Certifying supercompilation for Martin-Löf’s type theory

Abstract

The paper describes the design and implementation of a certifying supercompiler TT Lite SC, which takes an input program and produces a residual program and a proof of the fact that the residual program is equivalent to the input one. As far as we can judge from the literature, this is the first implementation of a certifying supercompiler for a non-trivial higher-order functional language. The proofs generated by TT Lite SC can be verified by a type checker which is independent from TT Lite SC and is not based on supercompilation. This is essential in cases where the reliability of results obtained by supercompilation is of fundamental importance. Currently, the proofs can be either verified by the type-checker built into TT Lite, or converted into Agda programs and checked by the Agda system. The main technical contribution is a simple but intricate interplay of supercompilation and type theory.