mercury/compiler/term_constr_fixpoint.m

%-----------------------------------------------------------------------------%
% vim: ft=mercury ts=4 sw=4 et
%-----------------------------------------------------------------------------%
% Copyright (C) 2002, 2005-2007 The University of Melbourne.
% This file may only be copied under the terms of the GNU General
% Public License - see the file COPYING in the Mercury distribution.
%-----------------------------------------------------------------------------%
%
% File: term_constr_fixpoint.m.
% Main author: juliensf.
%
% TODO:
% * code for handling calls could do with a cleanup.
%
% NOTE: the code in this module should not refer to things in the HLDS
% (with the exception of the termination2_info slots in the 
%  proc_sub_info structure)
% 
%-----------------------------------------------------------------------------%

:- module transform_hlds.term_constr_fixpoint.
:- interface.

:- import_module hlds.hlds_module. 
:- import_module hlds.hlds_pred.
:- import_module transform_hlds.term_constr_data.
:- import_module transform_hlds.term_constr_errors.

:- import_module io.
:- import_module list.

%-----------------------------------------------------------------------------%

    % Derive the argument size constraints for the procedures in this SCC.
    %
:- pred do_fixpoint_calculation(fixpoint_options::in, list(pred_proc_id)::in, 
    int::in, term2_errors::out, module_info::in, module_info::out,
    io::di, io::uo) is det.
    
    % This structure holds the values of options used to control
    % the fixpoint calculation.
    %
:- type fixpoint_options.

    % fixpoint_options_init(Widening, MaxMatrixSize).  Initialise the
    % fixpoint_options structure.  `Widening' is the threshold after
    % which we invoke widening.  `MaxMatrixSize' specifies the maximum
    % number of constraints we allow a matrix to grow to before we abort
    % and try other approximations.
    %
:- func fixpoint_options_init(widening, int) = fixpoint_options.

%-----------------------------------------------------------------------------%
%-----------------------------------------------------------------------------%

:- implementation.

:- import_module hlds.hlds_out.
:- import_module libs.compiler_util.
:- import_module libs.lp_rational. 
:- import_module libs.polyhedron.
:- import_module parse_tree.prog_data. 
:- import_module transform_hlds.term_constr_data.
:- import_module transform_hlds.term_constr_main.
:- import_module transform_hlds.term_constr_util.

:- import_module bool.
:- import_module int.
:- import_module maybe.
:- import_module set.
:- import_module string.
:- import_module term.
:- import_module varset.

%------------------------------------------------------------------------------%

:- type fixpoint_options 
    ---> fixpoint_options(
        widening :: widening,
        max_size :: int
    ).

fixpoint_options_init(Widening, MaxMatrixSize) = 
    fixpoint_options(Widening, MaxMatrixSize).

%------------------------------------------------------------------------------%
%
% Perform the fixpoint calculation on the AR.
%

    % The information for each procedure in the SCC returned by a single
    % iteration of the fixpoint calculation.
    %
:- type iteration_info 
    ---> iteration_info(
         pred_proc_id, 
         arg_size_poly :: polyhedron, 
         change_flag   :: bool
    ).

:- type iteration_infos == list(iteration_info).

do_fixpoint_calculation(Options, SCC, Iteration, [], !ModuleInfo, !IO) :-
    AbstractSCC = get_abstract_scc(!.ModuleInfo, SCC),  
    %
    % Carry out one iteration of fixpoint computation.  We need to
    % do this for all SCCs at least once in order to obtain the argument
    % size constraints for non-recursive procedures.  We could do that
    % during the build phase for non-recursive procedures (and in fact used
    % to) but the code ends up being a horrible mess.
    %
    list.foldl2(traverse_abstract_proc(Iteration, Options, !.ModuleInfo), 
        AbstractSCC, [], IterationInfos, !IO),
    ChangeFlag = or_flags(IterationInfos),
    (
        ChangeFlag = yes,
        list.foldl(update_size_info, IterationInfos, !ModuleInfo),
        do_fixpoint_calculation(Options, SCC, Iteration + 1,  
            _, !ModuleInfo, !IO) 
    ;
        ChangeFlag = no,
        % If one of the polyhedra in the SCC has `false' as its
        % argument size constraint then the analysis failed.  In that
        % case set the argument size constraints for every procedure
        % in the SCC to `true'.
        % XXX Should this be happening?
        % 
        ( 
            list.member(OneInfo, IterationInfos), 
            polyhedron.is_empty(OneInfo ^ arg_size_poly)
        ->
            ChangePoly = (func(Info0) = Info :-
                Identity = polyhedron.universe,
                Info = Info0 ^ arg_size_poly := Identity 
            ),
            list.foldl(update_size_info, list.map(ChangePoly, IterationInfos),
                !ModuleInfo)
        ;
            list.foldl(update_size_info, IterationInfos, !ModuleInfo)
        )
    ).

:- func or_flags(iteration_infos) = bool.

or_flags([]) = no. 
or_flags([Info | Infos]) = bool.or(Info ^ change_flag, or_flags(Infos)).

:- pred update_size_info(iteration_info::in, module_info::in, module_info::out)
    is det.

update_size_info(Info, !ModuleInfo) :-
    Info = iteration_info(PPId, Poly, _),
    update_arg_size_info(PPId, Poly, !ModuleInfo).

%------------------------------------------------------------------------------%

:- pred traverse_abstract_proc(int::in, fixpoint_options::in,
    module_info::in, abstract_proc::in, iteration_infos::in,
    iteration_infos::out, io::di, io::uo) is det.

traverse_abstract_proc(Iteration, Options, ModuleInfo, Proc, !IterationInfo,
        !IO) :-
    WideningInfo = Options ^ widening,
    MaxMatrixSize = Options ^ max_size,
    AbstractPPId = Proc ^ ppid,
    AbstractPPId = real(PPId),
    Varset = Proc ^ varset,
    Zeros  = Proc ^ zeros,
    HeadVars = Proc ^ head_vars,    
    % 
    % Print out the debugging traces.
    %
    maybe_write_trace(io.write(PPId), !IO),
    maybe_write_trace(io.write_string(": "), !IO),
    maybe_write_trace(hlds_out.write_pred_proc_id(ModuleInfo, PPId), !IO),
    maybe_write_trace(io.write_string(" "), !IO),
    maybe_write_trace(write_size_vars(Varset, HeadVars), !IO),
    maybe_write_trace(io.format("\nIteration %d:\n", [i(Iteration)]), !IO),
    %   
    % Begin by traversing the procedure and calculating the
    % IR approximation for this iteration.  
    %
    Info = init_fixpoint_info(ModuleInfo, Varset, PPId, MaxMatrixSize,
        HeadVars, Zeros),

    some [!Polyhedron] (    
        traverse_abstract_goal(Info, Proc ^ body, polyhedron.universe, 
            !:Polyhedron),
        polyhedron.optimize(Varset, !Polyhedron),
        %
        % XXX Bug workaround - the build pass sometimes stuffs up
        % the local variable set for if-then-elses.
        % (See comments in term_constr_build.m). 
        %
        BugConstrs0 = polyhedron.constraints(!.Polyhedron),
        ConstrVarsSet = get_vars_from_constraints(BugConstrs0),
        HeadVarSet = set.from_list(HeadVars),
        BadVarsSet = set.difference(ConstrVarsSet, HeadVarSet),
        BadVars = set.to_sorted_list(BadVarsSet),
        !:Polyhedron = polyhedron.project(BadVars, Varset, !.Polyhedron),
        polyhedron.optimize(Varset, !Polyhedron),
        %   
        % XXX End of bug workaround.    
        % Print out the polyhedron obtained during this iteration.
        %
        maybe_write_trace(polyhedron.write_polyhedron(!.Polyhedron, Varset),
            !IO),
        maybe_write_trace(io.nl, !IO),
        %       
        % Look up the constraints obtained during the previous
        % iteration.
        %
        ArgSizeInfo = lookup_proc_constr_arg_size_info(ModuleInfo, PPId),
        %
        % NOTE: `!.Polyhedron' is the set of constraints obtained by
        % *this* iteration.  `OldPolyhedron' is the set of constraints
        % obtained by the *previous* iteration -- which may in fact
        % be `empty' (false).
        %
        (
            % If there were no constraints for the procedure then
            % we are at the beginning of the analysis.
            %
            ArgSizeInfo = no,
            OldPolyhedron = polyhedron.empty
        ;
            ArgSizeInfo = yes(SizeInfo),
            OldPolyhedron = SizeInfo
        ),
        ( polyhedron.is_empty(!.Polyhedron) ->
            ( if    polyhedron.is_empty(OldPolyhedron)
              then  ChangeFlag = no 
              else  unexpected(this_file, "old polyhedron is empty.")
            )
        ;
            % If the procedure is not recursive then we need only perform one
            % pass over the AR - subsequent iterations will yield the same result.
            %
            ( if       Proc ^ recursion = none then ChangeFlag = no
              else if  polyhedron.is_empty(OldPolyhedron) then ChangeFlag = yes
              else     test_fixpoint_and_perhaps_widen(WideningInfo, Varset, 
                           Iteration, OldPolyhedron, !Polyhedron, ChangeFlag)
            )
        ),
        ThisIterationInfo = iteration_info(PPId, !.Polyhedron, ChangeFlag)
    ),
    list.cons(ThisIterationInfo, !IterationInfo).
    
%------------------------------------------------------------------------------%

:- type fixpoint_info 
    ---> fixpoint_info(
        module_info        :: module_info,
        varset             :: size_varset,
        ppid               :: pred_proc_id,
        max_matrix_size    :: int,
        curr_head_vars     :: head_vars,
        zeros              :: zero_vars
    ).

:- func init_fixpoint_info(module_info, size_varset, pred_proc_id, int, 
    head_vars, zero_vars) = fixpoint_info.

init_fixpoint_info(ModuleInfo, Varset, PPId, MaxMatrixSize, HeadVars, Zeros) = 
    fixpoint_info(ModuleInfo, Varset, PPId, MaxMatrixSize, HeadVars, Zeros).

%------------------------------------------------------------------------------%

:- pred traverse_abstract_goal(fixpoint_info::in, abstract_goal::in,
    polyhedron::in, polyhedron::out) is det.

traverse_abstract_goal(Info, term_disj(Goals, _Size, Locals, _),
        !Polyhedron) :- 
    %
    % There are number of possible improvements that should be made here:
    %
    %   - Take the intersection each disjunct with the constraints
    %     before the disjunction and compute the convex hull of that.
    %     This is more accurate but slower.  (XXX There is some code for this
    %     in term_constr_data.m but it needs to be moved here).  To do
    %     this you need to add the constraints that occur to 
    %     left of the disjunctions to `PriorConstraints'.
    %   
    %   - Try computing the convex hull of large disjunctions
    %     pairwise rather than linearly.  There is code to do this
    %     below but we currently don't use it.
    %
    PriorConstraints = polyhedron.universe,
    traverse_abstract_disj_linearly(Goals, Locals, Info, PriorConstraints,
        Polyhedron0),
    post_process_abstract_goal(Locals, Info, Polyhedron0, !Polyhedron).

traverse_abstract_goal(Info, term_conj(Goals, Locals, _), !Polyhedron) :- 
    list.foldl(traverse_abstract_goal(Info), Goals, polyhedron.universe,
        Polyhedron0),
    post_process_abstract_goal(Locals, Info, Polyhedron0, !Polyhedron).

traverse_abstract_goal(Info, AbstractGoal, !Polyhedron) :- 
    AbstractGoal = term_call(CallPPId0, _, CallVars, CallZeros, Locals, _,
        CallArgsPoly),
    CallPPId0 = real(CallPPId),
    module_info_pred_proc_info(Info ^ module_info, CallPPId, _, 
        CallProcInfo),
    proc_info_get_termination2_info(CallProcInfo, CallTerm2Info),
    CallArgSizeInfo = CallTerm2Info ^ success_constrs,
    ( 
        CallArgSizeInfo = no,
        !:Polyhedron = polyhedron.empty
    ;
        CallArgSizeInfo = yes(SizeInfo),
        ( polyhedron.is_empty(SizeInfo) ->
            !:Polyhedron = polyhedron.empty
        ;
            ( not polyhedron.is_universe(SizeInfo) ->
                HeadVars = CallTerm2Info ^ head_vars,
                SubstMap = create_var_substitution(CallVars, 
                    HeadVars),
                Polyhedron0 = polyhedron.substitute_vars(
                    SubstMap, SizeInfo), 
                Polyhedron1 = intersection(Polyhedron0, 
                    CallArgsPoly),
                % 
                % Set any zero_vars in the constraints
                % to zero (ie. delete the terms).  We need
                % to do this when polymorphic arguments
                % are zero sized.
                %
                Polyhedron2 = polyhedron.zero_vars(CallZeros,
                    Polyhedron1),
                post_process_abstract_goal(Locals, Info, 
                    Polyhedron2, !Polyhedron)
            ;
                true    % Constraint store += true  
            )
        )
    ).

traverse_abstract_goal(Info, term_primitive(Poly, Locals, _), !Polyhedron) :- 
    post_process_abstract_goal(Locals, Info, Poly, !Polyhedron).

%------------------------------------------------------------------------------%

:- pred post_process_abstract_goal(size_vars::in, fixpoint_info::in,
    polyhedron::in, polyhedron::in, polyhedron::out) is det.

post_process_abstract_goal(Locals, Info, GoalPolyhedron0, !Polyhedron) :- 
    ( if    polyhedron.is_empty(GoalPolyhedron0)
      then  GoalPolyhedron = polyhedron.empty
      else  GoalPolyhedron = polyhedron.project(Locals, Info ^ varset, 
            GoalPolyhedron0)
    ),  
    polyhedron.intersection(GoalPolyhedron, !Polyhedron).

%------------------------------------------------------------------------------%
%
% Predicates for handling disjunctions. 
%

    % This version computes the convex hull linearly.
    % That is, ( A ; B ; C ; D) is processed as:
    %
    %  ((((empty \/ A ) \/ B ) \/ C ) \/ D)
    %
:- pred traverse_abstract_disj_linearly(abstract_goals::in,
    size_vars::in, fixpoint_info::in, polyhedron::in, polyhedron::out)
    is det.

traverse_abstract_disj_linearly(Goals, Locals, Info, !Polyhedron) :-
    list.foldl(traverse_abstract_disj_linearly_2(Info, Locals),
        Goals, polyhedron.empty, ConvexUnion),
    polyhedron.intersection(ConvexUnion, !Polyhedron).

:- pred traverse_abstract_disj_linearly_2(fixpoint_info::in,
    size_vars::in, abstract_goal::in, polyhedron::in, polyhedron::out)
    is det.

traverse_abstract_disj_linearly_2(Info, Locals, Goal, !Polyhedron) :-
    Varset = Info ^ varset,
    traverse_abstract_goal(Info, Goal, polyhedron.universe, Polyhedron0),
    Polyhedron1 = polyhedron.project(Locals, Varset, Polyhedron0),
    polyhedron.convex_union(Varset, yes(Info ^ max_matrix_size),
        Polyhedron1, !Polyhedron).

    % This version computes the convex hull pairwise. That is
    % ( A ; B ; C ; D) is processed as: (( A \/ B ) \/ ( C \/ D)).
    %
    % XXX This code is currently unused.
    %
:- pred traverse_abstract_disj_pairwise(abstract_goals::in, size_vars::in,
    fixpoint_info::in, polyhedron::in, polyhedron::out) is det.
 
traverse_abstract_disj_pairwise(Goals, Locals, Info, !Polyhedron) :-
    Varset = Info ^ varset,
    % XXX at the moment, could be !.Poly...
    PolyToLeft = polyhedron.universe,
    %
    % First convert the list of goals into their corresponding
    % polyhedra
    %
    ToPoly = (func(Goal) = Poly :-
        traverse_abstract_goal(Info, Goal, PolyToLeft, Poly0),
        Poly = polyhedron.project(Locals, Varset, Poly0)
    ),
    Polyhedra0 = list.map(ToPoly, Goals),
    %
    % Now pairwise convex hull them.
    %
    HullOp = (func(A, B) = C :-
        polyhedron.convex_union(Varset, yes(Info ^ max_matrix_size),
            A, B, C)
    ),
    ConvexUnion = pairwise_map(HullOp, [ polyhedron.empty | Polyhedra0]),
    polyhedron.intersection(ConvexUnion, !Polyhedron).
    
    % This assumes that the operation in question is associative and
    % commutative.
    %
 :- func pairwise_map(func(T, T) = T, list(T)) = T.
 
pairwise_map(_, []) = _ :- unexpected(this_file, "pairwise_map: empty list").
pairwise_map(_,  [X]) = X.
pairwise_map(Op, List @ [_, _ | _]) = X :-
    pairwise_map_2(Op, List, [], X0),
    X = pairwise_map(Op, X0). 

:- pred pairwise_map_2(func(T, T) = T, list(T), list(T), list(T)).
:- mode pairwise_map_2(func(in, in) = out is det, in, in, out) is det.

pairwise_map_2(_,  [], !Acc).
pairwise_map_2(_,  [X], Acc, [X | Acc]).
pairwise_map_2(Op, [X, Y | Rest], !Acc) :- 
    list.cons(Op(X, Y), !Acc),
    pairwise_map_2(Op, Rest, !Acc). 

%------------------------------------------------------------------------------%
%
% Fixpoint test.
%

:- pred test_fixpoint_and_perhaps_widen(widening::in, size_varset::in, int::in, 
    polyhedron::in, polyhedron::in, polyhedron::out, bool::out) is det.

test_fixpoint_and_perhaps_widen(after_fixed_cutoff(Threshold), Varset, 
        Iteration, OldPoly, NewPoly, ResultPoly, ChangeFlag) :- 
    ( Iteration > Threshold ->
        ResultPoly = widen(OldPoly, NewPoly, Varset)
    ;
        ResultPoly = NewPoly
    ),
    ChangeFlag = test_fixpoint(NewPoly, OldPoly, Varset).

:- func test_fixpoint(polyhedron, polyhedron, size_varset) = bool. 

test_fixpoint(NewPoly, OldPoly, Varset) = ChangeFlag :-
    %
    % Constraints from this iteration.
    %
    NewConstraints = polyhedron.non_false_constraints(NewPoly),
    %
    % Constraints from previous iteration.
    %
    OldConstraints = polyhedron.non_false_constraints(OldPoly), 
    (
        some [OldConstraint] (
            list.member(OldConstraint, OldConstraints),
            not entailed(Varset, NewConstraints, OldConstraint)
        )
    ->
        ChangeFlag = yes
    ;  
        ChangeFlag = no
    ).

%-----------------------------------------------------------------------------

:- func this_file = string.

this_file = "term_constr_fixpoint.m".

%-----------------------------------------------------------------------------%
:- end_module transform_hlds.term_constr_fixpoint.
%-----------------------------------------------------------------------------%