A Theory of Staged Composition Synthesis ( Extended Version )

Composition synthesis is based on the idea of using inhabitation in combinatory logic with intersection types as a foundation for computing compositions from component repositories. Components implemented in a language L1 are exposed to composition synthesis in the form of typed combinator symbols. In practice, it is useful to augment the collection of components in the implementation language L1 with a collection of components implemented in a metalanguage L2 in order to define, e.g., higher-level (possibly application specific) composition operators and combinators that manipulate L1-code templates. By extending composition synthesis to encompass both object language (L1) and metalanguage (L2) combinators, composition synthesis becomes a powerful and flexible framework for the generation of L1-program compositions. In this report a framework for composition synthesis is provided, in which the execution of synthesized programs can be staged into composition-time code generation (L2) and run-time execution (L1). A system of modal intersection types is introduced into a combinatory composition language to control the distinction between L1and L2-combinators at the type level, thereby exposing the language distinction to composition synthesis. We provide a theory of correctness of the framework which ensures that generated compositions of component implementations are well typed and that their execution can be staged such that all metalanguage combinators can be computed away completely at composition time (stage 1), leaving only well typed L1-code for later run-time execution (stage 2). Our framework has been implemented, and we report on experiments. This is an extended version of the corresponding conference paper. In particular we present proofs for the main results. Furthermore, the appendix includes a detailed discussion of experiments.