We present an approach for automatic function inversion in Haskell. The inverse functions we generate are based on an extension of Haskell's computational model with non-determinism and free variables. We implement this functional logic extension of Haskell via a monadic lifting of functions and type declarations. Using inverse functions, we additionally show how Haskell's pattern matching can be augmented with support for functional patterns, which enable arbitrarily deep pattern matching in data structures. Finally, we provide a plugin for the Glasgow Haskell Compiler to seamlessly integrate inverses and functional patterns into the language, covering almost all of the Haskell2010 language standard.

The declarative programming language Curry amalgamates demand-driven evaluation from functional programming with non-determinism from logic programming. In contrast to Prolog, the search strategy for non-deterministic computations is not fixed so that complete or parallel strategies are reasonable for Curry. In particular, a desirable option is a fair strategy which frees the programmer from considering the influence of the search strategy to the success of a computation. In this paper we describe an implementation with this property. Based on recent developments on operational models for functional logic programming, we present a new implementation which transforms Curry programs in several transformation steps into Go programs. By exploiting lightweight threads in the form of goroutines, we obtain a complete and fair implementation which automatically uses multi-processing to speed up non-deterministic computations. This has the effect that, in some cases, non-deterministic algorithms are more efficiently evaluated than deterministic ones.

Abstract This paper presentsPFLP, a library for probabilistic programming in the functional logic programming language Curry. It demonstrates how the concepts of a functional logic programming language support the implementation of a library for probabilistic programming. In fact, the paradigms of functional logic and probabilistic programming are closely connected. That is, language characteristics from one area exist in the other and vice versa. For example, the concepts of non-deterministic choice and call-time choice as known from functional logic programming are related to and coincide with stochastic memoization and probabilistic choice in probabilistic programming, respectively. We will further see that an implementation based on the concepts of functional logic programming can have benefits with respect to performance compared to a standard list-based implementation and can even compete with full-blown probabilistic programming languages, which we illustrate by several benchmarks.