Abstract. Traditional combinatory logic is able to represent all Turing computable functions on natural numbers, but there are effectively calculable functions on the combinators themselves that cannot be so represented, because they have direct access to the internal structure of their arguments. Some of this expressive power is captured by adding a factorisation combinator. It supports structural equality, and more generally, a large class of generic queries for updating of, and selecting from, arbitrary structures. The resulting combinatory logic is structure complete in the sense of being able to represent pattern-matching functions, as well as simple abstractions. §1. Introduction. Traditional combinatory logic [21, 4, 10] is computationally equivalent to pure λ-calculus [3] and able to represent all of the Turing computable functions on natural numbers [23], but there are effectively calculable functions on the combinators themselves that cannot be so represented, as they examine the internal structure of their arguments.

Abstract. The bondi programming language is multi-polymorphic, in that it supports four polymorphic programming styles within a small core of computation, namely a typed pattern calculus. bondi’s expressive power is illustrated by considering the problem of assigning reviewers to a paper. As the context generalises from a committee to a committee with additional reviewers, to a conference, a federation or confederation, the solution incorporates polymorphism familiar from the functional, generic functional, relational, path-based and object-oriented programming styles, respectively. These experiments show that multipolymorphic programming is both practical and desirable. 1