Abstract † We introduce a new paradigm for the integration of functional and logic programming. Unlike most current research, our approach is not based on extending unification to general-purpose equation solving. Rather, we propose a computation delaying mechanism called residuation. This allows a clear distinction between functional evaluation and logical deduction. The former is based on the λ-calculus, and the latter on Horn clause resolution. In clear contrast with equation-solving approaches, our model supports higher-order function evaluation and efficient compilation of both functional and logic programming expressions, without being plagued by non-deterministic term-rewriting. In addition, residuation lends itself naturally to process synchronization and constrained search. Besides unification (equations), other residuations may be any ground-decidable goal, such as mutual exclusion (inequations), and comparisons (inequalities). We describe an implementation of the residuation paradigm as a prototype language called Le Fun—Logic, equations, and Functions.

: We propose a metalogic programming method for efficient induction of a fairly large class of list-handling logic programs delineated through restrictions on the hypothesis language. These restrictions take the form of predefined program recursion schemes (higher order "clich'es") from which the hypotheses programs in the induction process are derived by plugging in either simple, nonrecursive clause programs or invented predicates. Metalogic programming is applied for handling clauses as first class data objects in connection with program schemes, and moreover for obtaining a flexible control scheme during the induction, avoiding a blindfold generate-and-test against the given program examples. A metalogic program induction testbed has been constructed and has successfully been applied to some induction problems discussed in the literature. Keywords: Induction of logic programs, metalogic programming, higher order program clich'es, predicate invention, mixed bottom-up and top-down i...