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Diffstat (limited to 'kernel/cClosure.ml')
| -rw-r--r-- | kernel/cClosure.ml | 1069 |
1 files changed, 1069 insertions, 0 deletions
diff --git a/kernel/cClosure.ml b/kernel/cClosure.ml new file mode 100644 index 00000000..fe9ec579 --- /dev/null +++ b/kernel/cClosure.ml @@ -0,0 +1,1069 @@ +(************************************************************************) +(* v * The Coq Proof Assistant / The Coq Development Team *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) +(* \VV/ **************************************************************) +(* // * This file is distributed under the terms of the *) +(* * GNU Lesser General Public License Version 2.1 *) +(************************************************************************) + +(* Created by Bruno Barras with Benjamin Werner's account to implement + a call-by-value conversion algorithm and a lazy reduction machine + with sharing, Nov 1996 *) +(* Addition of zeta-reduction (let-in contraction) by Hugo Herbelin, Oct 2000 *) +(* Call-by-value machine moved to cbv.ml, Mar 01 *) +(* Additional tools for module subtyping by Jacek Chrzaszcz, Aug 2002 *) +(* Extension with closure optimization by Bruno Barras, Aug 2003 *) +(* Support for evar reduction by Bruno Barras, Feb 2009 *) +(* Miscellaneous other improvements by Bruno Barras, 1997-2009 *) + +(* This file implements a lazy reduction for the Calculus of Inductive + Constructions *) + +open CErrors +open Util +open Pp +open Names +open Term +open Vars +open Environ +open Esubst + +let stats = ref false +let share = ref true + +(* Profiling *) +let beta = ref 0 +let delta = ref 0 +let eta = ref 0 +let zeta = ref 0 +let evar = ref 0 +let nb_match = ref 0 +let fix = ref 0 +let cofix = ref 0 +let prune = ref 0 + +let reset () = + beta := 0; delta := 0; zeta := 0; evar := 0; nb_match := 0; fix := 0; + cofix := 0; evar := 0; prune := 0 + +let stop() = + Feedback.msg_debug (str "[Reds: beta=" ++ int !beta ++ str" delta=" ++ int !delta ++ + str " eta=" ++ int !eta ++ str" zeta=" ++ int !zeta ++ str" evar=" ++ + int !evar ++ str" match=" ++ int !nb_match ++ str" fix=" ++ int !fix ++ + str " cofix=" ++ int !cofix ++ str" prune=" ++ int !prune ++ + str"]") + +let incr_cnt red cnt = + if red then begin + if !stats then incr cnt; + true + end else + false + +let with_stats c = + if !stats then begin + reset(); + let r = Lazy.force c in + stop(); + r + end else + Lazy.force c + +let all_opaque = (Id.Pred.empty, Cpred.empty) +let all_transparent = (Id.Pred.full, Cpred.full) + +let is_transparent_variable (ids, _) id = Id.Pred.mem id ids +let is_transparent_constant (_, csts) cst = Cpred.mem cst csts + +module type RedFlagsSig = sig + type reds + type red_kind + val fBETA : red_kind + val fDELTA : red_kind + val fETA : red_kind + val fMATCH : red_kind + val fFIX : red_kind + val fCOFIX : red_kind + val fZETA : red_kind + val fCONST : constant -> red_kind + val fVAR : Id.t -> red_kind + val no_red : reds + val red_add : reds -> red_kind -> reds + val red_sub : reds -> red_kind -> reds + val red_add_transparent : reds -> transparent_state -> reds + val mkflags : red_kind list -> reds + val red_set : reds -> red_kind -> bool + val red_projection : reds -> projection -> bool +end + +module RedFlags = (struct + + (* [r_const=(true,cl)] means all constants but those in [cl] *) + (* [r_const=(false,cl)] means only those in [cl] *) + (* [r_delta=true] just mean [r_const=(true,[])] *) + + type reds = { + r_beta : bool; + r_delta : bool; + r_eta : bool; + r_const : transparent_state; + r_zeta : bool; + r_match : bool; + r_fix : bool; + r_cofix : bool } + + type red_kind = BETA | DELTA | ETA | MATCH | FIX + | COFIX | ZETA + | CONST of constant | VAR of Id.t + let fBETA = BETA + let fDELTA = DELTA + let fETA = ETA + let fMATCH = MATCH + let fFIX = FIX + let fCOFIX = COFIX + let fZETA = ZETA + let fCONST kn = CONST kn + let fVAR id = VAR id + let no_red = { + r_beta = false; + r_delta = false; + r_eta = false; + r_const = all_opaque; + r_zeta = false; + r_match = false; + r_fix = false; + r_cofix = false } + + let red_add red = function + | BETA -> { red with r_beta = true } + | ETA -> { red with r_eta = true } + | DELTA -> { red with r_delta = true; r_const = all_transparent } + | CONST kn -> + let (l1,l2) = red.r_const in + { red with r_const = l1, Cpred.add kn l2 } + | MATCH -> { red with r_match = true } + | FIX -> { red with r_fix = true } + | COFIX -> { red with r_cofix = true } + | ZETA -> { red with r_zeta = true } + | VAR id -> + let (l1,l2) = red.r_const in + { red with r_const = Id.Pred.add id l1, l2 } + + let red_sub red = function + | BETA -> { red with r_beta = false } + | ETA -> { red with r_eta = false } + | DELTA -> { red with r_delta = false } + | CONST kn -> + let (l1,l2) = red.r_const in + { red with r_const = l1, Cpred.remove kn l2 } + | MATCH -> { red with r_match = false } + | FIX -> { red with r_fix = false } + | COFIX -> { red with r_cofix = false } + | ZETA -> { red with r_zeta = false } + | VAR id -> + let (l1,l2) = red.r_const in + { red with r_const = Id.Pred.remove id l1, l2 } + + let red_add_transparent red tr = + { red with r_const = tr } + + let mkflags = List.fold_left red_add no_red + + let red_set red = function + | BETA -> incr_cnt red.r_beta beta + | ETA -> incr_cnt red.r_eta eta + | CONST kn -> + let (_,l) = red.r_const in + let c = Cpred.mem kn l in + incr_cnt c delta + | VAR id -> (* En attendant d'avoir des kn pour les Var *) + let (l,_) = red.r_const in + let c = Id.Pred.mem id l in + incr_cnt c delta + | ZETA -> incr_cnt red.r_zeta zeta + | MATCH -> incr_cnt red.r_match nb_match + | FIX -> incr_cnt red.r_fix fix + | COFIX -> incr_cnt red.r_cofix cofix + | DELTA -> (* Used for Rel/Var defined in context *) + incr_cnt red.r_delta delta + + let red_projection red p = + if Projection.unfolded p then true + else red_set red (fCONST (Projection.constant p)) + +end : RedFlagsSig) + +open RedFlags + +let all = mkflags [fBETA;fDELTA;fZETA;fMATCH;fFIX;fCOFIX] +let allnolet = mkflags [fBETA;fDELTA;fMATCH;fFIX;fCOFIX] +let beta = mkflags [fBETA] +let betadeltazeta = mkflags [fBETA;fDELTA;fZETA] +let betaiota = mkflags [fBETA;fMATCH;fFIX;fCOFIX] +let betaiotazeta = mkflags [fBETA;fMATCH;fFIX;fCOFIX;fZETA] +let betazeta = mkflags [fBETA;fZETA] +let delta = mkflags [fDELTA] +let zeta = mkflags [fZETA] +let nored = no_red + +(* Removing fZETA for finer behaviour would break many developments *) +let unfold_side_flags = [fBETA;fMATCH;fFIX;fCOFIX;fZETA] +let unfold_side_red = mkflags [fBETA;fMATCH;fFIX;fCOFIX;fZETA] +let unfold_red kn = + let flag = match kn with + | EvalVarRef id -> fVAR id + | EvalConstRef kn -> fCONST kn in + mkflags (flag::unfold_side_flags) + +(* Flags of reduction and cache of constants: 'a is a type that may be + * mapped to constr. 'a infos implements a cache for constants and + * abstractions, storing a representation (of type 'a) of the body of + * this constant or abstraction. + * * i_tab is the cache table of the results + * * i_repr is the function to get the representation from the current + * state of the cache and the body of the constant. The result + * is stored in the table. + * * i_rels is the array of free rel variables together with their optional + * body + * + * ref_value_cache searchs in the tab, otherwise uses i_repr to + * compute the result and store it in the table. If the constant can't + * be unfolded, returns None, but does not store this failure. * This + * doesn't take the RESET into account. You mustn't keep such a table + * after a Reset. * This type is not exported. Only its two + * instantiations (cbv or lazy) are. + *) + +type table_key = constant puniverses tableKey + +let eq_pconstant_key (c,u) (c',u') = + eq_constant_key c c' && Univ.Instance.equal u u' + +module IdKeyHash = +struct + open Hashset.Combine + type t = table_key + let equal = Names.eq_table_key eq_pconstant_key + let hash = function + | ConstKey (c, _) -> combinesmall 1 (Constant.UserOrd.hash c) + | VarKey id -> combinesmall 2 (Id.hash id) + | RelKey i -> combinesmall 3 (Int.hash i) +end + +module KeyTable = Hashtbl.Make(IdKeyHash) + +let eq_table_key = IdKeyHash.equal + +type 'a infos_cache = { + i_repr : 'a infos -> constr -> 'a; + i_env : env; + i_sigma : existential -> constr option; + i_rels : constr option array; + i_tab : 'a KeyTable.t } + +and 'a infos = { + i_flags : reds; + i_cache : 'a infos_cache } + +let info_flags info = info.i_flags +let info_env info = info.i_cache.i_env + +open Context.Named.Declaration + +let assoc_defined id env = match Environ.lookup_named id env with +| LocalDef (_, c, _) -> c +| _ -> raise Not_found + +let ref_value_cache ({i_cache = cache} as infos) ref = + try + Some (KeyTable.find cache.i_tab ref) + with Not_found -> + try + let body = + match ref with + | RelKey n -> + let len = Array.length cache.i_rels in + let i = n - 1 in + let () = if i < 0 || len <= i then raise Not_found in + begin match Array.unsafe_get cache.i_rels i with + | None -> raise Not_found + | Some t -> lift n t + end + | VarKey id -> assoc_defined id cache.i_env + | ConstKey cst -> constant_value_in cache.i_env cst + in + let v = cache.i_repr infos body in + KeyTable.add cache.i_tab ref v; + Some v + with + | Not_found (* List.assoc *) + | NotEvaluableConst _ (* Const *) + -> None + +let evar_value cache ev = + cache.i_sigma ev + +let defined_rels flags env = +(* if red_local_const (snd flags) then*) + let ctx = rel_context env in + let len = List.length ctx in + let ans = Array.make len None in + let open Context.Rel.Declaration in + let iter i = function + | LocalAssum _ -> () + | LocalDef (_,b,_) -> Array.unsafe_set ans i (Some b) + in + let () = List.iteri iter ctx in + ans +(* else (0,[])*) + +let create mk_cl flgs env evars = + let cache = + { i_repr = mk_cl; + i_env = env; + i_sigma = evars; + i_rels = defined_rels flgs env; + i_tab = KeyTable.create 17 } + in { i_flags = flgs; i_cache = cache } + + +(**********************************************************************) +(* Lazy reduction: the one used in kernel operations *) + +(* type of shared terms. fconstr and frterm are mutually recursive. + * Clone of the constr structure, but completely mutable, and + * annotated with reduction state (reducible or not). + * - FLIFT is a delayed shift; allows sharing between 2 lifted copies + * of a given term. + * - FCLOS is a delayed substitution applied to a constr + * - FLOCKED is used to erase the content of a reference that must + * be updated. This is to allow the garbage collector to work + * before the term is computed. + *) + +(* Norm means the term is fully normalized and cannot create a redex + when substituted + Cstr means the term is in head normal form and that it can + create a redex when substituted (i.e. constructor, fix, lambda) + Whnf means we reached the head normal form and that it cannot + create a redex when substituted + Red is used for terms that might be reduced +*) +type red_state = Norm | Cstr | Whnf | Red + +let neutr = function + | (Whnf|Norm) -> Whnf + | (Red|Cstr) -> Red + +type fconstr = { + mutable norm: red_state; + mutable term: fterm } + +and fterm = + | FRel of int + | FAtom of constr (* Metas and Sorts *) + | FCast of fconstr * cast_kind * fconstr + | FFlex of table_key + | FInd of pinductive + | FConstruct of pconstructor + | FApp of fconstr * fconstr array + | FProj of projection * fconstr + | FFix of fixpoint * fconstr subs + | FCoFix of cofixpoint * fconstr subs + | FCaseT of case_info * constr * fconstr * constr array * fconstr subs (* predicate and branches are closures *) + | FLambda of int * (Name.t * constr) list * constr * fconstr subs + | FProd of Name.t * fconstr * fconstr + | FLetIn of Name.t * fconstr * fconstr * constr * fconstr subs + | FEvar of existential * fconstr subs + | FLIFT of int * fconstr + | FCLOS of constr * fconstr subs + | FLOCKED + +let fterm_of v = v.term +let set_norm v = v.norm <- Norm +let is_val v = match v.norm with Norm -> true | _ -> false + +let mk_atom c = {norm=Norm;term=FAtom c} +let mk_red f = {norm=Red;term=f} + +(* Could issue a warning if no is still Red, pointing out that we loose + sharing. *) +let update v1 no t = + if !share then + (v1.norm <- no; + v1.term <- t; + v1) + else {norm=no;term=t} + +(**********************************************************************) +(* The type of (machine) stacks (= lambda-bar-calculus' contexts) *) + +type stack_member = + | Zapp of fconstr array + | ZcaseT of case_info * constr * constr array * fconstr subs + | Zproj of int * int * constant + | Zfix of fconstr * stack + | Zshift of int + | Zupdate of fconstr + +and stack = stack_member list + +let empty_stack = [] +let append_stack v s = + if Int.equal (Array.length v) 0 then s else + match s with + | Zapp l :: s -> Zapp (Array.append v l) :: s + | _ -> Zapp v :: s + +(* Collapse the shifts in the stack *) +let zshift n s = + match (n,s) with + (0,_) -> s + | (_,Zshift(k)::s) -> Zshift(n+k)::s + | _ -> Zshift(n)::s + +let rec stack_args_size = function + | Zapp v :: s -> Array.length v + stack_args_size s + | Zshift(_)::s -> stack_args_size s + | Zupdate(_)::s -> stack_args_size s + | _ -> 0 + +(* When used as an argument stack (only Zapp can appear) *) +let rec decomp_stack = function + | Zapp v :: s -> + (match Array.length v with + 0 -> decomp_stack s + | 1 -> Some (v.(0), s) + | _ -> + Some (v.(0), (Zapp (Array.sub v 1 (Array.length v - 1)) :: s))) + | _ -> None +let array_of_stack s = + let rec stackrec = function + | [] -> [] + | Zapp args :: s -> args :: (stackrec s) + | _ -> assert false + in Array.concat (stackrec s) +let rec stack_assign s p c = match s with + | Zapp args :: s -> + let q = Array.length args in + if p >= q then + Zapp args :: stack_assign s (p-q) c + else + (let nargs = Array.copy args in + nargs.(p) <- c; + Zapp nargs :: s) + | _ -> s +let rec stack_tail p s = + if Int.equal p 0 then s else + match s with + | Zapp args :: s -> + let q = Array.length args in + if p >= q then stack_tail (p-q) s + else Zapp (Array.sub args p (q-p)) :: s + | _ -> failwith "stack_tail" +let rec stack_nth s p = match s with + | Zapp args :: s -> + let q = Array.length args in + if p >= q then stack_nth s (p-q) + else args.(p) + | _ -> raise Not_found + +(* Lifting. Preserves sharing (useful only for cell with norm=Red). + lft_fconstr always create a new cell, while lift_fconstr avoids it + when the lift is 0. *) +let rec lft_fconstr n ft = + match ft.term with + | (FInd _|FConstruct _|FFlex(ConstKey _|VarKey _)) -> ft + | FRel i -> {norm=Norm;term=FRel(i+n)} + | FLambda(k,tys,f,e) -> {norm=Cstr; term=FLambda(k,tys,f,subs_shft(n,e))} + | FFix(fx,e) -> {norm=Cstr; term=FFix(fx,subs_shft(n,e))} + | FCoFix(cfx,e) -> {norm=Cstr; term=FCoFix(cfx,subs_shft(n,e))} + | FLIFT(k,m) -> lft_fconstr (n+k) m + | FLOCKED -> assert false + | _ -> {norm=ft.norm; term=FLIFT(n,ft)} +let lift_fconstr k f = + if Int.equal k 0 then f else lft_fconstr k f +let lift_fconstr_vect k v = + if Int.equal k 0 then v else CArray.Fun1.map lft_fconstr k v + +let clos_rel e i = + match expand_rel i e with + | Inl(n,mt) -> lift_fconstr n mt + | Inr(k,None) -> {norm=Norm; term= FRel k} + | Inr(k,Some p) -> + lift_fconstr (k-p) {norm=Red;term=FFlex(RelKey p)} + +(* since the head may be reducible, we might introduce lifts of 0 *) +let compact_stack head stk = + let rec strip_rec depth = function + | Zshift(k)::s -> strip_rec (depth+k) s + | Zupdate(m)::s -> + (* Be sure to create a new cell otherwise sharing would be + lost by the update operation *) + let h' = lft_fconstr depth head in + let _ = update m h'.norm h'.term in + strip_rec depth s + | stk -> zshift depth stk in + strip_rec 0 stk + +(* Put an update mark in the stack, only if needed *) +let zupdate m s = + if !share && begin match m.norm with Red -> true | _ -> false end + then + let s' = compact_stack m s in + let _ = m.term <- FLOCKED in + Zupdate(m)::s' + else s + +let mk_lambda env t = + let (rvars,t') = decompose_lam t in + FLambda(List.length rvars, List.rev rvars, t', env) + +let destFLambda clos_fun t = + match t.term with + FLambda(_,[(na,ty)],b,e) -> (na,clos_fun e ty,clos_fun (subs_lift e) b) + | FLambda(n,(na,ty)::tys,b,e) -> + (na,clos_fun e ty,{norm=Cstr;term=FLambda(n-1,tys,b,subs_lift e)}) + | _ -> assert false + (* t must be a FLambda and binding list cannot be empty *) + +(* Optimization: do not enclose variables in a closure. + Makes variable access much faster *) +let mk_clos e t = + match kind_of_term t with + | Rel i -> clos_rel e i + | Var x -> { norm = Red; term = FFlex (VarKey x) } + | Const c -> { norm = Red; term = FFlex (ConstKey c) } + | Meta _ | Sort _ -> { norm = Norm; term = FAtom t } + | Ind kn -> { norm = Norm; term = FInd kn } + | Construct kn -> { norm = Cstr; term = FConstruct kn } + | (CoFix _|Lambda _|Fix _|Prod _|Evar _|App _|Case _|Cast _|LetIn _|Proj _) -> + {norm = Red; term = FCLOS(t,e)} + +let mk_clos_vect env v = CArray.Fun1.map mk_clos env v + +(* Translate the head constructor of t from constr to fconstr. This + function is parameterized by the function to apply on the direct + subterms. + Could be used insted of mk_clos. *) +let mk_clos_deep clos_fun env t = + match kind_of_term t with + | (Rel _|Ind _|Const _|Construct _|Var _|Meta _ | Sort _) -> + mk_clos env t + | Cast (a,k,b) -> + { norm = Red; + term = FCast (clos_fun env a, k, clos_fun env b)} + | App (f,v) -> + { norm = Red; + term = FApp (clos_fun env f, CArray.Fun1.map clos_fun env v) } + | Proj (p,c) -> + { norm = Red; + term = FProj (p, clos_fun env c) } + | Case (ci,p,c,v) -> + { norm = Red; + term = FCaseT (ci, p, clos_fun env c, v, env) } + | Fix fx -> + { norm = Cstr; term = FFix (fx, env) } + | CoFix cfx -> + { norm = Cstr; term = FCoFix(cfx,env) } + | Lambda _ -> + { norm = Cstr; term = mk_lambda env t } + | Prod (n,t,c) -> + { norm = Whnf; + term = FProd (n, clos_fun env t, clos_fun (subs_lift env) c) } + | LetIn (n,b,t,c) -> + { norm = Red; + term = FLetIn (n, clos_fun env b, clos_fun env t, c, env) } + | Evar ev -> + { norm = Red; term = FEvar(ev,env) } + +(* A better mk_clos? *) +let mk_clos2 = mk_clos_deep mk_clos + +(* The inverse of mk_clos_deep: move back to constr *) +let rec to_constr constr_fun lfts v = + match v.term with + | FRel i -> mkRel (reloc_rel i lfts) + | FFlex (RelKey p) -> mkRel (reloc_rel p lfts) + | FFlex (VarKey x) -> mkVar x + | FAtom c -> exliftn lfts c + | FCast (a,k,b) -> + mkCast (constr_fun lfts a, k, constr_fun lfts b) + | FFlex (ConstKey op) -> mkConstU op + | FInd op -> mkIndU op + | FConstruct op -> mkConstructU op + | FCaseT (ci,p,c,ve,env) -> + mkCase (ci, constr_fun lfts (mk_clos env p), + constr_fun lfts c, + Array.map (fun b -> constr_fun lfts (mk_clos env b)) ve) + | FFix ((op,(lna,tys,bds)),e) -> + let n = Array.length bds in + let ftys = CArray.Fun1.map mk_clos e tys in + let fbds = CArray.Fun1.map mk_clos (subs_liftn n e) bds in + let lfts' = el_liftn n lfts in + mkFix (op, (lna, CArray.Fun1.map constr_fun lfts ftys, + CArray.Fun1.map constr_fun lfts' fbds)) + | FCoFix ((op,(lna,tys,bds)),e) -> + let n = Array.length bds in + let ftys = CArray.Fun1.map mk_clos e tys in + let fbds = CArray.Fun1.map mk_clos (subs_liftn n e) bds in + let lfts' = el_liftn (Array.length bds) lfts in + mkCoFix (op, (lna, CArray.Fun1.map constr_fun lfts ftys, + CArray.Fun1.map constr_fun lfts' fbds)) + | FApp (f,ve) -> + mkApp (constr_fun lfts f, + CArray.Fun1.map constr_fun lfts ve) + | FProj (p,c) -> + mkProj (p,constr_fun lfts c) + + | FLambda _ -> + let (na,ty,bd) = destFLambda mk_clos2 v in + mkLambda (na, constr_fun lfts ty, + constr_fun (el_lift lfts) bd) + | FProd (n,t,c) -> + mkProd (n, constr_fun lfts t, + constr_fun (el_lift lfts) c) + | FLetIn (n,b,t,f,e) -> + let fc = mk_clos2 (subs_lift e) f in + mkLetIn (n, constr_fun lfts b, + constr_fun lfts t, + constr_fun (el_lift lfts) fc) + | FEvar ((ev,args),env) -> + mkEvar(ev,Array.map (fun a -> constr_fun lfts (mk_clos2 env a)) args) + | FLIFT (k,a) -> to_constr constr_fun (el_shft k lfts) a + | FCLOS (t,env) -> + let fr = mk_clos2 env t in + let unfv = update v fr.norm fr.term in + to_constr constr_fun lfts unfv + | FLOCKED -> assert false (*mkVar(Id.of_string"_LOCK_")*) + +(* This function defines the correspondance between constr and + fconstr. When we find a closure whose substitution is the identity, + then we directly return the constr to avoid possibly huge + reallocation. *) +let term_of_fconstr = + let rec term_of_fconstr_lift lfts v = + match v.term with + | FCLOS(t,env) when is_subs_id env && is_lift_id lfts -> t + | FLambda(_,tys,f,e) when is_subs_id e && is_lift_id lfts -> + compose_lam (List.rev tys) f + | FFix(fx,e) when is_subs_id e && is_lift_id lfts -> mkFix fx + | FCoFix(cfx,e) when is_subs_id e && is_lift_id lfts -> mkCoFix cfx + | _ -> to_constr term_of_fconstr_lift lfts v in + term_of_fconstr_lift el_id + + + +(* fstrong applies unfreeze_fun recursively on the (freeze) term and + * yields a term. Assumes that the unfreeze_fun never returns a + * FCLOS term. +let rec fstrong unfreeze_fun lfts v = + to_constr (fstrong unfreeze_fun) lfts (unfreeze_fun v) +*) + +let rec zip m stk = + match stk with + | [] -> m + | Zapp args :: s -> zip {norm=neutr m.norm; term=FApp(m, args)} s + | ZcaseT(ci,p,br,e)::s -> + let t = FCaseT(ci, p, m, br, e) in + zip {norm=neutr m.norm; term=t} s + | Zproj (i,j,cst) :: s -> + zip {norm=neutr m.norm; term=FProj(Projection.make cst true,m)} s + | Zfix(fx,par)::s -> + zip fx (par @ append_stack [|m|] s) + | Zshift(n)::s -> + zip (lift_fconstr n m) s + | Zupdate(rf)::s -> + zip (update rf m.norm m.term) s + +let fapp_stack (m,stk) = zip m stk + +(*********************************************************************) + +(* The assertions in the functions below are granted because they are + called only when m is a constructor, a cofix + (strip_update_shift_app), a fix (get_nth_arg) or an abstraction + (strip_update_shift, through get_arg). *) + +(* optimised for the case where there are no shifts... *) +let strip_update_shift_app_red head stk = + let rec strip_rec rstk h depth = function + | Zshift(k) as e :: s -> + strip_rec (e::rstk) (lift_fconstr k h) (depth+k) s + | (Zapp args :: s) -> + strip_rec (Zapp args :: rstk) + {norm=h.norm;term=FApp(h,args)} depth s + | Zupdate(m)::s -> + strip_rec rstk (update m h.norm h.term) depth s + | stk -> (depth,List.rev rstk, stk) in + strip_rec [] head 0 stk + +let strip_update_shift_app head stack = + assert (match head.norm with Red -> false | _ -> true); + strip_update_shift_app_red head stack + +let get_nth_arg head n stk = + assert (match head.norm with Red -> false | _ -> true); + let rec strip_rec rstk h n = function + | Zshift(k) as e :: s -> + strip_rec (e::rstk) (lift_fconstr k h) n s + | Zapp args::s' -> + let q = Array.length args in + if n >= q + then + strip_rec (Zapp args::rstk) {norm=h.norm;term=FApp(h,args)} (n-q) s' + else + let bef = Array.sub args 0 n in + let aft = Array.sub args (n+1) (q-n-1) in + let stk' = + List.rev (if Int.equal n 0 then rstk else (Zapp bef :: rstk)) in + (Some (stk', args.(n)), append_stack aft s') + | Zupdate(m)::s -> + strip_rec rstk (update m h.norm h.term) n s + | s -> (None, List.rev rstk @ s) in + strip_rec [] head n stk + +(* Beta reduction: look for an applied argument in the stack. + Since the encountered update marks are removed, h must be a whnf *) +let rec get_args n tys f e stk = + match stk with + Zupdate r :: s -> + let _hd = update r Cstr (FLambda(n,tys,f,e)) in + get_args n tys f e s + | Zshift k :: s -> + get_args n tys f (subs_shft (k,e)) s + | Zapp l :: s -> + let na = Array.length l in + if n == na then (Inl (subs_cons(l,e)),s) + else if n < na then (* more arguments *) + let args = Array.sub l 0 n in + let eargs = Array.sub l n (na-n) in + (Inl (subs_cons(args,e)), Zapp eargs :: s) + else (* more lambdas *) + let etys = List.skipn na tys in + get_args (n-na) etys f (subs_cons(l,e)) s + | _ -> (Inr {norm=Cstr;term=FLambda(n,tys,f,e)}, stk) + +(* Eta expansion: add a reference to implicit surrounding lambda at end of stack *) +let rec eta_expand_stack = function + | (Zapp _ | Zfix _ | ZcaseT _ | Zproj _ + | Zshift _ | Zupdate _ as e) :: s -> + e :: eta_expand_stack s + | [] -> + [Zshift 1; Zapp [|{norm=Norm; term= FRel 1}|]] + +(* Iota reduction: extract the arguments to be passed to the Case + branches *) +let rec reloc_rargs_rec depth stk = + match stk with + Zapp args :: s -> + Zapp (lift_fconstr_vect depth args) :: reloc_rargs_rec depth s + | Zshift(k)::s -> if Int.equal k depth then s else reloc_rargs_rec (depth-k) s + | _ -> stk + +let reloc_rargs depth stk = + if Int.equal depth 0 then stk else reloc_rargs_rec depth stk + +let rec try_drop_parameters depth n argstk = + match argstk with + Zapp args::s -> + let q = Array.length args in + if n > q then try_drop_parameters depth (n-q) s + else if Int.equal n q then reloc_rargs depth s + else + let aft = Array.sub args n (q-n) in + reloc_rargs depth (append_stack aft s) + | Zshift(k)::s -> try_drop_parameters (depth-k) n s + | [] -> + if Int.equal n 0 then [] + else raise Not_found + | _ -> assert false + (* strip_update_shift_app only produces Zapp and Zshift items *) + +let drop_parameters depth n argstk = + try try_drop_parameters depth n argstk + with Not_found -> + (* we know that n < stack_args_size(argstk) (if well-typed term) *) + anomaly (Pp.str "ill-typed term: found a match on a partially applied constructor") + +(** [eta_expand_ind_stack env ind c s t] computes stacks corresponding + to the conversion of the eta expansion of t, considered as an inhabitant + of ind, and the Constructor c of this inductive type applied to arguments + s. + @assumes [t] is an irreducible term, and not a constructor. [ind] is the inductive + of the constructor term [c] + @raises Not_found if the inductive is not a primitive record, or if the + constructor is partially applied. + *) +let eta_expand_ind_stack env ind m s (f, s') = + let mib = lookup_mind (fst ind) env in + match mib.Declarations.mind_record with + | Some (Some (_,projs,pbs)) when + mib.Declarations.mind_finite == Decl_kinds.BiFinite -> + (* (Construct, pars1 .. parsm :: arg1...argn :: []) ~= (f, s') -> + arg1..argn ~= (proj1 t...projn t) where t = zip (f,s') *) + let pars = mib.Declarations.mind_nparams in + let right = fapp_stack (f, s') in + let (depth, args, s) = strip_update_shift_app m s in + (** Try to drop the params, might fail on partially applied constructors. *) + let argss = try_drop_parameters depth pars args in + let hstack = Array.map (fun p -> { norm = Red; (* right can't be a constructor though *) + term = FProj (Projection.make p true, right) }) projs in + argss, [Zapp hstack] + | _ -> raise Not_found (* disallow eta-exp for non-primitive records *) + +let rec project_nth_arg n argstk = + match argstk with + | Zapp args :: s -> + let q = Array.length args in + if n >= q then project_nth_arg (n - q) s + else (* n < q *) args.(n) + | _ -> assert false + (* After drop_parameters we have a purely applicative stack *) + + +(* Iota reduction: expansion of a fixpoint. + * Given a fixpoint and a substitution, returns the corresponding + * fixpoint body, and the substitution in which it should be + * evaluated: its first variables are the fixpoint bodies + * + * FCLOS(fix Fi {F0 := T0 .. Fn-1 := Tn-1}, S) + * -> (S. FCLOS(F0,S) . ... . FCLOS(Fn-1,S), Ti) + *) +(* does not deal with FLIFT *) +let contract_fix_vect fix = + let (thisbody, make_body, env, nfix) = + match fix with + | FFix (((reci,i),(_,_,bds as rdcl)),env) -> + (bds.(i), + (fun j -> { norm = Cstr; term = FFix (((reci,j),rdcl),env) }), + env, Array.length bds) + | FCoFix ((i,(_,_,bds as rdcl)),env) -> + (bds.(i), + (fun j -> { norm = Cstr; term = FCoFix ((j,rdcl),env) }), + env, Array.length bds) + | _ -> assert false + in + (subs_cons(Array.init nfix make_body, env), thisbody) + +(*********************************************************************) +(* A machine that inspects the head of a term until it finds an + atom or a subterm that may produce a redex (abstraction, + constructor, cofix, letin, constant), or a neutral term (product, + inductive) *) +let rec knh info m stk = + match m.term with + | FLIFT(k,a) -> knh info a (zshift k stk) + | FCLOS(t,e) -> knht info e t (zupdate m stk) + | FLOCKED -> assert false + | FApp(a,b) -> knh info a (append_stack b (zupdate m stk)) + | FCaseT(ci,p,t,br,e) -> knh info t (ZcaseT(ci,p,br,e)::zupdate m stk) + | FFix(((ri,n),(_,_,_)),_) -> + (match get_nth_arg m ri.(n) stk with + (Some(pars,arg),stk') -> knh info arg (Zfix(m,pars)::stk') + | (None, stk') -> (m,stk')) + | FCast(t,_,_) -> knh info t stk + | FProj (p,c) -> + let unf = Projection.unfolded p in + if unf || red_set info.i_flags (fCONST (Projection.constant p)) then + (match try Some (lookup_projection p (info_env info)) with Not_found -> None with + | None -> (m, stk) + | Some pb -> + knh info c (Zproj (pb.Declarations.proj_npars, pb.Declarations.proj_arg, + Projection.constant p) + :: zupdate m stk)) + else (m,stk) + +(* cases where knh stops *) + | (FFlex _|FLetIn _|FConstruct _|FEvar _| + FCoFix _|FLambda _|FRel _|FAtom _|FInd _|FProd _) -> + (m, stk) + +(* The same for pure terms *) +and knht info e t stk = + match kind_of_term t with + | App(a,b) -> + knht info e a (append_stack (mk_clos_vect e b) stk) + | Case(ci,p,t,br) -> + knht info e t (ZcaseT(ci, p, br, e)::stk) + | Fix _ -> knh info (mk_clos2 e t) stk + | Cast(a,_,_) -> knht info e a stk + | Rel n -> knh info (clos_rel e n) stk + | Proj (p,c) -> knh info (mk_clos2 e t) stk + | (Lambda _|Prod _|Construct _|CoFix _|Ind _| + LetIn _|Const _|Var _|Evar _|Meta _|Sort _) -> + (mk_clos2 e t, stk) + + +(************************************************************************) + +(* Computes a weak head normal form from the result of knh. *) +let rec knr info m stk = + match m.term with + | FLambda(n,tys,f,e) when red_set info.i_flags fBETA -> + (match get_args n tys f e stk with + Inl e', s -> knit info e' f s + | Inr lam, s -> (lam,s)) + | FFlex(ConstKey (kn,_ as c)) when red_set info.i_flags (fCONST kn) -> + (match ref_value_cache info (ConstKey c) with + Some v -> kni info v stk + | None -> (set_norm m; (m,stk))) + | FFlex(VarKey id) when red_set info.i_flags (fVAR id) -> + (match ref_value_cache info (VarKey id) with + Some v -> kni info v stk + | None -> (set_norm m; (m,stk))) + | FFlex(RelKey k) when red_set info.i_flags fDELTA -> + (match ref_value_cache info (RelKey k) with + Some v -> kni info v stk + | None -> (set_norm m; (m,stk))) + | FConstruct((ind,c),u) -> + let use_match = red_set info.i_flags fMATCH in + let use_fix = red_set info.i_flags fFIX in + if use_match || use_fix then + (match strip_update_shift_app m stk with + | (depth, args, ZcaseT(ci,_,br,e)::s) when use_match -> + assert (ci.ci_npar>=0); + let rargs = drop_parameters depth ci.ci_npar args in + knit info e br.(c-1) (rargs@s) + | (_, cargs, Zfix(fx,par)::s) when use_fix -> + let rarg = fapp_stack(m,cargs) in + let stk' = par @ append_stack [|rarg|] s in + let (fxe,fxbd) = contract_fix_vect fx.term in + knit info fxe fxbd stk' + | (depth, args, Zproj (n, m, cst)::s) when use_match -> + let rargs = drop_parameters depth n args in + let rarg = project_nth_arg m rargs in + kni info rarg s + | (_,args,s) -> (m,args@s)) + else (m,stk) + | FCoFix _ when red_set info.i_flags fCOFIX -> + (match strip_update_shift_app m stk with + (_, args, (((ZcaseT _|Zproj _)::_) as stk')) -> + let (fxe,fxbd) = contract_fix_vect m.term in + knit info fxe fxbd (args@stk') + | (_,args,s) -> (m,args@s)) + | FLetIn (_,v,_,bd,e) when red_set info.i_flags fZETA -> + knit info (subs_cons([|v|],e)) bd stk + | FEvar(ev,env) -> + (match evar_value info.i_cache ev with + Some c -> knit info env c stk + | None -> (m,stk)) + | _ -> (m,stk) + +(* Computes the weak head normal form of a term *) +and kni info m stk = + let (hm,s) = knh info m stk in + knr info hm s +and knit info e t stk = + let (ht,s) = knht info e t stk in + knr info ht s + +let kh info v stk = fapp_stack(kni info v stk) + +(************************************************************************) + +let rec zip_term zfun m stk = + match stk with + | [] -> m + | Zapp args :: s -> + zip_term zfun (mkApp(m, Array.map zfun args)) s + | ZcaseT(ci,p,br,e)::s -> + let t = mkCase(ci, zfun (mk_clos e p), m, + Array.map (fun b -> zfun (mk_clos e b)) br) in + zip_term zfun t s + | Zproj(_,_,p)::s -> + let t = mkProj (Projection.make p true, m) in + zip_term zfun t s + | Zfix(fx,par)::s -> + let h = mkApp(zip_term zfun (zfun fx) par,[|m|]) in + zip_term zfun h s + | Zshift(n)::s -> + zip_term zfun (lift n m) s + | Zupdate(rf)::s -> + zip_term zfun m s + +(* Computes the strong normal form of a term. + 1- Calls kni + 2- tries to rebuild the term. If a closure still has to be computed, + calls itself recursively. *) +let rec kl info m = + if is_val m then (incr prune; term_of_fconstr m) + else + let (nm,s) = kni info m [] in + let _ = fapp_stack(nm,s) in (* to unlock Zupdates! *) + zip_term (kl info) (norm_head info nm) s + +(* no redex: go up for atoms and already normalized terms, go down + otherwise. *) +and norm_head info m = + if is_val m then (incr prune; term_of_fconstr m) else + match m.term with + | FLambda(n,tys,f,e) -> + let (e',rvtys) = + List.fold_left (fun (e,ctxt) (na,ty) -> + (subs_lift e, (na,kl info (mk_clos e ty))::ctxt)) + (e,[]) tys in + let bd = kl info (mk_clos e' f) in + List.fold_left (fun b (na,ty) -> mkLambda(na,ty,b)) bd rvtys + | FLetIn(na,a,b,f,e) -> + let c = mk_clos (subs_lift e) f in + mkLetIn(na, kl info a, kl info b, kl info c) + | FProd(na,dom,rng) -> + mkProd(na, kl info dom, kl info rng) + | FCoFix((n,(na,tys,bds)),e) -> + let ftys = CArray.Fun1.map mk_clos e tys in + let fbds = + CArray.Fun1.map mk_clos (subs_liftn (Array.length na) e) bds in + mkCoFix(n,(na, CArray.Fun1.map kl info ftys, CArray.Fun1.map kl info fbds)) + | FFix((n,(na,tys,bds)),e) -> + let ftys = CArray.Fun1.map mk_clos e tys in + let fbds = + CArray.Fun1.map mk_clos (subs_liftn (Array.length na) e) bds in + mkFix(n,(na, CArray.Fun1.map kl info ftys, CArray.Fun1.map kl info fbds)) + | FEvar((i,args),env) -> + mkEvar(i, Array.map (fun a -> kl info (mk_clos env a)) args) + | FProj (p,c) -> + mkProj (p, kl info c) + | t -> term_of_fconstr m + +(* Initialization and then normalization *) + +(* weak reduction *) +let whd_val info v = + with_stats (lazy (term_of_fconstr (kh info v []))) + +(* strong reduction *) +let norm_val info v = + with_stats (lazy (kl info v)) + +let inject c = mk_clos (subs_id 0) c + +let whd_stack infos m stk = + let k = kni infos m stk in + let _ = fapp_stack k in (* to unlock Zupdates! *) + k + +(* cache of constants: the body is computed only when needed. *) +type clos_infos = fconstr infos + +let create_clos_infos ?(evars=fun _ -> None) flgs env = + create (fun _ -> inject) flgs env evars +let oracle_of_infos infos = Environ.oracle infos.i_cache.i_env + +let env_of_infos infos = infos.i_cache.i_env + +let infos_with_reds infos reds = + { infos with i_flags = reds } + +let unfold_reference info key = + match key with + | ConstKey (kn,_) -> + if red_set info.i_flags (fCONST kn) then + ref_value_cache info key + else None + | VarKey i -> + if red_set info.i_flags (fVAR i) then + ref_value_cache info key + else None + | _ -> ref_value_cache info key |