Automatic generation of provably correct parallelizing compilers

We show how parallelizing compilers can be automatically derived from denotational definitions of programming languages. In our approach, the denotational definition is expressed using definite clause grammars (syntax specification) and Horn Logic or Constraint Logic (semantic specification). 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 specification of the language is executable, and thus automatically yields a parallel interpreter. This interpreter can be partially evaluated with respect to a given program to automatically obtain (provably correct) 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.