Partial evaluation of Maple

Abstract

a b s t r a c tHaving been convinced of the potential benefits of partial evaluation, we wanted to apply these techniques to code written in Maple, our Computer Algebra System of choice. Maple is a very large language, with a number of non-standard features. When we tried to implement a partial evaluator for it, we ran into a number of difficulties for which we could find no solution in the literature. Undaunted, we persevered and ultimately implemented a working partial evaluator with which we were able to very successfully conduct our experiments, first on small codes, and now on actual routines taken from Maple's own library. Here, we document the techniques we had to invent or adapt to achieve these results.

Towards the Formal Specification and Verification of Maple Programs

“…The work focused to collect requirements for the pure type inference engine for existing Maple routines. The work was extended to develop the partial evaluator for Maple mentioned above [6].…”

Dynamic Elimination of Overflow Tests in a Trace Compiler

“…LIR: the low-level three-address code instruction representation that Nanojit receives as input. 4. Once the trace engine finds the original branch that started the recording process, the current segment is passed to Nanojit.…”

“…This type of partial evaluation in which the JIT compiler uses runtime values to produce better binaries is sometimes called specialization by need [21]. Implementations that use this kind of technique include Python's Psyco JIT compiler [21], Matlab [7,10] and Maple [4]. Partial evaluation has been used in the context of just-in-time compilation mostly as a form of type specialization [7,5,14].…”

“…However, our approach differs from previous works because we use values known only at runtime in order to put bounds on the range of values that integer variables might assume during the program execution. This is a form of partial evaluation [18], yet done at runtime [4], because our analysis is invoked by a just-in-time compiler while the target application is being interpreted. By relying on such values we are able to perform much more aggressive range inferences than traditional static analyses.…”

Optimizing Matlab through Just-In-Time Specialization

“…Run-time specialization accommodates Matlab's dynamic nature, and is a technique that has been applied in many other dynamic optimization contexts. The Psyco python virtual machine, for instance, implements specialization "by need" [19], a process similar to the online partial evaluation approaches applied to Matlab [5] and Maple [20]. This specialization technique involves interleaving program specialization and execution; the specializer can request facts such as the type of variables while a procedure is executing, and depending on the result, potentially modify the compiled code to be more efficient.…”