Program and proof optimizations with type systems

We demonstrate a method for describing data-flow analyses based program opti-mizations as compositional type systems with a transformation component. Analy-sis results are presented in terms of types ascribed to expressions and statements, certifiable by type derivations, and the transformation component carries out the optimizations that the type derivations license. We describe dead code elimina-tion and common subexpression elimination. In the case of common subexpression elimination we circumvent non-compositionality with a combined type system for a combination of two analyses. The motivation of this work lies in certified code applications, where an optimization of a program must be supported by a checkable justification. As an example application we highlight “proof optimization”, i.e., me-chanical transformation of a program’s functional correctness proof together with the program, based on the analysis type derivation