Automatic Generation of Provably Correct Parallelizing Compilers

We show how parallelizing compilers can be automatically derived from denotational deenitions of programming languages. In our approach, the denotational deenition is expressed using deenite clause grammars (syntax speciication) and Horn Logic or Constraint Logic (semantic speciication). The conditions for executing two or more statements in parallel (e.g., GCD test, Banerjee test, or exact test) are included as part of the (parallel) denotational semantics of the language. Solutions of diophantine equations, needed for parallelizing DO loops, can be expressed in constraint logic as well, and are thus easily incorporated in our denotational framework. This parallel denotational speciication of the language is executable, and thus automatically yields a parallel interpreter. This interpreter can be partially evaluated w.r.t. a given program to obtain parallel compiled code. In addition, the various syntactic and semantic restructuring transformations that have been proposed to expose more parallelism in sequential programs can also be expressed in our denotational framework. Partial evaluation of a program w.r.t. this interpreter will result in parallel code that is specialized to a given architecture. Automatic derivation of these parallelizing compilers becomes possible because of use of Horn Logic, instead of the traditional-calculus, for expressing denotational semantics. The major advantage of our approach is that the parallelizing compilers derived are provably correct, since they are automatically generated from language speciications.