An Open Challenge Problem Repository for Systems Supporting Binders

A variety of logical frameworks support the use of higher-order abstract syntax in representing formal systems; however, each system has its own set of benchmarks. Even worse, general proof assistants that provide special libraries for dealing with binders offer a very limited evaluation of such libraries, and the examples given often do not exercise and stress-test key aspects that arise in the presence of binders. In this paper we design an open repository ORBI (Open challenge problem Repository for systems supporting reasoning with BInders). We believe the field of reasoning about languages with binders has matured, and a common set of benchmarks provides an important basis for evaluation and qualitative comparison of different systems and libraries that support binders, and it will help to advance the field.Comment: In Proceedings LFMTP 2015, arXiv:1507.0759

Specializing Interpreters using Offline Partial Deduction

We present the latest version of the Logen partial evaluation system for logic programs. In particular we present new binding-types, and show how they can be used to effectively specialise a wide variety of interpreters.We show how to achieve Jones-optimality in a systematic way for several interpreters. Finally, we present and specialise a non-trivial interpreter for a small functional programming language. Experimental results are also presented, highlighting that the Logen system can be a good basis for generating compilers for high-level languages

Maude: specification and programming in rewriting logic

Maude is a high-level language and a high-performance system supporting executable specification and declarative programming in rewriting logic. Since rewriting logic contains equational logic, Maude also supports equational specification and programming in its sublanguage of functional modules and theories. The underlying equational logic chosen for Maude is membership equational logic, that has sorts, subsorts, operator overloading, and partiality definable by membership and equality conditions. Rewriting logic is reflective, in the sense of being able to express its own metalevel at the object level. Reflection is systematically exploited in Maude endowing the language with powerful metaprogramming capabilities, including both user-definable module operations and declarative strategies to guide the deduction process. This paper explains and illustrates with examples the main concepts of Maude's language design, including its underlying logic, functional, system and object-oriented modules, as well as parameterized modules, theories, and views. We also explain how Maude supports reflection, metaprogramming and internal strategies. The paper outlines the principles underlying the Maude system implementation, including its semicompilation techniques. We conclude with some remarks about applications, work on a formal environment for Maude, and a mobile language extension of Maude

Collection analysis for Horn clause programs

We consider approximating data structures with collections of the items that they contain. For examples, lists, binary trees, tuples, etc, can be approximated by sets or multisets of the items within them. Such approximations can be used to provide partial correctness properties of logic programs. For example, one might wish to specify than whenever the atom $sort(t,s)$ is proved then the two lists $t$ and $s$ contain the same multiset of items (that is, $s$ is a permutation of $t$). If sorting removes duplicates, then one would like to infer that the sets of items underlying $t$ and $s$ are the same. Such results could be useful to have if they can be determined statically and automatically. We present a scheme by which such collection analysis can be structured and automated. Central to this scheme is the use of linear logic as a omputational logic underlying the logic of Horn clauses