Staged Composition Synthesis

A framework for composition synthesis is provided in which metalanguage combinators are supported and the execution of synthesized programs can be staged into composition-time code generation (stage 1) and run-time execution (stage 2). 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. 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 stage 1, leaving only well typed L1-code for execution at stage 2. Furthermore, we report on experiments. Composition synthesis [Reh13] is based on the idea of using inhabitation in combinatory logic with intersection types [BCDC83] as a foundation for computing compositions from a repository of components. We can regard a combinatory type judgement Γ ⊢ e : τ as modeling the fact that combinatory expression e can be obtained by composition from a repository Γ of components which are exposed as combinator symbols and whose interfaces are exposed as combinator types enriched with intersection types that specify semantic properties of components. The decision problem of inhabitation, often indicated as Γ ⊢ ? : τ , is the question whether a combinatory expression e exists such that Γ ⊢ e : τ (such an expression e is called an inhabitant of τ ). An algorithm (or semi-algorithm) for solving the inhabitation problem searches for inhabitants and can be used to synthesize them. Under the propositions-as-types correspondence, inhabitation is the question of provability in a Hilbert-style presentation of a propositional logic, where Γ represents a propositional theory, τ represents a proposition to be proved, and e is a proof. Following [WY05], a level of semantic types is introduced to specify component interfaces and synthesis goals so as to direct synthesis by means of semantic concepts. Semantic types are not necessarily checked against component implementations (this is regarded as an orthogonal issue). In combinatory logic synthesis (CLS) [DMRU12, Reh13, DMR13] semantic types are represented by intersection types [BCDC83]. In addition to being inherently component-oriented, it is a possible advantage of the type-based approach of