Figure 1. Schematic representation of the Mathemagix compilation phases.

The Mathemagix compilation process is decomposed in several stages (see figure ?):

• The Mathemagix input file is first parsed into a mathemagix program. In the source code of the compiler, mathemagix programs have the type MMX.

• The main compilation process consists of finding an unambiguous meaning for every symbol in the input program. Whenever a variable var is used in different contexts (e.g. as a function argument, a local variable, a class field) or overloaded in a given context, then new symbols var#1, var#2, etc. are created which correspond to the different possible meanings of var.

  Internally, the compilation of a mathemagix program yields a typed program of type PRG. Such a program has a unique “type” (of type TYP) and a unique penalty (of type Penalty). Since Mathemagix allows for ambiguous expressions, the type of the compilation of any subexpression may be a so called “ambiguous type'. Of course, the overall program is required to have a single interpretation.

• After the main compilation, several post-treatments can take place. These post-treatments are quite independent from the main compilation process and done inside separate modules. More modules can be added later. Some useful modules are the following:

  • Inlining of all functions which were declared inline.

  • Nested functions, such as shift(x)(y) == x+y; are not supported by C++. A dedicated “unnesting” module transforms nested function declarations into plain functions, which manipulate suitable function objects.

  All post-treatments are performed on typed programs of type PRG. Libraries are provided for simple syntactic manipulations of mathemagix, typed and C++ programs. The typed programs are richer than pure mathemagix and C++ programs, because all such programs are required to have types, making their manipulation more rigid and safe.

• After compilation, optimization and other post-treatments, we obtain a typed program which can be transformed into a C++ program in a rather straightforward manner. Such C++ programs are generic expressions of type CPP.

  In principle, other back-ends are possible for the compiler. On the one hand, we plan to write back-ends for other languages, starting with C. On the other hand, the final Mathemagix program is suitable for efficient interpretation.

• Mathemagix provides a C++ pretty printer which transforms the C++ program tree into a string. The final object file or binary is obtained by using a standard C++ compiler.