Description:

• externalproc allows for binding the Sollya identifier identifier to an external code. After this binding, when Sollya encounters identifier applied to a list of actual parameters, it will evaluate these parameters and call the external code with these parameters. If the external code indicated success, it will receive the result produced by the external code, transform it to Sollya's internal representation and return it.
  
  In order to allow correct evaluation and typing of the data in parameter and in result to be passed to and received from the external code, externalproc has a third parameter argumenttype -> resulttype. Both argumenttype and resulttype are one of void, constant, function, object, range, integer, string, boolean, list of constant, list of function, list of object, list of range, list of integer, list of string, list of boolean.
  
  It is worth mentionning that the difference between the data and result type function and the type object is minimal and due to support of legacy Sollya code. Both Sollya functions and Sollya objects are transferred from and to the external procedure thru the C type sollya_obj_t. The difference is that Sollya will check that a certain object is a mathematical function when function is used as a type, and will skip this test if the object type is used. Similarly, Sollya relies on an object produced by the external procedure to be a mathematical function when function is used and will not make this assumption for object.
  
  If upon a usage of a procedure bound to an external procedure the type of the actual parameters given or its number is not correct, Sollya produces a type error. An external function not applied to arguments represents itself and prints out with its argument and result types.
  
  The external function is supposed to return an integer indicating success. It returns its result depending on its Sollya result type as follows. Here, the external procedure is assumed to be implemented as a C function.
  • If the Sollya result type is void, the C function has no pointer argument for the result.
  • If the Sollya result type is constant, the first argument of the C function is of C type mpfr_t *, the result is returned by affecting the MPFR variable.
  • If the Sollya result type is function, the first argument of the C function is of C type sollya_obj_t *, the result is returned by affecting the sollya_obj_t variable.
  • If the Sollya result type is object, the first argument of the C function is of C type sollya_obj_t *, the result is returned by affecting the sollya_obj_t variable.
  • If the Sollya result type is range, the first argument of the C function is of C type mpfi_t *, the result is returned by affecting the MPFI variable.
  • If the Sollya result type is integer, the first argument of the C function is of C type int *, the result is returned by affecting the int variable.
  • If the Sollya result type is string, the first argument of the C function is of C type char **, the result is returned by the char * pointed with a new char *.
  • If the Sollya result type is boolean, the first argument of the C function is of C type int *, the result is returned by affecting the int variable with a boolean value.
  • If the Sollya result type is list of type, the first argument of the C function is of a C type depending on the Sollya return type:
    • For a list of constant: sollya_constant_list_t *
    • For a list of function: sollya_obj_list_t *
    • For a list of object: sollya_obj_list_t *
    • For a list of range: sollya_constant_list_t *
    • For a list of integer: sollya_int_list_t *
    • For a list of string: sollya_string_list_t *
    • For a list of boolean: sollya_boolean_list_t *
  The external procedure affects its possible pointer argument if and only if it succeeds. This means, if the function returns an integer indicating failure, it does not leak any memory to the encompassing environment.
  
  The external procedure receives its arguments as follows: If the Sollya argument type is void, no argument array is given. Otherwise the C function receives a C void ** argument representing an array of size equal to the arity of the function where each entry (of C type void *) represents a value with a C type depending on the corresponding Sollya type.
  • If the Sollya type is constant, the void * is to be cast to mpfr_t *.
  • If the Sollya type is function, the void * is to be cast to sollya_obj_t.
  • If the Sollya type is object, the void * is to be cast to sollya_obj_t.
  • If the Sollya type is range, the void * is to be cast to mpfi_t *.
  • If the Sollya type is integer, the void * is to be cast to int *.
  • If the Sollya type is string, the void * is to be cast to char *.
  • If the Sollya type is boolean, the void * is to be cast to int *.
  • If the Sollya type is list of type, the void * is to be cast to a list of a type depending on the type of the list argument:
    • For a list of constant: sollya_constant_list_t
    • For a list of function: sollya_obj_list_t
    • For a list of object: sollya_obj_list_t
    • For a list of range: sollya_interval_list_t
    • For a list of integer: sollya_int_list_t
    • For a list of string: sollya_string_list_t
    • For a list of boolean: sollya_boolean_list_t
  The external procedure is not supposed to alter the memory pointed by its array argument void **.
  
  In both directions (argument and result values), empty lists are represented by NULL pointers.
  
  Similarly to internal procedures, externally bounded procedures can be considered to be objects inside Sollya that can be assigned to other variables, stored in list etc.
• The user should be aware that they may use the Sollya library in external codes to be dynamically bound to Sollya using externalproc. On most systems, it suffices to include the header of the Sollya library into the source code of the external procedure. Linking with the actual Sollya library is not necessary on most systems; as the interactive Sollya executable contains a superset of the Sollya library functions. On some systems, linking with the Sollya library or some of its dependencies may be necessary.
  
  In particular, the Sollya library – and, of course, its header file – contain a certain set of functions to manipulate lists with elements of certain types, such as sollya_constant_list_t, sollya_obj_list_t and so on. As explained above, these types are passed in argument to (and received back thru a reference from) an external procedure. These list manipulation functions are not strictly necessary to the use of the Sollya library in free-standing applications that do not use the functionality provided with externalproc. They are therefore provided as-is without any further documentation, besides the comments given in the Sollya library header file.
• The dynamic object file whose name is given to externalproc for binding of an external procedure may also define a destructor function int sollya_external_lib_close(void). If Sollya finds such a destructor function in the dynamic object file, it will call that function when closing the dynamic object file again. This happens when Sollya is terminated or when the current Sollya session is restarted using restart. The purpose of the destructor function is to allow the dynamically bound code to free any memory that it might have allocated before Sollya is terminated or restarted.
  
  The dynamic object file is not necessarily needed to define a destructor function. This ensure backward compatibility with older Sollya external library function object files.
  
  When defined, the destructor function is supposed to return an integer value indicating if an error has happened. Upon success, the destructor functions is to return a zero value, upon error a non-zero value.