Supercompilation for Martin-Lof's type theory

This paper describes the design and implementation of a TT Lite certifying supercompiler, which transforms a source program into a pair consisting of a residual program and a proof that the residual program is equivalent to the source one. As far as we can judge from the presently available literature, it is the first time that certifying supercompilation is implemented for a nontrivial higher-order functional language. Proofs generated by the TT Lite supercompiler can be verified by the type checker that does not depend on the supercompiler and is not based on supercompilation. This is especially important when reliability of results obtained by means of supercompilation is of primary concern.