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WeBWorK::PG::Translator - Evaluate PG code and evaluate answers safely


    my $pt = new WeBWorK::PG::Translator;      # create a translator;
    $pt->environment(\%envir);      # provide the environment variable for the problem
    $pt->initialize();              # initialize the translator
    $pt-> set_mask();               # set the operation mask for the translator safe compartment
    $pt->source_string($source);    # provide the source string for the problem

    $pt -> unrestricted_load("${courseScriptsDirectory}PG.pl");
                                    # load the unprotected macro files
                                    # these files are evaluated with the Safe compartment wide open
                                    # other macros are loaded from within the problem using loadMacros

    $pt ->translate();              # translate the problem (the out following 4 pieces of information are created)

    $PG_PROBLEM_TEXT_ARRAY_REF = $pt->ra_text();              # output text for the body of the HTML file (in array form)
    $PG_PROBLEM_TEXT_REF = $pt->r_text();                     # output text for the body of the HTML file
    $PG_HEADER_TEXT_REF = $pt->r_header;#\$PG_HEADER_TEXT;    # text for the header of the HTML file
    $PG_POST_HEADER_TEXT_REF = $pt->r_post_header
    $PG_ANSWER_HASH_REF = $pt->rh_correct_answers;            # a hash of answer evaluators
    $PG_FLAGS_REF = $pt ->rh_flags;                           # misc. status flags.

    $pt -> process_answers(\%inputs);    # evaluates all of the answers using submitted answers from %input

    my $rh_answer_results = $pt->rh_evaluated_answers;  # provides a hash of the results of evaluating the answers.
    my $rh_problem_result = $pt->grade_problem;         # grades the problem using the default problem grading method.


This module defines an object which will translate a problem written in the Problem Generating (PG) language


This creates a substitute for use strict; which cannot be used in PG problem sets or PG macro files. Use this way to imitate the behavior of use strict;

        BEGIN {
                be_strict(); # an alias for use strict.
                             # This means that all global variable
                             # must contain main:: as a prefix.


        Usage:  $obj -> evaluate_modules('WWPlot', 'Fun', 'Circle');
                $obj -> evaluate_modules('reset');

Adds the modules WWPlot.pm, Fun.pm and Circle.pm in the courseScripts directory to the list of modules which can be used by the PG problems. The keyword 'reset' or 'erase' erases the list of modules already loaded


        Usage:  $obj -> load_extra_packages('AlgParserWithImplicitExpand',

Loads extra packages for modules that contain more than one package. Works in conjunction with evaluate_modules. It is assumed that the file containing the extra packages (along with the base package name which is the same as the name of the file minus the .pm extension) has already been loaded using evaluate_modules


        Creates the translator object.

(b) The following routines defined within the PG module are shared:


In addition the environment hash %envir is shared. This variable is unpacked when PG.pl is run and provides most of the environment variables for each problem template.

        <A href =
        "${Global::webworkDocsURL}techdescription/pglanguage/PGenvironment.html"> environment variables</A>

(c) Sharing macros:

The macros shared with the safe compartment are


Safe compartment pass through macros


(e) Now we close the safe compartment. Only the certain operations can be used within PG problems and the PG macro files. These include the subroutines shared with the safe compartment as defined above and most Perl commands which do not involve file access, access to the system or evaluation.

Specifically the following are allowed

                # gives the current Unix time
                # used to determine whether solutions are visible.
        atan, sin cos exp log sqrt
                # arithemetic commands -- more are defined in PGauxiliaryFunctions.pl

The following are specifically not allowed:

        unlink, symlink, system, exec
        print require


This routine processes error messages by fixing file names and adding traceback information. It loops through the function calls via caller() in order to give more information about where the error occurred. Since the loadMacros() files and the .pg file itself are handled via various kinds of eval calls, the caller() information does not contain the file names. So we have saved them in the $main::__files__ hash, which we look up here and use to replace the (eval nnn) file names that are in the caller stack. We shorten the filenames by removing the templates or root directories when possible, so they are easier to read.

We skip any nested calls to Parser:: or Value:: so that these act more like perl built-in functions.

We stop when we find a routine in the WeBWorK:: package, or an __ANON__ routine, in order to avoid reporting the PG translator calls that surround the pg file. Finally, there is usually one more eval before that, so we remove it as well.

File names are shortened, when possible, by replacing the templates directory with [TMPL], the WeBWorK root directory by [WW] and the PG root directory by [PG].


 Produces warnings of this type in order to help you guess which local variable is undefined
 Warning: Use of uninitialized value in concatenation (.) or string at mpu.cgi line 25.
 Possible variables are:
           '$GLOBAL_VARIABLE' => \'global',
           '$t' => \undef,
           '$s' => \'regular output'


(3) Preprocess the problem text

The input text is subjected to two global replacements. First every incidence of

        problem text

is replaced by

        TEXT( EV3( <<'END_TEXT' ) );
        problem text

The first construction is syntactic sugar for the second. This is explained in PGbasicmacros.pl.

Second every incidence of \ (backslash) is replaced by \\ (double backslash). Third each incidence of ~~ is replaced by a single backslash.

This is done to alleviate a basic incompatibility between TeX and Perl. TeX uses backslashes constantly to denote a command word (as opposed to text which is to be entered literally). Perl uses backslash to escape the following symbol. This escape mechanism takes place immediately when a Perl script is compiled and takes place throughout the code and within every quoted string (both double and single quoted strings) with the single exception of single quoted "here" documents. That is backlashes which appear in

    ... text including \{   \} for example

are the only ones not immediately evaluated. This behavior makes it very difficult to use TeX notation for defining mathematics within text.

The initial global replacement, before compiling a PG problem, allows one to use backslashes within text without doubling them. (The anomolous behavior inside single quoted "here" documents is compensated for by the behavior of the evaluation macro EV3.) This makes typing TeX easy, but introduces one difficulty in entering normal Perl code.

The second global replacement provides a work around for this -- use ~~ when you would ordinarily use a backslash in Perl code. In order to define a carriage return use ~~n rather than \n; in order to define a reference to a variable you must use ~~@array rather than \@array. This is annoying and a source of simple compiler errors, but must be lived with.

The problems are not evaluated in strict mode, so global variables can be used without warnings.

(4) Evaluate the problem text

Evaluate the text within the safe compartment. Save the errors. The safe compartment is a new one unless the $safeCompartment was set to zero in which case the previously defined safe compartment is used. (See item 1.)

(5) Process errors

The error provided by Perl is truncated slightly and returned. In the text string which would normally contain the rendered problem.

The original text string is given line numbers and concatenated to the errors.

(6) Prepare return values

                        $PG_PROBLEM_TEXT_ARRAY_REF -- Reference to a string containing the rendered text.
                        $PG_HEADER_TEXT_REF -- Reference to a string containing material to placed in the header (for use by JavaScript)
                        $PG_POST_HEADER_TEXT_REF -- Reference to a string containing material to placed in body above form (for use by Sage)
                        $PG_ANSWER_HASH_REF -- Reference to an array containing the answer evaluators.
                               constructed from keys of $PGcore->{PG_ANSWERS_HASH}
                        $PG_FLAGS_REF -- Reference to a hash containing flags and other references:
                                'error_flag' is set to 1 if there were errors in rendering
                        $PGcore -- the PGcore object

Answer evaluation methods

access methods





        $obj->rh_problem_state(%problem_state);  # sets the current problem state


        ($filtered_ans, $errors) = $obj ->filter_ans($ans)
                               $obj ->rf_safety_filter()


Because of the way sort is optimized in Perl, the symbols $a and $b have special significance.

sort {$a<=$b} @list> sort {$a cmp $b} @list

sorts the list numerically and lexically respectively.

If my $a; is used in a problem, before the sort routine is defined in a macro, then things get badly confused. To correct this the macro PGsort is defined below. It is evaluated before the problem template is read. In PGbasicmacros.pl, the two subroutines

        PGsort sub { $_[0] < $_[1] }, @list;
        PGsort sub { $_[0] lt $_[1] }, @list;

(called num_sort and lex_sort) provide slightly slower, but safer, routines for the PG language. (The subroutines for ordering are required. Note the commas!)


        includePGtext($string_ref, $envir_ref)

This is now defined in PG::IO.pm



Evaluated in package 'main'. Result of last statement is returned. When called from within a safe compartment the safe compartment package is 'main'.



Evaluated in package defined by the current safe compartment. Result of last statement is returned. When called from within a safe compartment the safe compartment package is 'main'.

There is still some confusion about how these two evaluation subroutines work and how best to define them. It is useful to have two evaluation procedures since at some point one might like to make the answer evaluations more stringent.

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