Electromagnetic theory is central to physics. An undergraduate major in physics typically takes a semester or a year of electromagnetic theory as a junior or senior, and a graduate student in physics typically takes an additional semester or year at a more advanced level. In fall 2023, the author taught his undergraduate electricity and magnetism class using numerical methods in Haskell in parallel with traditional analytical methods. This article describes what functional programming has to offer to physics in general, and electromagnetic theory in particular. We give examples from vector calculus, the mathematical language in which electromagnetic theory is expressed, and electromagnetic theory itself.
The idea of functional programming has played a big role in shaping today's landscape of mainstream programming languages. Another concept that dominates the current programming style is Dijkstra's structured programming. Both concepts have been successfully married, for example in the programming language Scala. This paper proposes how the same can be achieved for structured programming and PURELY functional programming via the notion of LINEAR SCOPE. One advantage of this proposal is that mainstream programmers can reap the benefits of purely functional programming like easily exploitable pa…
This report aggregates the papers presented at the twenty-first annual Scheme and Functional Programming Workshop, hosted on August 28th, 2020, online and co-located with the twenty-fifth International Conference on Functional Programming. The Scheme and Functional Programming Workshop is held every year to provide an opportunity for researchers and practitioners using Scheme and related functional programming languages like Racket, Clojure, and Lisp, to share research findings and discuss the future of the Scheme programming language.
The Seventh International Workshop on Trends in Functional Programming in Education, TFPIE 2018, was held on 14th of June 2018 at Chalmers University in Gothenburg, Sweden, and was co-located with TFP, the Symposium on Trends in Functional Programming. The goal of TFPIE is to gather researchers, professors, teachers, and all professionals interested in functional programming in education. This includes the teaching of functional programming, but also the application of functional programming as a tool for teaching other topics, e.g. computational concepts, complexity, logic and reasoning, and …
The Sixth International Workshops on Trends in Functional Programming in Education, TFPIE 2017, was held on 22 June 2017 at the University of Kent, in Canterbury, UK, and was co-located with TFP, the Symposium on Trends in Functional Programming. The goal of TFPIE is to gather researchers, professors, teachers, and all professionals interested in functional programming in education. This includes the teaching of functional programming, but also the application of functional programming as a tool for teaching other topics and disciplines. A particular topic of this year's TFPIE was that of MOOC…
This document is intended as a stand-alone textbook chapter to be used for introducing some functional programming concepts into a course in which the primary teaching language is Java. For details of the approach, please see the paper "Functional programming, in the data structures course, in Java" by J. MacCormick, which appears in the Journal of Computing Sciences in Colleges (2023).
This volume constitutes the pre-proceedings of the 28th International Workshop on Functional and Logic Programming (WFLP 2020), organized by the University of Bologna, Italy, as part of Bologna Federated Conference on Programming Languages 2020. The international Workshop on Functional and (constraint) Logic Programming (WFLP) aims at bringing together researchers, students, and practitioners interested in functional programming, logic programming, and their integration. WFLP has a reputation for being a lively and friendly forum, and it is open for presenting and discussing work in progress, …
This volume contains the papers, accepted after post-reviewing, based on presentations submitted to TFPIE 2021 and TFPIE 2022 that took place online, in collaboration with LambdaDays 2021/22 in Kraków, Poland. TFPIE stands for Trends in Functional Programming in Education, where authors present research and experiences in teaching concepts of functional programming at any level.
Functional languages have provided major benefits to the verification community. Although features such as purity, a strong type system, and computational abstractions can help guide programmers away from costly errors, these can present challenges when used in a reactive system. Functional Reactive Programming is a paradigm that allows users the benefits of functional languages and an easy interface to a reactive environment. We present a tool for building autonomous vehicle controllers in FRP using Haskell.
A paper has recently been published in SIAM-JC. This paper is faulty: 1) The standard requirements about the definition of an algorithm are not respected, 2) The main point in the complexity study, namely the functional programming component, is absent. The Editorial Board of the SIAM JC had been warned a confirmed publication would be openly commented, it is the role of this text.
We formally define an elegant multi-paradigm unification of Functional Reactive Programming, Actor Systems, and Object-Oriented Programming. This enables an intuitive form of declarative programming, harvesting the power of concurrency while maintaining safety. We use object and reference capabilities to highlight and tame imperative features: reference capabilities track aliasing and mutability, and object capabilities track I/O. Formally, our type system limits the scope, impact and interactions of impure code. - Scope: Expressions whose input is pure will behave deterministically. - Impact:…
This paper presents PFLP, 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 stoch…
In this paper we introduce the Functional Modelling System (FMS). The system introduces the Functional Modelling Language (FML), which is a modelling language for NP-complete search problems based on concepts of functional programming. Internally, we translate FML specifications to an Answer Set Program to obtain models. We give a general overview of the new FML language, and how this language is handled in the system. We give a step-by-step walkthrough of the system, pointing out what features are in place, and what improvements are still possible.
This volume contains the proceedings of the Ninth Workshop on Mathematically Structured Functional Programming (MSFP 2022). The meeting took place on the 2nd of April as a satellite of European Joint Conferences on Theory & Practice of Software (ETAPS 2022). The MSFP workshop highlights applications of mathematical structures to programming applications. We promote the use of category theory, type theory, and formal language semantics to the development of simple and reasonable programs. As the range of papers presented in this year's workshop shows, this continues to be a fruitful interface.
A Proof Theoretic Approach to Failure in Functional Logic Programming
如何从程序中提取负信息是逻辑程序设计中的一个重要问题。在这里，我们解决问题的功能逻辑程序，从证明理论的角度来看。我们工作的出发点是CRWL（Constructor based ReWriting Logic），它是一个成熟的函数逻辑编程理论框架，其基本概念是非严格非确定函数。我们提出了一个证明演算，CRWLF，这是能够推导出否定信息的CRWL程序。特别是，CRWLF能够证明CRWL内的复位有限失败。
We present a linear functional calculus with both the safety guarantees expressible with linear types and the rich language of combinators and composition provided by functional programming. Unlike previous combinations of linear typing and functional programming, we compromise neither the linear side (for example, our linear values are first-class citizens of the language) nor the functional side (for example, we do not require duplicate definitions of compositions for linear and unrestricted functions). To do so, we must generalize abstraction and application to encompass both linear and unr…
Logic programming is a flexible programming paradigm due to the use of predicates without a fixed data flow. To extend logic languages with the compact notation of functional programming, there are various proposals to map evaluable functions into predicates in order to stay in the logic programming framework. Since amalgamated functional logic languages offer flexible as well as efficient evaluation strategies, we propose an opposite approach in this paper. By mapping logic programs into functional logic programs with a transformation based on inferring functional dependencies, we develop a f…
This volume contains the proceedings of the Eighth Workshop on Mathematically Structured Functional Programming (MSFP 2020). The meeting was originally scheduled to take place in Dublin, Ireland on the 25th of April as a satellite event of the European Joint Conferences on Theory & Practice of Software (ETAPS 2020). Due to the COVID-19 pandemic, ETAPS 2020, and consequently MSFP 2020, has been postponed to a date yet to be determined. The MSFP workshop highlights applications of mathematical structures to programming applications. We promote the use of category theory, type theory, and formal …
Throughout the history of functional programming, recursion has emerged as a natural method for describing loops in programs. However, there does often exist a substantial cognitive distance between the recursive definition and the simplest explanation of an algorithm even for the basic list processing functions such as map, concat, or unique; when we explain these functions, we seldom use recursion explicitly as we do in functional programming. For example, map is often explained as follows: the map function takes a function and a list and returns a list of the results of applying the functio…
Functional Programming has seen a resurgence in interest in the last few years and is often mentioned in opposition to Object-Orientated Programming. However, Object-Orientated Programming can actually absorb some of the lessons of Functional Programming to improve performance and reliability. This paper examines three ways in which Immutability, a common Functional Programming technique, can be used to develop immutable objects in Ruby.
Most functional languages rely on some garbage collection for automatic memory management. They usually eschew reference counting in favor of a tracing garbage collector, which has less bookkeeping overhead at runtime. On the other hand, having an exact reference count of each value can enable optimizations, such as destructive updates. We explore these optimization opportunities in the context of an eager, purely functional programming language. We propose a new mechanism for efficiently reclaiming memory used by nonshared values, reducing stress on the global memory allocator. We describe an…
We propose a call-by-value lambda calculus extended with a new construct inspired by abductive inference and motivated by the programming idioms of machine learning. Although syntactically simple the abductive construct has a complex and subtle operational semantics which we express using a style based on the Geometry of Interaction. We show that the calculus is sound, in the sense that well typed programs terminate normally. We also give a visual implementation of the semantics which relies on additional garbage collection rules, which we also prove sound.
In machine learning (ML), researchers and engineers seem to be at odds. System implementers would prefer models to be declarative, with detailed type information and semantic restrictions that allow models to be optimised, rearranged and parallelised. Yet practitioners show an overwhelming preference for dynamic, imperative languages with mutable state, and much engineering effort is spent bridging the resulting semantic divide. Is there a fundamental conflict? This article explores why imperative and functional styles are used, and how future language designs might get the best of both worlds…
Managing resources---file handles, database connections, etc.---is a hard problem. Debugging resource leaks and runtime errors due to resource mismanagement are difficult in evolving production code. Programming languages with static type systems are great tools to ensure erroneous code is detected at compile time. However, modern static type systems do little in the aspect of resource management as resources are treated as normal values. We propose a type system, Qub, based on the logic of bunched implications (BI) which models resources as first class citizens. We distinguish two kinds of pr…
This paper presents the design and implementation of Juniper: a functional reactive programming language (FRP) targeting the Arduino and related microcontroller systems. Juniper provides a number of high level features, including parametric polymorphic functions, anonymous functions, automatic memory management, and immutable data structures. Also included is a standard library which offers many useful FRP signal processing functions. Juniper is translated to standard C++ and compiled with the existing Arduino development tools, allowing Juniper programs to fit on resource-constrained devices,…
Anglican is a probabilistic programming system designed to interoperate with Clojure and other JVM languages. We introduce the programming language Anglican, outline our design choices, and discuss in depth the implementation of the Anglican language and runtime, including macro-based compilation, extended CPS-based evaluation model, and functional representations for probabilistic paradigms, such as a distribution, a random process, and an inference algorithm. We show that a probabilistic functional language can be implemented efficiently and integrated tightly with a conventional functional …
Choreographic programming is an emerging programming paradigm for concurrent and distributed systems, whereby developers write the communications that should be enacted and then a distributed implementation is automatically obtained by means of a compiler. Theories of choreographic programming typically come with strong theoretical guarantees about the compilation process, most notably: the generated implementations operationally correspond to their source choreographies and are deadlock-free. Currently, the most advanced incarnation of the paradigm is Choral, an object-oriented choreographic …
This paper presents Gemini, a functional programming language for hardware description that provides features such as parametric polymorphism, recursive datatypes, higher-order functions, and type inference for higher expressivity compared to modern hardware description languages. Gemini demonstrates the theory and implementation of novel type-theoretical concepts through its unique type system consisting of multiple atomic kinds and dependent types, which allows the language to model both software and hardware constructs safely and perform type inference through multi-staged compilation. The …
Pull-tabbing is an evaluation technique for functional logic programs which computes all non-deterministic results in a single graph structure. Pull-tab steps are local graph transformations to move non-deterministic choices towards the root of an expression. Pull-tabbing is independent of a search strategy so that different strategies (depth-first, breadth-first, parallel) can be used to extract the results of a computation. It has been used to compile functional logic languages into imperative or purely functional target languages. Pull-tab steps might duplicate choices in case of shared sub…
The Workshops on (Constraint) Logic Programming (WLP) are the annual meeting of the German Society of Logic Programming (Gesellschaft für Logische Programmierung e.V., GLP) and bring together researchers interested in logic programming, constraint programming, answer set programming, and related areas like databases and artificial intelligence (not only from Germany). The International Workshops on Functional and (Constraint) Logic Programming (WFLP) aim at bringing together researchers, students, and practitioners interested in functional programming, logic programming, and their integration.…
This volume contains five papers, accepted after post-reviewing, based on presentations submitted to TFPIE 2019 and TFPIE 2020 that took places in Vancouver, Canada and Krakow, Poland respectively. TFPIE stands for Trends in Functional Programming in Education, where authors present research and experiences in teaching concepts of functional programming at any level.
Abstract interpreters are complex pieces of software: even if the abstract interpretation theory and companion algorithms are well understood, their implementations are subject to bugs, that might question the soundness of their computations. While some formally verified abstract interpreters have been written in the past, writing and understanding them requires expertise in the use of proof assistants, and requires a non-trivial amount of interactive proofs. This paper presents a formally verified abstract interpreter fully programmed and proved correct in the F* verified programming environm…
Implementing a complex concept as an executable model in a strongly typed, purely functional language hits a sweet spot between mere simulation and formal specification. For research and education it is often desirable to enrich the algorithmic code with meta-logical annotations, variously embodied as assertions, theorems or test cases. Checking frameworks use the inherent logical power of the functional paradigm to approximate theorem proving by heuristic testing. Here we propose several novel idioms to enhance the practical expressivity of checking, namely meta-language marking, nominal axio…
In this paper, we argue that modern functional programming languages - in particular, FSharp on the .NET platform - are well suited for the development of distributed, web and cloud applications on the Internet. We emphasize that FSharp can be successfully used in a range of scenarios - starting from simple ASP.NET web applications, and including cloud data processing tasks and data-driven web applications. In particular, we show how some of the FSharp features (eg. quotations) can be effectively used to develop a distributed web system using single code-base, and describe the commercial WebSh…
This volume contains the proceedings of the Fifth Workshop on Mathematically Structured Functional Programming (MSFP 2014), taking place on 12 April, 2014 in Grenoble, France, as a satellite event of the European Joint Conferences on Theory and Practice of Software, ETAPS 2014. MSFP is devoted to the derivation of functionality from structure. It highlights concepts from algebra, semantics and type theory as they are increasingly reflected in programming practice, especially functional programming. As the range of papers presented in this year's workshop shows, this continues to be a fruitful …
This volume contains the proceedings of the Fourth Workshop on Mathematically Structured Functional Programming (MSFP 2012), taking place on 25 March, 2012 in Tallinn, Estonia, as a satellite event of the European Joint Conferences on Theory and Practice of Software, ETAPS 2012. MSFP is devoted to the derivation of functionality from structure. It highlights concepts from algebra, semantics and type theory as they are increasingly reflected in programming practice, especially functional programming. The workshop consists of two invited presentations and eight contributed papers on a range of t…
The sixth workshop on Mathematically Structured Functional Programming is devoted to the derivation of functionality from structure. It is a celebration of the direct impact of Theoretical Computer Science on programs as we write them today. Modern programming languages, and in particular functional languages, support the direct expression of mathematical structures, equipping programmers with tools of remarkable power and abstraction. Where would Haskell be without monads? Functional reactive programming without arrows? Call-by-push-value without adjunctions? The list goes on. This workshop i…
While modern software development heavily uses versioned packages, programming languages rarely support the concept of versions in their semantics, which makes software updates more bulky and unsafe. This paper proposes a programming language that intrinsically supports versions. The main goals are to design core language features to support multiple versions in one program and establish a proper notion of type safety with those features. The proposed core calculus, called Lambda VL, has versioned values, each containing different values under different versions. We show the construction of th…
Functional programming represents a modern tool for applying and implementing software. The state of the art in functional programming reports an increasing number of methodologies in this paradigm. However, extensive interdisciplinary applications are missing. Our goal is to increase student interest in pursuing further studies in functional programming with the use of an application: the ray tracer. We conducted a teaching experience, with positive results and student feedback, described here in this paper.
Paisley is an extensible lightweight embedded domain-specific language for nondeterministic pattern matching in Java. Using simple APIs and programming idioms, it brings the power of functional-logic processing of arbitrary data objects to the Java platform, without constraining the underlying object-oriented semantics. Here we present an extension to the Paisley framework that adds pattern-based control flow. It exploits recent additions to the Java language, namely functional interfaces and lambda expressions, for an explicit and transparent continuation-passing style approach to control. We…
Functional programming languages are seen by many as instrumental to effectively utilizing the computational power of multi-core platforms. As a result, there is growing interest to introduce functional programming and functional thinking as early as possible within the computer science curriculum. Bricklayer is an API, written in SML, that provides a set of abstractions for creating LEGO artifacts which can be viewed using LEGO Digital Designer. The goal of Bricklayer is to create a problem space (i.e., a set of LEGO artifacts) that is accessible and engaging to programmers (especially novice…
The seventh workshop on Mathematically Structured Functional Programming is devoted to the derivation of functionality from structure. It is a celebration of the direct impact of Theoretical Computer Science on programs as we write them today. Modern programming languages, and in particular functional languages, support the direct expression of mathematical structures, equipping programmers with tools of remarkable power and abstraction. Where would Haskell be without monads? Functional reactive programming without arrows? Call-by-push-value without adjunctions? The list goes on. This workshop…
Declarative styles such as functional programming (FP) are rapidly gaining ground on their imperative cousins, including procedural and object-oriented programming. The shift is subtle because it is happening within the context of multiparadigm programming languages such as JavaScript. FP is better suited to modern processes like test-driven development (TDD), and architectures like massively parallel, cloud-based computing. This article describes the technical details that characterize the shift from imperative to FP and implications for software quality management, particularly reuse and tes…
This volume contains the proceedings of the Fourth and Fifth International Workshops on Trends in Functional Programming in Education, TFPIE 2015 and TFPIE 2016, which were held on June 2, 2015 in Sophia-Antipolis, France, and on June 7, 2016 at the University of Maryland College Park in the USA, respectively.
We present the design of a new functional programming language, MLTS, that uses the lambda-tree syntax approach to encoding bindings appearing within data structures. In this approach, bindings never become free nor escape their scope: instead, binders in data structures are permitted to move to binders within programs. The design of MLTS includes additional sites within programs that directly support this movement of bindings. In order to formally define the language's operational semantics, we present an abstract syntax for MLTS and a natural semantics for its evaluation. We shall view such …
The goal of TFPIE is to gather researchers, professors, teachers, and all professionals interested in functional programming in education. This includes the teaching of functional programming, but also the application of functional programming as a tool for teaching other topics. The post-workshop review process received 13 submissions, which were vetted by the program committee, assuming scientific journal standards of publication. The six articles in this volume were selected for publication as the result of this process.
This volume constitutes the pre-proceedings of the 26th International Workshop on Functional and Logic Programming (WFLP 2018). It is formed of those papers selected by the program committee for presentation at the workshop. After discussion at the workshop, the program committee will select a number of papers to be invited for the second round of refereeing and selection for the formal proceedings.
