Deriving backtracking monad transformers

Abstract

In a paper about pretty printing J. Hughes introduced two fundamental techniques for deriving programs from their specification, where a specification consists of a signature and properties that the operations of the signature are required to satisfy. Briefly, the first technique, the term implementation, represents the operations by terms and works by defining a mapping from operations to observations --- this mapping can be seen as defining a simple interpreter. The second, the context-passing implementation, represents operations as functions from their calling context to observations. We apply both techniques to derive a backtracking monad transformer that adds backtracking to an arbitrary monad. In addition to the usual backtracking operations --- failure and nondeterministic choice --- the prolog cut and an operation for delimiting the effect of a cut are supported.