Abstract

In this paper we explore ways of capturing well-formed patterns of recursion in the form of generic reductions. These reductions, called uniform traversal combinators, can substantially help the theorem proving process by eliminating the need for induction and can also be an aid in achieving effective program synthesis. 1 Introduction Recursive structures, such as lists and trees, can be defined inductively in most functional languages [6]. The recursive types of these structures can be formalized using axiom sets generated automatically from their type definition, which are basically equivalent to Hoare's axioms for recursive data structures [5]. Programs that operate on instances of these types can be expressed as recursive functions in a pure applicative language. Theorems about these functions can be proved using induction principles on the structure of the parameter types of these functions. The Boyer-Moore theorem prover [3], for example, proves theorems about recursive function...

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