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Diffstat (limited to 'lib/dialyzer/src/cerl_closurean.erl')
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diff --git a/lib/dialyzer/src/cerl_closurean.erl b/lib/dialyzer/src/cerl_closurean.erl deleted file mode 100644 index 55dcfeed1d..0000000000 --- a/lib/dialyzer/src/cerl_closurean.erl +++ /dev/null @@ -1,856 +0,0 @@ -%% 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. -%% -%% @copyright 2001-2002 Richard Carlsson -%% @author Richard Carlsson <carlsson.richard@gmail.com> -%% @doc Closure analysis of Core Erlang programs. - -%% TODO: might need a "top" (`any') element for any-length value lists. - --module(cerl_closurean). - --export([analyze/1, annotate/1]). -%% The following functions are exported from this module since they -%% are also used by Dialyzer (file dialyzer/src/dialyzer_dep.erl) --export([is_escape_op/2, is_escape_op/3, is_literal_op/2, is_literal_op/3]). - --import(cerl, [ann_c_apply/3, ann_c_fun/3, ann_c_var/2, apply_args/1, - apply_op/1, atom_val/1, bitstr_size/1, bitstr_val/1, - binary_segments/1, c_letrec/2, c_seq/2, c_tuple/1, - c_nil/0, call_args/1, call_module/1, call_name/1, - case_arg/1, case_clauses/1, catch_body/1, clause_body/1, - clause_guard/1, clause_pats/1, cons_hd/1, cons_tl/1, - fun_body/1, fun_vars/1, get_ann/1, is_c_atom/1, - let_arg/1, let_body/1, let_vars/1, letrec_body/1, - letrec_defs/1, module_defs/1, module_defs/1, - module_exports/1, pat_vars/1, primop_args/1, - primop_name/1, receive_action/1, receive_clauses/1, - receive_timeout/1, seq_arg/1, seq_body/1, set_ann/2, - try_arg/1, try_body/1, try_vars/1, try_evars/1, - try_handler/1, tuple_es/1, type/1, values_es/1]). - --import(cerl_trees, [get_label/1]). - -%% =========================================================================== - --type label() :: integer() | 'top' | 'external' | 'external_call'. --type ordset(X) :: [X]. % XXX: TAKE ME OUT --type labelset() :: ordset(label()). --type outlist() :: [labelset()] | 'none'. --type escapes() :: labelset(). - -%% =========================================================================== -%% annotate(Tree) -> {Tree1, OutList, Outputs, Escapes, Dependencies, Parents} -%% -%% Tree = cerl:cerl() -%% -%% Analyzes `Tree' (see `analyze') and appends terms `{callers, -%% Labels}' and `{calls, Labels}' to the annotation list of each -%% fun-expression node and apply-expression node of `Tree', -%% respectively, where `Labels' is an ordered-set list of labels of -%% fun-expressions in `Tree', possibly also containing the atom -%% `external', corresponding to the dependency information derived -%% by the analysis. Any previous such annotations are removed from -%% `Tree'. `Tree1' is the modified tree; for details on `OutList', -%% `Outputs' , `Dependencies', `Escapes' and `Parents', see -%% `analyze'. -%% -%% Note: `Tree' must be annotated with labels in order to use this -%% function; see `analyze' for details. - --spec annotate(cerl:cerl()) -> - {cerl:cerl(), outlist(), dict:dict(), - escapes(), dict:dict(), dict:dict()}. - -annotate(Tree) -> - {Xs, Out, Esc, Deps, Par} = analyze(Tree), - F = fun (T) -> - case type(T) of - 'fun' -> - L = get_label(T), - X = case dict:find(L, Deps) of - {ok, X1} -> X1; - error -> set__new() - end, - set_ann(T, append_ann(callers, - set__to_list(X), - get_ann(T))); - apply -> - L = get_label(T), - X = case dict:find(L, Deps) of - {ok, X1} -> X1; - error -> set__new() - end, - set_ann(T, append_ann(calls, - set__to_list(X), - get_ann(T))); - _ -> -%%% set_ann(T, []) % debug - T - end - end, - {cerl_trees:map(F, Tree), Xs, Out, Esc, Deps, Par}. - -append_ann(Tag, Val, [X | Xs]) -> - if tuple_size(X) >= 1, element(1, X) =:= Tag -> - append_ann(Tag, Val, Xs); - true -> - [X | append_ann(Tag, Val, Xs)] - end; -append_ann(Tag, Val, []) -> - [{Tag, Val}]. - -%% ===================================================================== -%% analyze(Tree) -> {OutList, Outputs, Escapes, Dependencies, Parents} -%% -%% Tree = cerl() -%% OutList = [LabelSet] | none -%% Outputs = dict(Label, OutList) -%% Escapes = LabelSet -%% Dependencies = dict(Label, LabelSet) -%% LabelSet = ordset(Label) -%% Label = integer() | top | external | external_call -%% Parents = dict(Label, Label) -%% -%% Analyzes a module or an expression represented by `Tree'. -%% -%% The returned `OutList' is a list of sets of labels of -%% fun-expressions which correspond to the possible closures in the -%% value list produced by `Tree' (viewed as an expression; the -%% "value" of a module contains its exported functions). The atom -%% `none' denotes missing or conflicting information. -%% -%% The atom `external' in any label set denotes any possible -%% function outside `Tree', including those in `Escapes'. The atom -%% `top' denotes the top-level expression `Tree'. -%% -%% `Outputs' is a mapping from the labels of fun-expressions in -%% `Tree' to corresponding lists of sets of labels of -%% fun-expressions (or the atom `none'), representing the possible -%% closures in the value lists returned by the respective -%% functions. -%% -%% `Dependencies' is a similar mapping from the labels of -%% fun-expressions and apply-expressions in `Tree' to sets of -%% labels of corresponding fun-expressions which may contain call -%% sites of the functions or be called from the call sites, -%% respectively. Any such label not defined in `Dependencies' -%% represents an unreachable function or a dead or faulty -%% application. -%% -%% `Escapes' is the set of labels of fun-expressions in `Tree' such -%% that corresponding closures may be accessed from outside `Tree'. -%% -%% `Parents' is a mapping from labels of fun-expressions in `Tree' -%% to the corresponding label of the nearest containing -%% fun-expression or top-level expression. This can be used to -%% extend the dependency graph, for certain analyses. -%% -%% Note: `Tree' must be annotated with labels (as done by the -%% function `cerl_trees:label/1') in order to use this function. -%% The label annotation `{label, L}' (where L should be an integer) -%% must be the first element of the annotation list of each node in -%% the tree. Instances of variables bound in `Tree' which denote -%% the same variable must have the same label; apart from this, -%% labels should be unique. Constant literals do not need to be -%% labeled. - --record(state, {vars, out, dep, work, funs, par}). - -%% Note: In order to keep our domain simple, we assume that all remote -%% calls and primops return a single value, if any. - -%% We use the terms `closure', `label', `lambda' and `fun-expression' -%% interchangeably. The exact meaning in each case can be grasped from -%% the context. -%% -%% Rules: -%% 1) The implicit top level lambda escapes. -%% 2) A lambda returned by an escaped lambda also escapes. -%% 3) An escaped lambda can be passed an external lambda as argument. -%% 4) A lambda passed as argument to an external lambda also escapes. -%% 5) An argument passed to an unknown operation escapes. -%% 6) A call to an unknown operation can return an external lambda. -%% -%% Escaped lambdas become part of the set of external lambdas, but this -%% does not need to be represented explicitly. - -%% We wrap the given syntax tree T in a fun-expression labeled `top', -%% which is initially in the set of escaped labels. `top' will be -%% visited at least once. -%% -%% We create a separate function labeled `external', defined as: -%% "'external'/1 = fun (Escape) -> do apply 'external'/1(apply Escape()) -%% 'external'/1", which will represent any and all functions outside T, -%% and which returns itself, and contains a recursive call; this models -%% rules 2 and 4 above. It will be revisited if the set of escaped -%% labels changes, or at least once. Its parameter `Escape' is a -%% variable labeled `escape', which will hold the set of escaped labels. -%% initially it contains `top' and `external'. - --spec analyze(cerl:cerl()) -> - {outlist(), dict:dict(), escapes(), dict:dict(), dict:dict()}. - -analyze(Tree) -> - %% Note that we use different name spaces for variable labels and - %% function/call site labels, so we can reuse some names here. We - %% assume that the labeling of Tree only uses integers, not atoms. - External = ann_c_var([{label, external}], {external, 1}), - Escape = ann_c_var([{label, escape}], 'Escape'), - ExtBody = c_seq(ann_c_apply([{label, loop}], External, - [ann_c_apply([{label, external_call}], - Escape, [])]), - External), - ExtFun = ann_c_fun([{label, external}], [Escape], ExtBody), -%%% io:fwrite("external fun:\n~s.\n", -%%% [cerl_prettypr:format(ExtFun, [noann])]), - Top = ann_c_var([{label, top}], {top, 0}), - TopFun = ann_c_fun([{label, top}], [], Tree), - - %% The "start fun" just makes the initialisation easier. It will not - %% be marked as escaped, and thus cannot be called. - StartFun = ann_c_fun([{label, start}], [], - c_letrec([{External, ExtFun}, {Top, TopFun}], - c_nil())), -%%% io:fwrite("start fun:\n~s.\n", -%%% [cerl_prettypr:format(StartFun, [noann])]), - - %% Gather a database of all fun-expressions in Tree and initialise - %% all their outputs and parameter variables. Bind all module- and - %% letrec-defined variables to their corresponding labels. - Funs0 = dict:new(), - Vars0 = dict:new(), - Out0 = dict:new(), - Empty = empty(), - F = fun (T, S = {Fs, Vs, Os}) -> - case type(T) of - 'fun' -> - L = get_label(T), - As = fun_vars(T), - {dict:store(L, T, Fs), - bind_vars_single(As, Empty, Vs), - dict:store(L, none, Os)}; - letrec -> - {Fs, bind_defs(letrec_defs(T), Vs), Os}; - module -> - {Fs, bind_defs(module_defs(T), Vs), Os}; - _ -> - S - end - end, - {Funs, Vars, Out} = cerl_trees:fold(F, {Funs0, Vars0, Out0}, - StartFun), - - %% Initialise Escape to the minimal set of escaped labels. - Vars1 = dict:store(escape, from_label_list([top, external]), Vars), - - %% Enter the fixpoint iteration at the StartFun. - St = loop(StartFun, start, #state{vars = Vars1, - out = Out, - dep = dict:new(), - work = init_work(), - funs = Funs, - par = dict:new()}), -%%% io:fwrite("dependencies: ~p.\n", -%%% [[{X, set__to_list(Y)} -%%% || {X, Y} <- dict:to_list(St#state.dep)]]), - {dict:fetch(top, St#state.out), - tidy_dict([start, top, external], St#state.out), - dict:fetch(escape, St#state.vars), - tidy_dict([loop], St#state.dep), - St#state.par}. - -tidy_dict([X | Xs], D) -> - tidy_dict(Xs, dict:erase(X, D)); -tidy_dict([], D) -> - D. - -loop(T, L, St0) -> -%%% io:fwrite("analyzing: ~w.\n", [L]), -%%% io:fwrite("work: ~w.\n", [St0#state.work]), - Xs0 = dict:fetch(L, St0#state.out), - {Xs, St1} = visit(fun_body(T), L, St0), - {W, M} = case equal(Xs0, Xs) of - true -> - {St1#state.work, St1#state.out}; - false -> -%%% io:fwrite("out (~w) changed: ~w <- ~w.\n", -%%% [L, Xs, Xs0]), - M1 = dict:store(L, Xs, St1#state.out), - case dict:find(L, St1#state.dep) of - {ok, S} -> - {add_work(set__to_list(S), St1#state.work), - M1}; - error -> - {St1#state.work, M1} - end - end, - St2 = St1#state{out = M}, - case take_work(W) of - {ok, L1, W1} -> - T1 = dict:fetch(L1, St2#state.funs), - loop(T1, L1, St2#state{work = W1}); - none -> - St2 - end. - -visit(T, L, St) -> - case type(T) of - literal -> - {[empty()], St}; - var -> - %% If a variable is not already in the store here, we - %% initialize it to empty(). - L1 = get_label(T), - Vars = St#state.vars, - case dict:find(L1, Vars) of - {ok, X} -> - {[X], St}; - error -> - X = empty(), - St1 = St#state{vars = dict:store(L1, X, Vars)}, - {[X], St1} - end; - 'fun' -> - %% Must revisit the fun also, because its environment might - %% have changed. (We don't keep track of such dependencies.) - L1 = get_label(T), - St1 = St#state{work = add_work([L1], St#state.work), - par = set_parent([L1], L, St#state.par)}, - {[singleton(L1)], St1}; - values -> - visit_list(values_es(T), L, St); - cons -> - {Xs, St1} = visit_list([cons_hd(T), cons_tl(T)], L, St), - {[join_single_list(Xs)], St1}; - tuple -> - {Xs, St1} = visit_list(tuple_es(T), L, St), - {[join_single_list(Xs)], St1}; - 'let' -> - {Xs, St1} = visit(let_arg(T), L, St), - Vars = bind_vars(let_vars(T), Xs, St1#state.vars), - visit(let_body(T), L, St1#state{vars = Vars}); - seq -> - {_, St1} = visit(seq_arg(T), L, St), - visit(seq_body(T), L, St1); - apply -> - {Xs, St1} = visit(apply_op(T), L, St), - {As, St2} = visit_list(apply_args(T), L, St1), - case Xs of - [X] -> - %% We store the dependency from the call site to the - %% called functions - Ls = set__to_list(X), - Out = St2#state.out, - Xs1 = join_list([dict:fetch(Lx, Out) || Lx <- Ls]), - St3 = call_site(Ls, L, As, St2), - L1 = get_label(T), - D = dict:store(L1, X, St3#state.dep), - {Xs1, St3#state{dep = D}}; - none -> - {none, St2} - end; - call -> - M = call_module(T), - F = call_name(T), - {_, St1} = visit(M, L, St), - {_, St2} = visit(F, L, St1), - {Xs, St3} = visit_list(call_args(T), L, St2), - remote_call(M, F, Xs, St3); - primop -> - As = primop_args(T), - {Xs, St1} = visit_list(As, L, St), - primop_call(atom_val(primop_name(T)), length(Xs), Xs, St1); - 'case' -> - {Xs, St1} = visit(case_arg(T), L, St), - visit_clauses(Xs, case_clauses(T), L, St1); - 'receive' -> - X = singleton(external), - {Xs1, St1} = visit_clauses([X], receive_clauses(T), L, St), - {_, St2} = visit(receive_timeout(T), L, St1), - {Xs2, St3} = visit(receive_action(T), L, St2), - {join(Xs1, Xs2), St3}; - 'try' -> - {Xs1, St1} = visit(try_arg(T), L, St), - X = singleton(external), - Vars = bind_vars(try_vars(T), [X], St1#state.vars), - {Xs2, St2} = visit(try_body(T), L, St1#state{vars = Vars}), - Evars = bind_vars(try_evars(T), [X, X, X], St2#state.vars), - {Xs3, St3} = visit(try_handler(T), L, St2#state{vars = Evars}), - {join(join(Xs1, Xs2), Xs3), St3}; - 'catch' -> - {_, St1} = visit(catch_body(T), L, St), - {[singleton(external)], St1}; - binary -> - {_, St1} = visit_list(binary_segments(T), L, St), - {[empty()], St1}; - bitstr -> - %% The other fields are constant literals. - {_, St1} = visit(bitstr_val(T), L, St), - {_, St2} = visit(bitstr_size(T), L, St1), - {none, St2}; - letrec -> - %% All the bound funs should be revisited, because the - %% environment might have changed. - Ls = [get_label(F) || {_, F} <- letrec_defs(T)], - St1 = St#state{work = add_work(Ls, St#state.work), - par = set_parent(Ls, L, St#state.par)}, - visit(letrec_body(T), L, St1); - module -> - %% All the exported functions escape, and can thus be passed - %% any external closures as arguments. We regard a module as - %% a tuple of function variables in the body of a `letrec'. - visit(c_letrec(module_defs(T), c_tuple(module_exports(T))), - L, St) - end. - -visit_clause(T, Xs, L, St) -> - Vars = bind_pats(clause_pats(T), Xs, St#state.vars), - {_, St1} = visit(clause_guard(T), L, St#state{vars = Vars}), - visit(clause_body(T), L, St1). - -%% We assume correct value-list typing. - -visit_list([T | Ts], L, St) -> - {Xs, St1} = visit(T, L, St), - {Xs1, St2} = visit_list(Ts, L, St1), - X = case Xs of - [X1] -> X1; - none -> none - end, - {[X | Xs1], St2}; -visit_list([], _L, St) -> - {[], St}. - -visit_clauses(Xs, [T | Ts], L, St) -> - {Xs1, St1} = visit_clause(T, Xs, L, St), - {Xs2, St2} = visit_clauses(Xs, Ts, L, St1), - {join(Xs1, Xs2), St2}; -visit_clauses(_, [], _L, St) -> - {none, St}. - -bind_defs([{V, F} | Ds], Vars) -> - bind_defs(Ds, dict:store(get_label(V), singleton(get_label(F)), - Vars)); -bind_defs([], Vars) -> - Vars. - -bind_pats(Ps, none, Vars) -> - bind_pats_single(Ps, empty(), Vars); -bind_pats(Ps, Xs, Vars) -> - if length(Xs) =:= length(Ps) -> - bind_pats_list(Ps, Xs, Vars); - true -> - bind_pats_single(Ps, empty(), Vars) - end. - -bind_pats_list([P | Ps], [X | Xs], Vars) -> - bind_pats_list(Ps, Xs, bind_vars_single(pat_vars(P), X, Vars)); -bind_pats_list([], [], Vars) -> - Vars. - -bind_pats_single([P | Ps], X, Vars) -> - bind_pats_single(Ps, X, bind_vars_single(pat_vars(P), X, Vars)); -bind_pats_single([], _X, Vars) -> - Vars. - -bind_vars(Vs, none, Vars) -> - bind_vars_single(Vs, empty(), Vars); -bind_vars(Vs, Xs, Vars) -> - if length(Vs) =:= length(Xs) -> - bind_vars_list(Vs, Xs, Vars); - true -> - bind_vars_single(Vs, empty(), Vars) - end. - -bind_vars_list([V | Vs], [X | Xs], Vars) -> - bind_vars_list(Vs, Xs, dict:store(get_label(V), X, Vars)); -bind_vars_list([], [], Vars) -> - Vars. - -bind_vars_single([V | Vs], X, Vars) -> - bind_vars_single(Vs, X, dict:store(get_label(V), X, Vars)); -bind_vars_single([], _X, Vars) -> - Vars. - -%% This handles a call site - adding dependencies and updating parameter -%% variables with respect to the actual parameters. The 'external' -%% function is handled specially, since it can get an arbitrary number -%% of arguments, which must be unified into a single argument. - -call_site(Ls, L, Xs, St) -> -%%% io:fwrite("call site: ~w -> ~w (~w).\n", [L, Ls, Xs]), - {D, W, V} = call_site(Ls, L, Xs, St#state.dep, St#state.work, - St#state.vars, St#state.funs), - St#state{dep = D, work = W, vars = V}. - -call_site([external | Ls], T, Xs, D, W, V, Fs) -> - D1 = add_dep(external, T, D), - X = join_single_list(Xs), - case bind_arg(escape, X, V) of - {V1, true} -> -%%% io:fwrite("escape changed: ~w <- ~w + ~w.\n", -%%% [dict:fetch(escape, V1), dict:fetch(escape, V), -%%% X]), - {W1, V2} = update_esc(set__to_list(X), W, V1, Fs), - call_site(Ls, T, Xs, D1, add_work([external], W1), V2, Fs); - {V1, false} -> - call_site(Ls, T, Xs, D1, W, V1, Fs) - end; -call_site([L | Ls], T, Xs, D, W, V, Fs) -> - D1 = add_dep(L, T, D), - Vs = fun_vars(dict:fetch(L, Fs)), - case bind_args(Vs, Xs, V) of - {V1, true} -> - call_site(Ls, T, Xs, D1, add_work([L], W), V1, Fs); - {V1, false} -> - call_site(Ls, T, Xs, D1, W, V1, Fs) - end; -call_site([], _, _, D, W, V, _) -> - {D, W, V}. - -%% Note that `visit' makes sure all lambdas are visited at least once. -%% For every called function, we add a dependency from the *called* -%% function to the function containing the call site. - -add_dep(Source, Target, Deps) -> - case dict:find(Source, Deps) of - {ok, X} -> - case set__is_member(Target, X) of - true -> - Deps; - false -> -%%% io:fwrite("new dep: ~w <- ~w.\n", [Target, Source]), - dict:store(Source, set__add(Target, X), Deps) - end; - error -> -%%% io:fwrite("new dep: ~w <- ~w.\n", [Target, Source]), - dict:store(Source, set__singleton(Target), Deps) - end. - -%% If the arity does not match the call, nothing is done here. - -bind_args(Vs, Xs, Vars) -> - if length(Vs) =:= length(Xs) -> - bind_args(Vs, Xs, Vars, false); - true -> - {Vars, false} - end. - -bind_args([V | Vs], [X | Xs], Vars, Ch) -> - L = get_label(V), - {Vars1, Ch1} = bind_arg(L, X, Vars, Ch), - bind_args(Vs, Xs, Vars1, Ch1); -bind_args([], [], Vars, Ch) -> - {Vars, Ch}. - -bind_args_single(Vs, X, Vars) -> - bind_args_single(Vs, X, Vars, false). - -bind_args_single([V | Vs], X, Vars, Ch) -> - L = get_label(V), - {Vars1, Ch1} = bind_arg(L, X, Vars, Ch), - bind_args_single(Vs, X, Vars1, Ch1); -bind_args_single([], _, Vars, Ch) -> - {Vars, Ch}. - -bind_arg(L, X, Vars) -> - bind_arg(L, X, Vars, false). - -bind_arg(L, X, Vars, Ch) -> - X0 = dict:fetch(L, Vars), - X1 = join_single(X, X0), - case equal_single(X0, X1) of - true -> - {Vars, Ch}; - false -> -%%% io:fwrite("arg (~w) changed: ~w <- ~w + ~w.\n", -%%% [L, X1, X0, X]), - {dict:store(L, X1, Vars), true} - end. - -%% This handles escapes from things like primops and remote calls. - -%% escape(none, St) -> -%% St; -escape([X], St) -> - Vars = St#state.vars, - X0 = dict:fetch(escape, Vars), - X1 = join_single(X, X0), - case equal_single(X0, X1) of - true -> - St; - false -> -%%% io:fwrite("escape changed: ~w <- ~w + ~w.\n", [X1, X0, X]), -%%% io:fwrite("updating escaping funs: ~w.\n", [set__to_list(X)]), - Vars1 = dict:store(escape, X1, Vars), - {W, Vars2} = update_esc(set__to_list(set__subtract(X, X0)), - St#state.work, Vars1, - St#state.funs), - St#state{work = add_work([external], W), vars = Vars2} - end. - -%% For all escaping lambdas, since they might be called from outside the -%% program, all their arguments may be an external lambda. (Note that we -%% only have to include the `external' label once per escaping lambda.) -%% If the escape set has changed, we need to revisit the `external' fun. - -update_esc(Ls, W, V, Fs) -> - update_esc(Ls, singleton(external), W, V, Fs). - -%% The external lambda is skipped here - the Escape variable is known to -%% contain `external' from the start. - -update_esc([external | Ls], X, W, V, Fs) -> - update_esc(Ls, X, W, V, Fs); -update_esc([L | Ls], X, W, V, Fs) -> - Vs = fun_vars(dict:fetch(L, Fs)), - case bind_args_single(Vs, X, V) of - {V1, true} -> - update_esc(Ls, X, add_work([L], W), V1, Fs); - {V1, false} -> - update_esc(Ls, X, W, V1, Fs) - end; -update_esc([], _, W, V, _) -> - {W, V}. - -set_parent([L | Ls], L1, D) -> - set_parent(Ls, L1, dict:store(L, L1, D)); -set_parent([], _L1, D) -> - D. - -%% Handle primop calls: (At present, we assume that all unknown primops -%% yield exactly one value. This might have to be changed.) - -primop_call(F, A, Xs, St0) -> - case is_pure_op(F, A) of - %% XXX: this case is currently not possible -- commented out. - %% true -> - %% case is_literal_op(F, A) of - %% true -> {[empty()], St0}; - %% false -> {[join_single_list(Xs)], St0} - %% end; - false -> - St1 = case is_escape_op(F, A) of - true -> escape([join_single_list(Xs)], St0); - false -> St0 - end, - case is_literal_op(F, A) of - true -> {none, St1}; - false -> {[singleton(external)], St1} - end - end. - -%% Handle remote-calls: (At present, we assume that all unknown calls -%% yield exactly one value. This might have to be changed.) - -remote_call(M, F, Xs, St) -> - case is_c_atom(M) andalso is_c_atom(F) of - true -> - remote_call_1(atom_val(M), atom_val(F), length(Xs), Xs, St); - false -> - %% Unknown function - {[singleton(external)], escape([join_single_list(Xs)], St)} - end. - -remote_call_1(M, F, A, Xs, St0) -> - case is_pure_op(M, F, A) of - true -> - case is_literal_op(M, F, A) of - true -> {[empty()], St0}; - false -> {[join_single_list(Xs)], St0} - end; - false -> - St1 = case is_escape_op(M, F, A) of - true -> escape([join_single_list(Xs)], St0); - false -> St0 - end, - case is_literal_op(M, F, A) of - true -> {[empty()], St1}; - false -> {[singleton(external)], St1} - end - end. - -%% Domain: none | [Vs], where Vs = set(integer()). - -join(none, Xs2) -> Xs2; -join(Xs1, none) -> Xs1; -join(Xs1, Xs2) -> - if length(Xs1) =:= length(Xs2) -> - join_1(Xs1, Xs2); - true -> - none - end. - -join_1([X1 | Xs1], [X2 | Xs2]) -> - [join_single(X1, X2) | join_1(Xs1, Xs2)]; -join_1([], []) -> - []. - -empty() -> set__new(). - -singleton(X) -> set__singleton(X). - -from_label_list(X) -> set__from_list(X). - -join_single(none, Y) -> Y; -join_single(X, none) -> X; -join_single(X, Y) -> set__union(X, Y). - -join_list([Xs | Xss]) -> - join(Xs, join_list(Xss)); -join_list([]) -> - none. - -join_single_list([X | Xs]) -> - join_single(X, join_single_list(Xs)); -join_single_list([]) -> - empty(). - -equal(none, none) -> true; -equal(none, _) -> false; -equal(_, none) -> false; -equal(X1, X2) -> equal_1(X1, X2). - -equal_1([X1 | Xs1], [X2 | Xs2]) -> - equal_single(X1, X2) andalso equal_1(Xs1, Xs2); -equal_1([], []) -> true; -equal_1(_, _) -> false. - -equal_single(X, Y) -> set__equal(X, Y). - -%% Set abstraction for label sets in the domain. - -set__new() -> []. - -set__singleton(X) -> [X]. - -set__to_list(S) -> S. - -set__from_list(S) -> ordsets:from_list(S). - -set__union(X, Y) -> ordsets:union(X, Y). - -set__add(X, S) -> ordsets:add_element(X, S). - -set__is_member(X, S) -> ordsets:is_element(X, S). - -set__subtract(X, Y) -> ordsets:subtract(X, Y). - -set__equal(X, Y) -> X =:= Y. - -%% A simple but efficient functional queue. - -queue__new() -> {[], []}. - -queue__put(X, {In, Out}) -> {[X | In], Out}. - -queue__get({In, [X | Out]}) -> {ok, X, {In, Out}}; -queue__get({[], _}) -> empty; -queue__get({In, _}) -> - [X | In1] = lists:reverse(In), - {ok, X, {[], In1}}. - -%% The work list - a queue without repeated elements. - -init_work() -> - {queue__new(), sets:new()}. - -add_work(Ls, {Q, Set}) -> - add_work(Ls, Q, Set). - -%% Note that the elements are enqueued in order. - -add_work([L | Ls], Q, Set) -> - case sets:is_element(L, Set) of - true -> - add_work(Ls, Q, Set); - false -> - add_work(Ls, queue__put(L, Q), sets:add_element(L, Set)) - end; -add_work([], Q, Set) -> - {Q, Set}. - -take_work({Queue0, Set0}) -> - case queue__get(Queue0) of - {ok, L, Queue1} -> - Set1 = sets:del_element(L, Set0), - {ok, L, {Queue1, Set1}}; - empty -> - none - end. - -%% Escape operators may let their arguments escape. Unless we know -%% otherwise, and the function is not pure, we assume this is the case. -%% Error-raising functions (fault/match_fail) are not considered as -%% escapes (but throw/exit are). Zero-argument functions need not be -%% listed. - --spec is_escape_op(atom(), arity()) -> boolean(). - -is_escape_op(match_fail, 1) -> false; -is_escape_op(recv_wait_timeout, 1) -> false; -is_escape_op(F, A) when is_atom(F), is_integer(A) -> true. - --spec is_escape_op(atom(), atom(), arity()) -> boolean(). - -is_escape_op(erlang, error, 1) -> false; -is_escape_op(erlang, error, 2) -> false; -is_escape_op(M, F, A) when is_atom(M), is_atom(F), is_integer(A) -> true. - -%% "Literal" operators will never return functional values even when -%% found in their arguments. Unless we know otherwise, we assume this is -%% not the case. (More functions can be added to this list, if needed -%% for better precision. Note that the result of `term_to_binary' still -%% contains an encoding of the closure.) - --spec is_literal_op(atom(), arity()) -> boolean(). - -is_literal_op(recv_wait_timeout, 1) -> true; -is_literal_op(match_fail, 1) -> true; -is_literal_op(F, A) when is_atom(F), is_integer(A) -> false. - --spec is_literal_op(atom(), atom(), arity()) -> boolean(). - -is_literal_op(erlang, '+', 2) -> true; -is_literal_op(erlang, '-', 2) -> true; -is_literal_op(erlang, '*', 2) -> true; -is_literal_op(erlang, '/', 2) -> true; -is_literal_op(erlang, '=:=', 2) -> true; -is_literal_op(erlang, '==', 2) -> true; -is_literal_op(erlang, '=/=', 2) -> true; -is_literal_op(erlang, '/=', 2) -> true; -is_literal_op(erlang, '<', 2) -> true; -is_literal_op(erlang, '=<', 2) -> true; -is_literal_op(erlang, '>', 2) -> true; -is_literal_op(erlang, '>=', 2) -> true; -is_literal_op(erlang, 'and', 2) -> true; -is_literal_op(erlang, 'or', 2) -> true; -is_literal_op(erlang, 'not', 1) -> true; -is_literal_op(erlang, length, 1) -> true; -is_literal_op(erlang, size, 1) -> true; -is_literal_op(erlang, fun_info, 1) -> true; -is_literal_op(erlang, fun_info, 2) -> true; -is_literal_op(erlang, fun_to_list, 1) -> true; -is_literal_op(erlang, throw, 1) -> true; -is_literal_op(erlang, exit, 1) -> true; -is_literal_op(erlang, error, 1) -> true; -is_literal_op(erlang, error, 2) -> true; -is_literal_op(M, F, A) when is_atom(M), is_atom(F), is_integer(A) -> false. - -%% Pure functions neither affect the state, nor depend on it. - -is_pure_op(F, A) when is_atom(F), is_integer(A) -> false. - -is_pure_op(M, F, A) -> erl_bifs:is_pure(M, F, A). - -%% ===================================================================== |