Implementing a Library for Probabilistic Programming Using Non-strict Non-determinism

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.

A rewrite-based computational model for functional logic programming

Functional logic programming extends the functional programming style with two important features: the possibility to define nondeterministic operations with overlapping rules, and the usage of logic variables in both defining rules and expressions to evaluate. Conditional constructor-based term rewrite systems (CB-CTRSs) emerged as a suitable model for functional logic programs, because they can be easily transformed into an equivalent program in a core language where computations can be performed more efficiently.We consider a recent proposal by Antoy and Hanus, of translating CB-CTRSs into an equivalent class of programs where computation can be performed by mere rewriting. His computational model has the limitation of computing only ground answer substitutions for equations with strict semantics interpreted as joinability to a value.We propose two adjustments of their computational models, which are capable to compute non-ground answers.

Default rules for Curry

In functional logic programs, rules are applicable independently of textual order, i.e., any rule can potentially be used to evaluate an expression. This is similar to logic languages and contrary to functional languages, e.g., Haskell enforces a strict sequential interpretation of rules. However, in some situations it is convenient to express alternatives by means of compact default rules. Although default rules are often used in functional programs, the non-deterministic nature of functional logic programs does not allow to directly transfer this concept from functional to functional logic languages in a meaningful way. In this paper, we propose a new concept of default rules for Curry that supports a programming style similar to functional programming while preserving the core properties of functional logic programming, i.e., completeness, non-determinism, and logic-oriented use of functions. We discuss the basic concept and propose an implementation which exploits advanced features of functional logic languages.

A liberal type system for functional logic programs

We propose a new type system for functional logic programming which is more liberal than the classical Damas–Milner usually adopted, but it is also restrictive enough to ensure type soundness. Starting from Damas–Milner typing of expressions, we propose a new notion of well-typed program that adds support for type-indexed functions, a particular form of existential types, opaque higher-order patterns and generic functions – as shown by an extensive collection of examples that illustrate the possibilities of our proposal. In the negative side, the types of functions must be declared, and therefore types are checked but not inferred. Another consequence is that parametricity is lost, although the impact of this flaw is limited as ‘free theorems’ were already compromised in functional logic programming because of non-determinism.