Lambda Calculus with Explicit Recursion

AbstractThis paper is concerned with the study ofλ-calculus with explicit recursion, namely of cyclicλ-graphs. The starting point is to treat aλ-graph as a system of recursion equations involvingλ-terms and to manipulate such systems in an unrestricted manner, using equational logic, just as is possible for first-order term rewriting. Surprisingly, now the confluence property breaks down in an essential way. Confluence can be restored by introducing a restraining mechanism on the substitution operation. This leads to a family ofλ-graph calculi, which can be seen as an extension of the family ofλσ-calculi (λ-calculi with explicit substitution). While theλσ-calculi treat the let-construct as a first-class citizen, our calculi support the letrec, a feature that is essential to reason about time and space behavior of functional languages and also about compilation and optimizations of program

Automated Deduction – CADE 28

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions

Twenty years of rewriting logic

AbstractRewriting logic is a simple computational logic that can naturally express both concurrent computation and logical deduction with great generality. This paper provides a gentle, intuitive introduction to its main ideas, as well as a survey of the work that many researchers have carried out over the last twenty years in advancing: (i) its foundations; (ii) its semantic framework and logical framework uses; (iii) its language implementations and its formal tools; and (iv) its many applications to automated deduction, software and hardware specification and verification, security, real-time and cyber-physical systems, probabilistic systems, bioinformatics and chemical systems

Hybrid eager and lazy evaluation for efficient compilation of Haskell

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2002.Includes bibliographical references (p. 208-220).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.The advantage of a non-strict, purely functional language such as Haskell lies in its clean equational semantics. However, lazy implementations of Haskell fall short: they cannot express tail recursion gracefully without annotation. We describe resource-bounded hybrid evaluation, a mixture of strict and lazy evaluation, and its realization in Eager Haskell. From the programmer's perspective, Eager Haskell is simply another implementation of Haskell with the same clean equational semantics. Iteration can be expressed using tail recursion, without the need to resort to program annotations. Under hybrid evaluation, computations are ordinarily executed in program order just as in a strict functional language. When particular stack, heap, or time bounds are exceeded, suspensions are generated for all outstanding computations. These suspensions are re-started in a demand-driven fashion from the root. The Eager Haskell compiler translates Ac, the compiler's intermediate representation, to efficient C code. We use an equational semantics for Ac to develop simple correctness proofs for program transformations, and connect actions in the run-time system to steps in the hybrid evaluation strategy.(cont.) The focus of compilation is efficiency in the common case of straight-line execution; the handling of non-strictness and suspension are left to the run-time system. Several additional contributions have resulted from the implementation of hybrid evaluation. Eager Haskell is the first eager compiler to use a call stack. Our generational garbage collector uses this stack as an additional predictor of object lifetime. Objects above a stack watermark are assumed to be likely to die; we avoid promoting them. Those below are likely to remain untouched and therefore are good candidates for promotion. To avoid eagerly evaluating error checks, they are compiled into special bottom thunks, which are treated specially by the run-time system. The compiler identifies error handling code using a mixture of strictness and type information. This information is also used to avoid inlining error handlers, and to enable aggressive program transformation in the presence of error handling.by Jan-Willem Maessen.Ph.D

Deduction-Based Software Component Retrieval

Deduction-based software component retrieval is a software reuse technique that uses formal specifications as component descriptors and as search keys; matching components are identified using an automated theorem prover. This dissertation contains a detailed theoretical investigation of the concept as well as the first substantial experimental evaluation of its technical feasibility.Deduktionsbasiertes Kompenentenretrieval ist eine Softwarereusetechnik, in der formale Spezifikationen zur Beschreibung von Komponenten sowie als Anfragen verwendet werden; passende Komponenten werden mit Hilfe eines automatischen Theorembeweisers ermittelt. Diese Arbeit enthält eine detaillierte theoretische Untersuchung dieses Konzeptes und die erste ausführliche experimentelle Evaluierung seiner technischen Realisierbarkeit

Automated Reasoning

This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book

Programming Languages and Systems

This open access book constitutes the proceedings of the 29th European Symposium on Programming, ESOP 2020, which was planned to take place in Dublin, Ireland, in April 2020, as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The actual ETAPS 2020 meeting was postponed due to the Corona pandemic. The papers deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems

Finding parallel functional pearls : automatic parallel recursion scheme detection in Haskell functions via anti-unification

This work has been partially supported by the EU H2020 grant “RePhrase: Refactoring Parallel Heterogeneous Resource-Aware Applications–a Software Engineering Approach” (ICT-644235), by COST Action IC1202 (TACLe), supported by COST (European Cooperation in Science and Technology) , by EPSRC grant “Discovery: Pattern Discovery and Program Shaping for Manycore Systems” (EP/P020631/1), and by Scottish Enterprise PS7305CA44.This paper describes a new technique for identifying potentially parallelisable code structures in functional programs. Higher-order functions enable simple and easily understood abstractions that can be used to implement a variety of common recursion schemes, such as maps and folds over traversable data structures. Many of these recursion schemes have natural parallel implementations in the form of algorithmic skeletons. This paper presents a technique that detects instances of potentially parallelisable recursion schemes in Haskell 98 functions. Unusually, we exploit anti-unification to expose these recursion schemes from source-level definitions whose structures match a recursion scheme, but which are not necessarily written directly in terms of maps, folds, etc. This allows us to automatically introduce parallelism, without requiring the programmer to structure their code a priori in terms of specific higher-order functions. We have implemented our approach in the Haskell refactoring tool, HaRe, and demonstrated its use on a range of common benchmarking examples. Using our technique, we show that recursion schemes can be easily detected, that parallel implementations can be easily introduced, and that we can achieve real parallel speedups (up to 23 . 79 × the sequential performance on 28 physical cores, or 32 . 93 × the sequential performance with hyper-threading enabled).PostprintPeer reviewe