function [sendup,sendup_status]=pref2inf(expr,gp)

%PREF2INF Utility function to recursively extract arguments from a prefix 

%expression and convert to infix where possible.

%

%   (c) Dominic Searson 2009

%

%   v1.0

%

%   See also: PICKNODE, EXTRACT



%get indices of nodes of any type 

ind=picknode(expr,6,gp);

if isempty(ind)

    sendup=expr;%exits if current expression has no further extractable args

    sendup_status=0;

    return

end



%get first node

ind=ind(1);



%get number of arguments of node

try

    args=gp.nodes.functions.arity_argt0(findstr(gp.nodes.functions.afid,expr(ind)));



    if isempty(args)

        % if has zero arity then exit

        sendup=[expr];

        sendup_status=0;

        return;

    end

catch

    %also exit if error

    sendup=[expr];

    sendup_status=0;

    return;

end



if args==1



    %get subtree rooted in this node

    [main_tree,sub_tree]=extract(ind,expr);

    node=sub_tree(1);



    %get index of 2nd node in 'sub_tree' (i.e. first logical argument)

    keynode_ind=picknode(sub_tree,6,gp); %

    keynode_ind=keynode_ind(2);



    %extract the 1st argument expression

    [remainder,arg1]=extract(keynode_ind,sub_tree);



    [rec1,rec1_status]=pref2inf(arg1,gp);



    if rec1_status==1

        arg1=rec1;

    end



    sendup=[node '(' arg1 ')'];

    sendup_status=1;





elseif args>2

    %get subtree rooted in this node

    [main_tree,sub_tree]=extract(ind,expr);

    node=sub_tree(1);



    %get index of 2nd node in 'sub_tree' (i.e. first logical argument)

    keynode_ind=picknode(sub_tree,6,gp); %

    keynode_ind=keynode_ind(2);



    %extract the 1st argument expression

    [remainder,arg1]=extract(keynode_ind,sub_tree);



    %extract the second argument expression from the remainder

    % find the 1st node after $ in the remainder as this will be the

    % keynode of the 2nd argument we wish to extract

    keynode_ind=picknode(remainder,6,gp);

    token_ind=findstr(remainder,'$');



    hib=find(keynode_ind>token_ind);

    keynode_ind=keynode_ind(hib);

    keynode_ind_1=keynode_ind(1);

    [remainder2,arg2]=extract(keynode_ind_1,remainder);





    %extract the thirdargument expression from the remainder

    % find the 1st node after $ in remainder2 as this will be the keynode of

    % the 3nd argument we wish to extract

    keynode_ind=picknode(remainder2,6,gp);

    token_ind=findstr(remainder2,'$');



    hib=find(keynode_ind>max(token_ind));

    keynode_ind=keynode_ind(hib);

    keynode_ind_1=keynode_ind(1);

    [remainder3,arg3]=extract(keynode_ind_1,remainder2);



    [rec1,rec1_status]=pref2inf(arg1,gp);

    [rec2,rec2_status]=pref2inf(arg2,gp);

    [rec3,rec3_status]=pref2inf(arg3,gp);



    if rec1_status==1

        arg1=rec1;

    end



    if rec2_status==1

        arg2=rec2;

    end



    if rec3_status==1

        arg3=rec3;

    end



    sendup=[node '(' arg1 ',' arg2 ',' arg3 ')'];

    sendup_status=1;



    if args>3



        %extract the fourth argument expression from the remainder

        % find the 1st node after $ in remainder3 as this will be the keynode of

        % the 4nd argument we wish to extract

        keynode_ind=picknode(remainder3,6,gp);

        token_ind=findstr(remainder3,'$');



        hib=find(keynode_ind>max(token_ind));

        keynode_ind=keynode_ind(hib);

        keynode_ind_1=keynode_ind(1);

        [remainder4,arg4]=extract(keynode_ind_1,remainder3);

        [rec4,rec4_status]=pref2inf(arg4,gp);



        if rec4_status==1

            arg4=rec4;

        end



        sendup=[node '(' arg1 ',' arg2 ',' arg3 ',' arg4 ')'];

        sendup_status=1;

    end







else %must have exactly 2 args



    ind=picknode(expr,6,gp);

    %get subtree rooted in this node

    [main_tree,sub_tree]=extract(ind,expr);

    node=sub_tree(1);



    %get index of 2nd node in 'sub_tree' (i.e. first logical argument)

    keynode_ind=picknode(sub_tree,6,gp); %

    keynode_ind=keynode_ind(2);



    %extract the 1st argument expression

    [remainder,arg1]=extract(keynode_ind,sub_tree);



    %extract the second argument expression from the remainder

    % find the 1st node after $ in the remainder as this will be the

    % keynode of the 2nd argument we wish to extract

    keynode_ind=picknode(remainder,6,gp);

    token_ind=findstr(remainder,'$');



    hib=find(keynode_ind>token_ind);

    keynode_ind=keynode_ind(hib);

    keynode_ind_1=keynode_ind(1);

    [remainder2,arg2]=extract(keynode_ind_1,remainder);









    %process arguments of these arguments if any exist

    [rec1,rec1_status]=pref2inf(arg1,gp);

    [rec2,rec2_status]=pref2inf(arg2,gp);





    if rec1_status==1

        arg1=rec1;

    end



    if rec2_status==1

        arg2=rec2;

    end





    %If the node is of infix type (for Matlab symbolic purposes)

    % then send up the results differently

    afid_ind = findstr(node, gp.nodes.functions.afid);

    nodename = gp.nodes.functions.active_name_UC{afid_ind};



    if strcmpi(nodename,'times') || strcmpi(nodename,'minus') || strcmpi(nodename,'plus') || strcmpi(nodename,'rdivide')



        sendup=['(' arg1 ')' node '(' arg2 ')'];

    else

        sendup= [node '(' arg1 ',' arg2 ')'];

    end

    sendup=strrep(main_tree,'$',sendup);



    sendup_status=1; %i.e. ok

end