Obstacles to a totally functional programming style

"Totally functional programming" (TFP) advocates the complete replacement of symbolic representations for data by functions. TFP is motivated by observations from practice in language extensibility and functional programming. Its technical essence extends the role of "fold" functions in structuring functional programs to include methods that make comparisons on elements of data structures. The obstacles that currently prevent the immediate uptake of TFP as a style within functional programming equally indicate future research directions in the areas of theoretical foundations, supporting technical infrastructure, demonstrated practical applicability, and relationship to OOP.

Functional Programming With Relations

While programming in a relational framework has much to offer over the functional style in terms of expressiveness, computing with relations is less efficient, and more semantically troublesome. In this paper we propose a novel blend of the functional and relational styles. We identify a class of "causal relations", which inherit some of the bi-directionality properties of relations, but retain the efficiency and semantic foundations of the functional style.

Formal methods within a totally functional approach to programming

Taking functional programming to its extremities in search of simplicity still requires integration with other development (e.g. formal) methods. Induction is the key to deriving and verifying functional programs, but can be simplified through packaging proofs with functions, particularly folds, on data (structures). Totally Functional Programming avoids the complexities of interpretation by directly representing data (structures) as platonic combinators - the functions characteristic to the data. The link between the two simplifications is that platonic combinators are a kind of partially-applied fold, which means that platonic combinators inherit fold-theoretic properties, but with some apparent simplifications due to the platonic combinator representation. However, despite observable behaviour within functional programming that suggests that TFP is widely-applicable, significant work remains before TFP as such could be widely adopted.

Higher-order lazy functional slicing

Program slicing is a well known family of techniques intended to identify and isolate code fragments which depend on, or are depended upon, specific program entities. This is particularly useful in the areas of reverse engineering, program understanding, testing and software maintenance. Most slicing methods, and corresponding tools, target either the imperative or the object oriented paradigms, where program slices are computed with respect to a variable or a program statement. Taking a complementary point of view, this paper focuses on the slicing of higher-order functional programs under a lazy evaluation strategy. A prototype of a Haskell slicer, built as proof-of-concept for these ideas, is also introduced

Relational and Allegorical Semantics for Constraint Logic Programming

El cálculo de relaciones binarias fue creado por De Morgan en 1860 para ser posteriormente desarrollado en gran medida por Peirce y Schröder. Tarski, Givant, Freyd y Scedrov demostraron que las álgebras relacionales son capaces de formalizar la lógica de primer orden, la lógica de orden superior así como la teoría de conjuntos. A partir de los resultados matemáticos de Tarski y Freyd, esta tesis desarrolla semánticas denotacionales y operacionales para la programación lógica con restricciones usando el álgebra relacional como base. La idea principal es la utilización del concepto de semántica ejecutable, semánticas cuya característica principal es el que la ejecución es posible utilizando el razonamiento estándar del universo semántico, este caso, razonamiento ecuacional. En el caso de este trabajo, se muestra que las álgebras relacionales distributivas con un operador de punto fijo capturan toda la teoría y metateoría estándar de la programación lógica con restricciones incluyendo los árboles utilizados en la búsqueda de demostraciones. La mayor parte de técnicas de optimización de programas, evaluación parcial e interpretación abstracta pueden ser llevadas a cabo utilizando las semánticas aquí presentadas. La demostración de la corrección de la implementación resulta extremadamente sencilla. En la primera parte de la tesis, un programa lógico con restricciones es traducido a un conjunto de términos relacionales. La interpretación estándar en la teoría de conjuntos de dichas relaciones coincide con la semántica estándar para CLP. Las consultas contra el programa traducido son llevadas a cabo mediante la reescritura de relaciones. Para concluir la primera parte, se demuestra la corrección y equivalencia operacional de esta nueva semántica, así como se define un algoritmo de unificación mediante la reescritura de relaciones. La segunda parte de la tesis desarrolla una semántica para la programación lógica con restricciones usando la teoría de alegorías—versión categórica del álgebra de relaciones—de Freyd. Para ello, se definen dos nuevos conceptos de Categoría Regular de Lawvere y _-Alegoría, en las cuales es posible interpretar un programa lógico. La ventaja fundamental que el enfoque categórico aporta es la definición de una máquina categórica que mejora e sistema de reescritura presentado en la primera parte. Gracias al uso de relaciones tabulares, la máquina modela la ejecución eficiente sin salir de un marco estrictamente formal. Utilizando la reescritura de diagramas, se define un algoritmo para el cálculo de pullbacks en Categorías Regulares de Lawvere. Los dominios de las tabulaciones aportan información sobre la utilización de memoria y variable libres, mientras que el estado compartido queda capturado por los diagramas. La especificación de la máquina induce la derivación formal de un juego de instrucciones eficiente. El marco categórico aporta otras importantes ventajas, como la posibilidad de incorporar tipos de datos algebraicos, funciones y otras extensiones a Prolog, a la vez que se conserva el carácter 100% declarativo de nuestra semántica. ABSTRACT The calculus of binary relations was introduced by De Morgan in 1860, to be greatly developed by Peirce and Schröder, as well as many others in the twentieth century. Using different formulations of relational structures, Tarski, Givant, Freyd, and Scedrov have shown how relation algebras can provide a variable-free way of formalizing first order logic, higher order logic and set theory, among other formal systems. Building on those mathematical results, we develop denotational and operational semantics for Constraint Logic Programming using relation algebra. The idea of executable semantics plays a fundamental role in this work, both as a philosophical and technical foundation. We call a semantics executable when program execution can be carried out using the regular theory and tools that define the semantic universe. Throughout this work, the use of pure algebraic reasoning is the basis of denotational and operational results, eliminating all the classical non-equational meta-theory associated to traditional semantics for Logic Programming. All algebraic reasoning, including execution, is performed in an algebraic way, to the point we could state that the denotational semantics of a CLP program is directly executable. Techniques like optimization, partial evaluation and abstract interpretation find a natural place in our algebraic models. Other properties, like correctness of the implementation or program transformation are easy to check, as they are carried out using instances of the general equational theory. In the first part of the work, we translate Constraint Logic Programs to binary relations in a modified version of the distributive relation algebras used by Tarski. Execution is carried out by a rewriting system. We prove adequacy and operational equivalence of the semantics. In the second part of the work, the relation algebraic approach is improved by using allegory theory, a categorical version of the algebra of relations developed by Freyd and Scedrov. The use of allegories lifts the semantics to typed relations, which capture the number of logical variables used by a predicate or program state in a declarative way. A logic program is interpreted in a _-allegory, which is in turn generated from a new notion of Regular Lawvere Category. As in the untyped case, program translation coincides with program interpretation. Thus, we develop a categorical machine directly from the semantics. The machine is based on relation composition, with a pullback calculation algorithm at its core. The algorithm is defined with the help of a notion of diagram rewriting. In this operational interpretation, types represent information about memory allocation and the execution mechanism is more efficient, thanks to the faithful representation of shared state by categorical projections. We finish the work by illustrating how the categorical semantics allows the incorporation into Prolog of constructs typical of Functional Programming, like abstract data types, and strict and lazy functions.

A syntactic approach to combining functional notation, lazy evaluation, and higher-order in LP systems

Nondeterminism and partially instantiated data structures give logic programming expressive power beyond that of functional programming. However, functional programming often provides convenient syntactic features, such as having a designated implicit output argument, which allow function cali nesting and sometimes results in more compact code. Functional programming also sometimes allows a more direct encoding of lazy evaluation, with its ability to deal with infinite data structures. We present a syntactic functional extensión, used in the Ciao system, which can be implemented in ISO-standard Prolog systems and covers function application, predefined evaluable functors, functional definitions, quoting, and lazy evaluation. The extensión is also composable with higher-order features and can be combined with other extensions to ISO-Prolog such as constraints. We also highlight the features of the Ciao system which help implementation and present some data on the overhead of using lazy evaluation with respect to eager evaluation.

Functional notation and lazy evaluation in Ciao

Certain aspects of functional programming provide syntactic convenience, such as having a designated implicit output argument, which allows function cali nesting and sometimes results in more compact code. Functional programming also sometimes allows a more direct encoding of lazy evaluation, with its ability to deal with infinite data structures. We present a syntactic functional extensión of Prolog covering function application, predefined evaluable functors, functional definitions, quoting, and lazy evaluation. The extensión is also composable with higher-order features. We also highlight the Ciao features which help implementation and present some data on the overhead of using lazy evaluation with respect to eager evaluation.

A Language for Compositional Programming: A Rationale and Design

Бойко Бл. Банчев - Представена е обосновка и описание на език за програмиране в композиционен стил за опитни и учебни цели. Под “композиционен” имаме предвид функционален стил на програмиране, при който пресмятането е йерархия от композиции и прилагания на функции. Един от данновите типове на езика е този на геометричните фигури, които могат да бъдат получавани чрез прости правила за съотнасяне и така също образуват йерархични композиции. Езикът е силно повлиян от GeomLab, но по редица свойства се различава от него значително. Статията разглежда основните черти на езика; подробното му описание и фигурноконструктивните му възможности ще бъдат представени в съпътстваща публикация.

JSONYA/FN: Functional Computation in JSON

Functional programming has a lot to offer to the developers of global Internet-centric applications, but is often applicable only to a small part of the system or requires major architectural changes. The data model used for functional computation is often simply considered a consequence of the chosen programming style, although inappropriate choice of such model can make integration with imperative parts much harder. In this paper we do the opposite: we start from a data model based on JSON and then derive the functional approach from it. We outline the identified principles and present Jsonya/fn — a low-level functional language that is defined in and operates with the selected data model. We use several Jsonya/fn implementations and the architecture of a recently developed application to show that our approach can improve interoperability and can achieve additional reuse of representations and operations at relatively low cost. ACM Computing Classification System (1998): D.3.2, D.3.4.

Compositional Geometry and Programming

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2014

Program slicing by calculation

Program slicing is a well known family of techniques used to identify code fragments which depend on or are depended upon specific program entities. They are particularly useful in the areas of reverse engineering, program understanding, testing and software maintenance. Most slicing methods, usually oriented towards the imperative or object paradigms, are based on some sort of graph structure representing program dependencies. Slicing techniques amount, therefore, to (sophisticated) graph transversal algorithms. This paper proposes a completely different approach to the slicing problem for functional programs. Instead of extracting program information to build an underlying dependencies’ structure, we resort to standard program calculation strategies, based on the so-called Bird-Meertens formalism. The slicing criterion is specified either as a projection or a hiding function which, once composed with the original program, leads to the identification of the intended slice. Going through a number of examples, the paper suggests this approach may be an interesting, even if not completely general, alternative to slicing functional programs

A logical foundation for session-based concurrent computation

Linear logic has long been heralded for its potential of providing a logical basis for concurrency. While over the years many research attempts were made in this regard, a Curry-Howard correspondence between linear logic and concurrent computation was only found recently, bridging the proof theory of linear logic and session-typed process calculus. Building upon this work, we have developed a theory of intuitionistic linear logic as a logical foundation for session-based concurrent computation, exploring several concurrency related phenomena such as value-dependent session types and polymorphic sessions within our logical framework in an arguably clean and elegant way, establishing with relative ease strong typing guarantees due to the logical basis, which ensure the fundamental properties of type preservation and global progress, entailing the absence of deadlocks in communication. We develop a general purpose concurrent programming language based on the logical interpretation, combining functional programming with a concurrent, session-based process layer through the form of a contextual monad, preserving our strong typing guarantees of type preservation and deadlock-freedom in the presence of general recursion and higher-order process communication. We introduce a notion of linear logical relations for session typed concurrent processes, developing an arguably uniform technique for reasoning about sophisticated properties of session-based concurrent computation such as termination or equivalence based on our logical approach, further supporting our goal of establishing intuitionistic linear logic as a logical foundation for sessionbased concurrency.