The paper describes the algorithm of the supercompiler HOSC 1.5, an experimental specializer dealing with programs written in a higher-order functional language. The design decisions behind the algorithm are illustrated through a series of examples. Of particular interest are the decisions related to generalization and homeomorphic embedding of expressions with bound variables.

The paper presents a number of improvements to the method of two-level supercompilation: a fast technique of lemma discovering by analyzing the expressions in the partial process tree, an enhancement to the algorithm of checking improvement lemmas based on the normalization of tick annotations, and a few techniques of finding simplified versions of lemmas discovered in the process of two-level supercompilation.

The paper deals with some aspects of metasystem transitions in the context of supercompilation. We consider the manifestations of the law of branching growth of the penultimate level in the case of higher-level supercompilation and argue that this law provides some useful hints regarding the ways of constructing metasystems by combining supercompilers. In particular we show the usefulness of multi-result supercompilation for proving the equivalence of expressions and in two-level supercompilation.

The paper explains the principles of multi-result supercompilation. We introduce a formalism for representing supercompilation algorithms as rewriting rules for graphs of congurations. Some low-level technical details related to the implementation of multi-result supercompilation in MRSC are discussed. In particular, we consider the advantages of using spaghetti stacks for representing graphs of configurations.