Experiments on generating compilers by specializing specializers with respect to interpreters have shown that the compilers thus obtained have a natural structure only if the specializer does variable splitting. Variable splitting can result in a residual program using several variables to represent the values of a single variable of the original program. In the case of functional programming variable splitting is done by raising the arities of functions. The paper describes the structure and principles of operation of an arity raiser dealing with programs in a subset of pure Lisp.
S. A. Romanenko. Arity Raiser and its Use in Program Specialization. In Proceedings of the Third European Symposium on Programming on ESOP '90 (Copenhagen, Denmark). N. Jones, Ed. Springer-Verlag New York, New York, NY, 341-360.

This paper describes the structure of, and the ideas behind, a self-applicable specializer of programs, as well as the principles of operation of a compiler generator that has been produced automatically by specializing the specializer with respect to itself. It has been found that the structure of the compilers produced can be improved by making use of such devices as introducing different representations for the values of K- and U-parameters, splitting the subject program into K-and U-program, and automatically raising the arity of functions in the residual program.
S.A.Romanenko. A Compiler Generator Produced by a Self-Applicable Specializer Can Have a Surprisingly Natural and Understandable Structure. In D.Bjorner, A.P.Ershov and N.D.Jones, editors, Partial Evaluation and Mixed Computation, pages 445-463, North-Holland, 1988.

One of the applications of supercompilation is proving properties of programs. We focus in this paper on a specific task: proving term equivalence for a higher-order lazy functional language. The "classical" way to prove equivalence of two terms t1 and t2 is to write an equality function equals and to simplify the term (equals t1 t2). However, this works only when certain conditions are met. The paper presents another approach to proving term equivalence by means of supercompilation. In this approach we supercompile both terms and compare supercompiled terms syntactically. Some applications of the technique are discussed. In particular, one of these applications may lead to the development of a more powerful "higher-level" supercompiler.
Ilya Klyuchnikov and Sergei Romanenko. Proving the Equivalence of Higher-Order Terms by Means of Supercompilation. In: Perspectives of Systems Informatics (Proceedings of Seventh International Andrei Ershov Memorial Conference, PSI 2009, Novosibirsk, Russia, June 15-19, 2009). Novosibirsk: A.P. Ershov Institute of Informatics Systems, 2009, pages 150-158.