 = ccnv CONV infos el1 el2 c1 c'1 cuniv in + ccnv cv_pb infos (el_lift el1) (el_lift el2) c2 c'2 u1 + + (* Inductive types: MutInd MutConstruct Fix Cofix *) + + | (FInd (kn1,i1), FInd (kn2,i2)) -> + if i1 = i2 && mind_equiv infos kn1 kn2 + then + convert_stacks infos lft1 lft2 v1 v2 cuniv + else raise NotConvertible + + | (FConstruct ((kn1,i1),j1), FConstruct ((kn2,i2),j2)) -> + if i1 = i2 && j1 = j2 && mind_equiv infos kn1 kn2 + then + convert_stacks infos lft1 lft2 v1 v2 cuniv + else raise NotConvertible + + | (FFix ((op1,(_,tys1,cl1)),e1), FFix((op2,(_,tys2,cl2)),e2)) -> + if op1 = op2 + then + let n = Array.length cl1 in + let fty1 = Array.map (mk_clos e1) tys1 in + let fty2 = Array.map (mk_clos e2) tys2 in + let fcl1 = Array.map (mk_clos (subs_liftn n e1)) cl1 in + let fcl2 = Array.map (mk_clos (subs_liftn n e2)) cl2 in + let u1 = convert_vect infos el1 el2 fty1 fty2 cuniv in + let u2 = + convert_vect infos + (el_liftn n el1) (el_liftn n el2) fcl1 fcl2 u1 in + convert_stacks infos lft1 lft2 v1 v2 u2 + else raise NotConvertible + + | (FCoFix ((op1,(_,tys1,cl1)),e1), FCoFix((op2,(_,tys2,cl2)),e2)) -> + if op1 = op2 + then + let n = Array.length cl1 in + let fty1 = Array.map (mk_clos e1) tys1 in + let fty2 = Array.map (mk_clos e2) tys2 in + let fcl1 = Array.map (mk_clos (subs_liftn n e1)) cl1 in + let fcl2 = Array.map (mk_clos (subs_liftn n e2)) cl2 in + let u1 = convert_vect infos el1 el2 fty1 fty2 cuniv in + let u2 = + convert_vect infos + (el_liftn n el1) (el_liftn n el2) fcl1 fcl2 u1 in + convert_stacks infos lft1 lft2 v1 v2 u2 + else raise NotConvertible + + | ( (FLetIn _, _) | (_, FLetIn _) | (FCases _,_) | (_,FCases _) + | (FApp _,_) | (_,FApp _) | (FCLOS _, _) | (_,FCLOS _) + | (FLIFT _, _) | (_,FLIFT _) | (FLOCKED,_) | (_,FLOCKED)) -> + anomaly "Unexpected term returned by fhnf" + + | _ -> raise NotConvertible + +and convert_stacks infos lft1 lft2 stk1 stk2 cuniv = + compare_stacks + (fun (l1,t1) (l2,t2) c -> ccnv CONV infos l1 l2 t1 t2 c) + (fun (mind1,i1) (mind2,i2) -> i1=i2 && mind_equiv infos mind1 mind2) + lft1 stk1 lft2 stk2 cuniv + +and convert_vect infos lft1 lft2 v1 v2 cuniv = + let lv1 = Array.length v1 in + let lv2 = Array.length v2 in + if lv1 = lv2 + then + let rec fold n univ = + if n >= lv1 then univ + else + let u1 = ccnv CONV infos lft1 lft2 v1.(n) v2.(n) univ in + fold (n+1) u1 in + fold 0 cuniv + else raise NotConvertible + + + +let fconv cv_pb env t1 t2 = + if eq_constr t1 t2 then + Constraint.empty + else + let infos = create_clos_infos betaiotazeta env in + ccnv cv_pb infos ELID ELID (inject t1) (inject t2) + Constraint.empty + +let conv = fconv CONV +let conv_leq = fconv CUMUL + +let conv_leq_vecti env v1 v2 = + array_fold_left2_i + (fun i c t1 t2 -> + let c' = + try conv_leq env t1 t2 + with NotConvertible -> raise (NotConvertibleVect i) in + Constraint.union c c') + Constraint.empty + v1 + v2 + +(* +let convleqkey = Profile.declare_profile "Kernel_reduction.conv_leq";; +let conv_leq env t1 t2 = + Profile.profile4 convleqkey conv_leq env t1 t2;; + +let convkey = Profile.declare_profile "Kernel_reduction.conv";; +let conv env t1 t2 = + Profile.profile4 convleqkey conv env t1 t2;; +*) + +(********************************************************************) +(* Special-Purpose Reduction *) +(********************************************************************) + +(* pseudo-reduction rule: + * [hnf_prod_app env s (Prod(_,B)) N --> B[N] + * with an HNF on the first argument to produce a product. + * if this does not work, then we use the string S as part of our + * error message. *) + +let hnf_prod_app env t n = + match kind_of_term (whd_betadeltaiota env t) with + | Prod (_,_,b) -> subst1 n b + | _ -> anomaly "hnf_prod_app: Need a product" + +let hnf_prod_applist env t nl = + List.fold_left (hnf_prod_app env) t nl + +(* Dealing with arities *) + +let dest_prod env = + let rec decrec env m c = + let t = whd_betadeltaiota env c in + match kind_of_term t with + | Prod (n,a,c0) -> + let d = (n,None,a) in + decrec (push_rel d env) (Sign.add_rel_decl d m) c0 + | _ -> m,t + in + decrec env Sign.empty_rel_context + +(* The same but preserving lets *) +let dest_prod_assum env = + let rec prodec_rec env l ty = + let rty = whd_betadeltaiota_nolet env ty in + match kind_of_term rty with + | Prod (x,t,c) -> + let d = (x,None,t) in + prodec_rec (push_rel d env) (Sign.add_rel_decl d l) c + | LetIn (x,b,t,c) -> + let d = (x,Some b,t) in + prodec_rec (push_rel d env) (Sign.add_rel_decl d l) c + | Cast (c,_) -> prodec_rec env l c + | _ -> l,rty + in + prodec_rec env Sign.empty_rel_context + +let dest_arity env c = + let l, c = dest_prod env c in + match kind_of_term c with + | Sort s -> l,s + | _ -> error "not an arity" + +let is_arity env c = + try + let _ = dest_arity env c in + true + with UserError _ -> false + -- cgit v1.2.3