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Diffstat (limited to 'lib/compiler/src/v3_life.erl')
| -rw-r--r-- | lib/compiler/src/v3_life.erl | 468 |
1 files changed, 0 insertions, 468 deletions
diff --git a/lib/compiler/src/v3_life.erl b/lib/compiler/src/v3_life.erl deleted file mode 100644 index be3ade47ff..0000000000 --- a/lib/compiler/src/v3_life.erl +++ /dev/null @@ -1,468 +0,0 @@ -%% -%% %CopyrightBegin% -%% -%% Copyright Ericsson AB 1999-2016. All Rights Reserved. -%% -%% Licensed under the Apache License, Version 2.0 (the "License"); -%% you may not use this file except in compliance with the License. -%% You may obtain a copy of the License at -%% -%% http://www.apache.org/licenses/LICENSE-2.0 -%% -%% Unless required by applicable law or agreed to in writing, software -%% distributed under the License is distributed on an "AS IS" BASIS, -%% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -%% See the License for the specific language governing permissions and -%% limitations under the License. -%% -%% %CopyrightEnd% -%% -%% Purpose : Convert annotated kernel expressions to annotated beam format. - -%% This module creates beam format annotated with variable lifetime -%% information. Each thing is given an index and for each variable we -%% store the first and last index for its occurrence. The variable -%% database, VDB, attached to each thing is only relevant internally -%% for that thing. -%% -%% For nested things like matches the numbering continues locally and -%% the VDB for that thing refers to the variable usage within that -%% thing. Variables which live through a such a thing are internally -%% given a very large last index. Internally the indexes continue -%% after the index of that thing. This creates no problems as the -%% internal variable info never escapes and externally we only see -%% variable which are alive both before or after. -%% -%% This means that variables never "escape" from a thing and the only -%% way to get values from a thing is to "return" them, with 'break' or -%% 'return'. Externally these values become the return values of the -%% thing. This is no real limitation as most nested things have -%% multiple threads so working out a common best variable usage is -%% difficult. - --module(v3_life). - --export([module/2]). - --export([vdb_find/2]). - --import(lists, [member/2,map/2,reverse/1,sort/1]). --import(ordsets, [add_element/2,intersection/2,union/2]). - --include("v3_kernel.hrl"). --include("v3_life.hrl"). - --type fa() :: {atom(),arity()}. - -%% These are not defined in v3_kernel.hrl. -get_kanno(Kthing) -> element(2, Kthing). -%%set_kanno(Kthing, Anno) -> setelement(2, Kthing, Anno). - --spec module(#k_mdef{}, [compile:option()]) -> - {'ok',{module(),[fa()],[_],[_]}}. - -module(#k_mdef{name=M,exports=Es,attributes=As,body=Fs0}, _Opts) -> - Fs1 = functions(Fs0, []), - {ok,{M,Es,As,Fs1}}. - -functions([F|Fs], Acc) -> - functions(Fs, [function(F)|Acc]); -functions([], Acc) -> reverse(Acc). - -%% function(Kfunc) -> Func. - -function(#k_fdef{anno=#k{a=Anno},func=F,arity=Ar,vars=Vs,body=Kb}) -> - try - As = var_list(Vs), - Vdb0 = init_vars(As), - %% Force a top-level match! - B0 = case Kb of - #k_match{} -> Kb; - _ -> - Ka = get_kanno(Kb), - #k_match{anno=#k{us=Ka#k.us,ns=[],a=Ka#k.a}, - vars=Vs,body=Kb,ret=[]} - end, - {B1,_,Vdb1} = body(B0, 1, Vdb0), - {function,F,Ar,As,B1,Vdb1,Anno} - catch - Class:Error -> - Stack = erlang:get_stacktrace(), - io:fwrite("Function: ~w/~w\n", [F,Ar]), - erlang:raise(Class, Error, Stack) - end. - -%% body(Kbody, I, Vdb) -> {[Expr],MaxI,Vdb}. -%% Handle a body. - -body(#k_seq{arg=Ke,body=Kb}, I, Vdb0) -> - %%ok = io:fwrite("life ~w:~p~n", [?LINE,{Ke,I,Vdb0}]), - A = get_kanno(Ke), - Vdb1 = use_vars(union(A#k.us, A#k.ns), I, Vdb0), - {Es,MaxI,Vdb2} = body(Kb, I+1, Vdb1), - E = expr(Ke, I, Vdb2), - {[E|Es],MaxI,Vdb2}; -body(Ke, I, Vdb0) -> - %%ok = io:fwrite("life ~w:~p~n", [?LINE,{Ke,I,Vdb0}]), - A = get_kanno(Ke), - Vdb1 = use_vars(union(A#k.us, A#k.ns), I, Vdb0), - E = expr(Ke, I, Vdb1), - {[E],I,Vdb1}. - -%% protected(Kprotected, I, Vdb) -> Protected. -%% Only used in guards. - -protected(#k_protected{anno=A,arg=Ts,ret=Rs}, I, Vdb) -> - %% Lock variables that are alive before try and used afterwards. - %% Don't lock variables that are only used inside the protected - %% expression. - Pdb0 = vdb_sub(I, I+1, Vdb), - {T,MaxI,Pdb1} = body(Ts, I+1, Pdb0), - Pdb2 = use_vars(A#k.ns, MaxI+1, Pdb1), %Save "return" values - #l{ke={protected,T,var_list(Rs)},i=I,a=A#k.a,vdb=Pdb2}. - -%% expr(Kexpr, I, Vdb) -> Expr. - -expr(#k_test{anno=A,op=Op,args=As,inverted=Inverted}, I, _Vdb) -> - #l{ke={test,test_op(Op),atomic_list(As),Inverted},i=I,a=A#k.a}; -expr(#k_call{anno=A,op=Op,args=As,ret=Rs}, I, _Vdb) -> - #l{ke={call,call_op(Op),atomic_list(As),var_list(Rs)},i=I,a=A#k.a}; -expr(#k_enter{anno=A,op=Op,args=As}, I, _Vdb) -> - #l{ke={enter,call_op(Op),atomic_list(As)},i=I,a=A#k.a}; -expr(#k_bif{anno=A,op=Op,args=As,ret=Rs}, I, _Vdb) -> - Bif = k_bif(A, Op, As, Rs), - #l{ke=Bif,i=I,a=A#k.a}; -expr(#k_match{anno=A,body=Kb,ret=Rs}, I, Vdb) -> - %% Work out imported variables which need to be locked. - Mdb = vdb_sub(I, I+1, Vdb), - M = match(Kb, A#k.us, I+1, [], Mdb), - #l{ke={match,M,var_list(Rs)},i=I,vdb=use_vars(A#k.us, I+1, Mdb),a=A#k.a}; -expr(#k_guard_match{anno=A,body=Kb,ret=Rs}, I, Vdb) -> - %% Work out imported variables which need to be locked. - Mdb = vdb_sub(I, I+1, Vdb), - M = match(Kb, A#k.us, I+1, [], Mdb), - #l{ke={guard_match,M,var_list(Rs)},i=I,vdb=use_vars(A#k.us, I+1, Mdb),a=A#k.a}; -expr(#k_try{}=Try, I, Vdb) -> - body_try(Try, I, Vdb); -expr(#k_protected{}=Protected, I, Vdb) -> - protected(Protected, I, Vdb); -expr(#k_try_enter{anno=A,arg=Ka,vars=Vs,body=Kb,evars=Evs,handler=Kh}, I, Vdb) -> - %% Lock variables that are alive before the catch and used afterwards. - %% Don't lock variables that are only used inside the try. - Tdb0 = vdb_sub(I, I+1, Vdb), - %% This is the tricky bit. Lock variables in Arg that are used in - %% the body and handler. Add try tag 'variable'. - Ab = get_kanno(Kb), - Ah = get_kanno(Kh), - Tdb1 = use_vars(union(Ab#k.us, Ah#k.us), I+3, Tdb0), - Tdb2 = vdb_sub(I, I+2, Tdb1), - Vnames = fun (Kvar) -> Kvar#k_var.name end, %Get the variable names - {Aes,_,Adb} = body(Ka, I+2, add_var({catch_tag,I+1}, I+1, 1000000, Tdb2)), - {Bes,_,Bdb} = body(Kb, I+4, new_vars(sort(map(Vnames, Vs)), I+3, Tdb2)), - {Hes,_,Hdb} = body(Kh, I+4, new_vars(sort(map(Vnames, Evs)), I+3, Tdb2)), - #l{ke={try_enter,#l{ke={block,Aes},i=I+1,vdb=Adb,a=[]}, - var_list(Vs),#l{ke={block,Bes},i=I+3,vdb=Bdb,a=[]}, - var_list(Evs),#l{ke={block,Hes},i=I+3,vdb=Hdb,a=[]}}, - i=I,vdb=Tdb1,a=A#k.a}; -expr(#k_catch{anno=A,body=Kb,ret=[R]}, I, Vdb) -> - %% Lock variables that are alive before the catch and used afterwards. - %% Don't lock variables that are only used inside the catch. - %% Add catch tag 'variable'. - Cdb0 = vdb_sub(I, I+1, Vdb), - {Es,_,Cdb1} = body(Kb, I+1, add_var({catch_tag,I}, I, locked, Cdb0)), - #l{ke={'catch',Es,variable(R)},i=I,vdb=Cdb1,a=A#k.a}; -expr(#k_receive{anno=A,var=V,body=Kb,timeout=T,action=Ka,ret=Rs}, I, Vdb) -> - %% Work out imported variables which need to be locked. - Rdb = vdb_sub(I, I+1, Vdb), - M = match(Kb, add_element(V#k_var.name, A#k.us), I+1, [], - new_vars([V#k_var.name], I, Rdb)), - {Tes,_,Adb} = body(Ka, I+1, Rdb), - #l{ke={receive_loop,atomic(T),variable(V),M, - #l{ke=Tes,i=I+1,vdb=Adb,a=[]},var_list(Rs)}, - i=I,vdb=use_vars(A#k.us, I+1, Vdb),a=A#k.a}; -expr(#k_receive_accept{anno=A}, I, _Vdb) -> - #l{ke=receive_accept,i=I,a=A#k.a}; -expr(#k_receive_next{anno=A}, I, _Vdb) -> - #l{ke=receive_next,i=I,a=A#k.a}; -expr(#k_put{anno=A,arg=Arg,ret=Rs}, I, _Vdb) -> - #l{ke={set,var_list(Rs),literal(Arg, [])},i=I,a=A#k.a}; -expr(#k_break{anno=A,args=As}, I, _Vdb) -> - #l{ke={break,atomic_list(As)},i=I,a=A#k.a}; -expr(#k_guard_break{anno=A,args=As}, I, Vdb) -> - Locked = [V || {V,_,_} <- Vdb], - #l{ke={guard_break,atomic_list(As),Locked},i=I,a=A#k.a}; -expr(#k_return{anno=A,args=As}, I, _Vdb) -> - #l{ke={return,atomic_list(As)},i=I,a=A#k.a}. - -body_try(#k_try{anno=A,arg=Ka,vars=Vs,body=Kb,evars=Evs,handler=Kh,ret=Rs}, - I, Vdb) -> - %% Lock variables that are alive before the catch and used afterwards. - %% Don't lock variables that are only used inside the try. - Tdb0 = vdb_sub(I, I+1, Vdb), - %% This is the tricky bit. Lock variables in Arg that are used in - %% the body and handler. Add try tag 'variable'. - Ab = get_kanno(Kb), - Ah = get_kanno(Kh), - Tdb1 = use_vars(union(Ab#k.us, Ah#k.us), I+3, Tdb0), - Tdb2 = vdb_sub(I, I+2, Tdb1), - Vnames = fun (Kvar) -> Kvar#k_var.name end, %Get the variable names - {Aes,_,Adb} = body(Ka, I+2, add_var({catch_tag,I+1}, I+1, locked, Tdb2)), - {Bes,_,Bdb} = body(Kb, I+4, new_vars(sort(map(Vnames, Vs)), I+3, Tdb2)), - {Hes,_,Hdb} = body(Kh, I+4, new_vars(sort(map(Vnames, Evs)), I+3, Tdb2)), - #l{ke={'try',#l{ke={block,Aes},i=I+1,vdb=Adb,a=[]}, - var_list(Vs),#l{ke={block,Bes},i=I+3,vdb=Bdb,a=[]}, - var_list(Evs),#l{ke={block,Hes},i=I+3,vdb=Hdb,a=[]}, - var_list(Rs)}, - i=I,vdb=Tdb1,a=A#k.a}. - -%% call_op(Op) -> Op. -%% test_op(Op) -> Op. -%% Do any necessary name translations here to munge into beam format. - -call_op(#k_local{name=N}) -> N; -call_op(#k_remote{mod=M,name=N}) -> {remote,atomic(M),atomic(N)}; -call_op(Other) -> variable(Other). - -test_op(#k_remote{mod=#k_atom{val=erlang},name=#k_atom{val=N}}) -> N. - -%% k_bif(Anno, Op, [Arg], [Ret], Vdb) -> Expr. -%% Build bifs. - -k_bif(_A, #k_internal{name=Name}, As, Rs) -> - {internal,Name,atomic_list(As),var_list(Rs)}; -k_bif(_A, #k_remote{mod=#k_atom{val=erlang},name=#k_atom{val=Name}}, As, Rs) -> - Ar = length(As), - case is_gc_bif(Name, Ar) of - false -> - {bif,Name,atomic_list(As),var_list(Rs)}; - true -> - {gc_bif,Name,atomic_list(As),var_list(Rs)} - end. - -%% match(Kexpr, [LockVar], I, Vdb) -> Expr. -%% Convert match tree to old format. - -match(#k_alt{anno=A,first=Kf,then=Kt}, Ls, I, Ctxt, Vdb0) -> - Vdb1 = use_vars(union(A#k.us, Ls), I, Vdb0), - F = match(Kf, Ls, I+1, Ctxt, Vdb1), - T = match(Kt, Ls, I+1, Ctxt, Vdb1), - #l{ke={alt,F,T},i=I,vdb=Vdb1,a=A#k.a}; -match(#k_select{anno=A,var=V,types=Kts}, Ls0, I, Ctxt, Vdb0) -> - Vanno = get_kanno(V), - Ls1 = case member(no_usage, Vanno) of - false -> add_element(V#k_var.name, Ls0); - true -> Ls0 - end, - Anno = case member(reuse_for_context, Vanno) of - true -> [reuse_for_context|A#k.a]; - false -> A#k.a - end, - Vdb1 = use_vars(union(A#k.us, Ls1), I, Vdb0), - Ts = [type_clause(Tc, Ls1, I+1, Ctxt, Vdb1) || Tc <- Kts], - #l{ke={select,literal(V, Ctxt),Ts},i=I,vdb=Vdb1,a=Anno}; -match(#k_guard{anno=A,clauses=Kcs}, Ls, I, Ctxt, Vdb0) -> - Vdb1 = use_vars(union(A#k.us, Ls), I, Vdb0), - Cs = [guard_clause(G, Ls, I+1, Ctxt, Vdb1) || G <- Kcs], - #l{ke={guard,Cs},i=I,vdb=Vdb1,a=A#k.a}; -match(Other, Ls, I, _Ctxt, Vdb0) -> - Vdb1 = use_vars(Ls, I, Vdb0), - {B,_,Vdb2} = body(Other, I+1, Vdb1), - #l{ke={block,B},i=I,vdb=Vdb2,a=[]}. - -type_clause(#k_type_clause{anno=A,type=T,values=Kvs}, Ls, I, Ctxt, Vdb0) -> - %%ok = io:format("life ~w: ~p~n", [?LINE,{T,Kvs}]), - Vdb1 = use_vars(union(A#k.us, Ls), I+1, Vdb0), - Vs = [val_clause(Vc, Ls, I+1, Ctxt, Vdb1) || Vc <- Kvs], - #l{ke={type_clause,type(T),Vs},i=I,vdb=Vdb1,a=A#k.a}. - -val_clause(#k_val_clause{anno=A,val=V,body=Kb}, Ls0, I, Ctxt0, Vdb0) -> - New = (get_kanno(V))#k.ns, - Bus = (get_kanno(Kb))#k.us, - %%ok = io:format("Ls0 = ~p, Used=~p\n New=~p, Bus=~p\n", [Ls0,Used,New,Bus]), - Ls1 = union(intersection(New, Bus), Ls0), %Lock for safety - Vdb1 = use_vars(union(A#k.us, Ls1), I+1, new_vars(New, I, Vdb0)), - Ctxt = case V of - #k_binary{segs=#k_var{name=C0}} -> C0; - _ -> Ctxt0 - end, - B = match(Kb, Ls1, I+1, Ctxt, Vdb1), - #l{ke={val_clause,literal(V, Ctxt),B},i=I,vdb=use_vars(Bus, I+1, Vdb1),a=A#k.a}. - -guard_clause(#k_guard_clause{anno=A,guard=Kg,body=Kb}, Ls, I, Ctxt, Vdb0) -> - Vdb1 = use_vars(union(A#k.us, Ls), I+2, Vdb0), - Gdb = vdb_sub(I+1, I+2, Vdb1), - G = protected(Kg, I+1, Gdb), - B = match(Kb, Ls, I+2, Ctxt, Vdb1), - #l{ke={guard_clause,G,B}, - i=I,vdb=use_vars((get_kanno(Kg))#k.us, I+2, Vdb1), - a=A#k.a}. - -%% type(Ktype) -> Type. - -type(k_literal) -> literal; -type(k_int) -> integer; -%%type(k_char) -> integer; %Hhhmmm??? -type(k_float) -> float; -type(k_atom) -> atom; -type(k_nil) -> nil; -type(k_cons) -> cons; -type(k_tuple) -> tuple; -type(k_binary) -> binary; -type(k_bin_seg) -> bin_seg; -type(k_bin_int) -> bin_int; -type(k_bin_end) -> bin_end; -type(k_map) -> map. - -%% variable(Klit) -> Lit. -%% var_list([Klit]) -> [Lit]. - -variable(#k_var{name=N}) -> {var,N}. - -var_list(Ks) -> [variable(K) || K <- Ks]. - -%% atomic(Klit) -> Lit. -%% atomic_list([Klit]) -> [Lit]. - -atomic(#k_literal{val=V}) -> {literal,V}; -atomic(#k_var{name=N}) -> {var,N}; -atomic(#k_int{val=I}) -> {integer,I}; -atomic(#k_float{val=F}) -> {float,F}; -atomic(#k_atom{val=N}) -> {atom,N}; -%%atomic(#k_char{val=C}) -> {char,C}; -atomic(#k_nil{}) -> nil. - -atomic_list(Ks) -> [atomic(K) || K <- Ks]. - -%% literal(Klit) -> Lit. -%% literal_list([Klit]) -> [Lit]. - -literal(#k_var{name=N}, _) -> {var,N}; -literal(#k_literal{val=I}, _) -> {literal,I}; -literal(#k_int{val=I}, _) -> {integer,I}; -literal(#k_float{val=F}, _) -> {float,F}; -literal(#k_atom{val=N}, _) -> {atom,N}; -%%literal(#k_char{val=C}, _) -> {char,C}; -literal(#k_nil{}, _) -> nil; -literal(#k_cons{hd=H,tl=T}, Ctxt) -> - {cons,[literal(H, Ctxt),literal(T, Ctxt)]}; -literal(#k_binary{segs=V}, Ctxt) -> - {binary,literal(V, Ctxt)}; -literal(#k_bin_seg{size=S,unit=U,type=T,flags=Fs,seg=Seg,next=[]}, Ctxt) -> - %% Only occurs in patterns. - {bin_seg,Ctxt,literal(S, Ctxt),U,T,Fs,[literal(Seg, Ctxt)]}; -literal(#k_bin_seg{size=S,unit=U,type=T,flags=Fs,seg=Seg,next=N}, Ctxt) -> - {bin_seg,Ctxt,literal(S, Ctxt),U,T,Fs, - [literal(Seg, Ctxt),literal(N, Ctxt)]}; -literal(#k_bin_int{size=S,unit=U,flags=Fs,val=Int,next=N}, Ctxt) -> - %% Only occurs in patterns. - {bin_int,Ctxt,literal(S, Ctxt),U,Fs,Int, - [literal(N, Ctxt)]}; -literal(#k_bin_end{}, Ctxt) -> - {bin_end,Ctxt}; -literal(#k_tuple{es=Es}, Ctxt) -> - {tuple,literal_list(Es, Ctxt)}; -literal(#k_map{op=Op,var=Var,es=Es0}, Ctxt) -> - {map,Op,literal(Var, Ctxt),literal_list(Es0, Ctxt)}; -literal(#k_map_pair{key=K,val=V}, Ctxt) -> - {map_pair,literal(K, Ctxt),literal(V, Ctxt)}. - -literal_list(Ks, Ctxt) -> - [literal(K, Ctxt) || K <- Ks]. - - -%% is_gc_bif(Name, Arity) -> true|false -%% Determines whether the BIF Name/Arity might do a GC. - -is_gc_bif(hd, 1) -> false; -is_gc_bif(tl, 1) -> false; -is_gc_bif(self, 0) -> false; -is_gc_bif(node, 0) -> false; -is_gc_bif(node, 1) -> false; -is_gc_bif(element, 2) -> false; -is_gc_bif(get, 1) -> false; -is_gc_bif(tuple_size, 1) -> false; -is_gc_bif(Bif, Arity) -> - not (erl_internal:bool_op(Bif, Arity) orelse - erl_internal:new_type_test(Bif, Arity) orelse - erl_internal:comp_op(Bif, Arity)). - -%% Keep track of life time for variables. -%% -%% init_vars([{var,VarName}]) -> Vdb. -%% new_vars([VarName], I, Vdb) -> Vdb. -%% use_vars([VarName], I, Vdb) -> Vdb. -%% add_var(VarName, F, L, Vdb) -> Vdb. -%% -%% The list of variable names for new_vars/3 and use_vars/3 -%% must be sorted. - -init_vars(Vs) -> - vdb_new(Vs). - -new_vars([], _, Vdb) -> Vdb; -new_vars([V], I, Vdb) -> vdb_store_new(V, {V,I,I}, Vdb); -new_vars(Vs, I, Vdb) -> vdb_update_vars(Vs, Vdb, I). - -use_vars([], _, Vdb) -> - Vdb; -use_vars([V], I, Vdb) -> - case vdb_find(V, Vdb) of - {V,F,L} when I > L -> vdb_update(V, {V,F,I}, Vdb); - {V,_,_} -> Vdb; - error -> vdb_store_new(V, {V,I,I}, Vdb) - end; -use_vars(Vs, I, Vdb) -> vdb_update_vars(Vs, Vdb, I). - -add_var(V, F, L, Vdb) -> - vdb_store_new(V, {V,F,L}, Vdb). - -%% vdb - -vdb_new(Vs) -> - sort([{V,0,0} || {var,V} <- Vs]). - --type var() :: atom(). - --spec vdb_find(var(), [vdb_entry()]) -> 'error' | vdb_entry(). - -vdb_find(V, Vdb) -> - case lists:keyfind(V, 1, Vdb) of - false -> error; - Vd -> Vd - end. - -vdb_update(V, Update, [{V,_,_}|Vdb]) -> - [Update|Vdb]; -vdb_update(V, Update, [Vd|Vdb]) -> - [Vd|vdb_update(V, Update, Vdb)]. - -vdb_store_new(V, New, [{V1,_,_}=Vd|Vdb]) when V > V1 -> - [Vd|vdb_store_new(V, New, Vdb)]; -vdb_store_new(V, New, [{V1,_,_}|_]=Vdb) when V < V1 -> - [New|Vdb]; -vdb_store_new(_, New, []) -> [New]. - -vdb_update_vars([V|_]=Vs, [{V1,_,_}=Vd|Vdb], I) when V > V1 -> - [Vd|vdb_update_vars(Vs, Vdb, I)]; -vdb_update_vars([V|Vs], [{V1,_,_}|_]=Vdb, I) when V < V1 -> - %% New variable. - [{V,I,I}|vdb_update_vars(Vs, Vdb, I)]; -vdb_update_vars([V|Vs], [{_,F,L}=Vd|Vdb], I) -> - %% Existing variable. - if - I > L -> [{V,F,I}|vdb_update_vars(Vs, Vdb, I)]; - true -> [Vd|vdb_update_vars(Vs, Vdb, I)] - end; -vdb_update_vars([V|Vs], [], I) -> - %% New variable. - [{V,I,I}|vdb_update_vars(Vs, [], I)]; -vdb_update_vars([], Vdb, _) -> Vdb. - -%% vdb_sub(Min, Max, Vdb) -> Vdb. -%% Extract variables which are used before and after Min. Lock -%% variables alive after Max. - -vdb_sub(Min, Max, Vdb) -> - [ if L >= Max -> {V,F,locked}; - true -> Vd - end || {V,F,L}=Vd <- Vdb, F < Min, L >= Min ]. |