Towards a Categorical Semantics of Type Classes

1992 ◽  
Vol 16 (2) ◽  
pp. 127-147
Author(s):  
Barney P. Hilken ◽  
David E. Rydeheard
Keyword(s):  
Programming Languages ◽  
Functional Programming ◽  
Functional Programming Languages ◽  
Type Classes ◽  
Indexed Categories ◽  
Categorical Semantics

This is an exercise in the description of programming languages as indexed categories. Type classes have been introduced into functional programming languages to provide a uniform framework for ‘overloading’. We establish a correspondence between type classes and comprehension schemata in categories. A coherence result allows us to describe subclasses and implicit conversions between types.

scholarly journals Categorical semantics for arrows

2009 ◽  
Vol 19 (3-4) ◽  
pp. 403-438 ◽  
Author(s):  
BART JACOBS ◽  
CHRIS HEUNEN ◽  
ICHIRO HASUO
Keyword(s):  
Programming Languages ◽  
Functional Programming ◽  
Denotational Semantics ◽  
Functional Programming Languages ◽  
Categorical Semantics

AbstractArrows are an extension of the well-established notion of a monad in functional-programming languages. This paper presents several examples and constructions and develops denotational semantics of arrows as monoids in categories of bifunctors Cop × C → C. Observing similarities to monads – which are monoids in categories of endofunctors C → C – it then considers Eilenberg–Moore and Kleisli constructions for arrows. The latter yields Freyd categories, mathematically formulating the folklore claim ‘Arrows are Freyd categories.’

Explaining binomial heaps

1999 ◽  
Vol 9 (1) ◽  
pp. 93-104 ◽  
Author(s):  
RALF HINZE
Keyword(s):  
Data Structure ◽  
Programming Languages ◽  
Data Structures ◽  
Functional Programming ◽  
Priority Queue ◽  
Algorithms And Data Structures ◽  
Functional Programming Languages ◽  
Reading And Writing ◽  
Type Classes ◽  
Excellent Tool

Functional programming languages are an excellent tool for teaching algorithms and data structures. This paper explains binomial heaps, a beautiful data structure for priority queues, using the functional programming language Haskell (Peterson and Hammond, 1997). We largely follow a deductive approach: using the metaphor of a tennis tournament we show that binomial heaps arise naturally through a number of logical steps. Haskell supports the deductive style of presentation very well: new types are introduced at ease, algorithms can be expressed clearly and succinctly, and Haskell's type classes allow to capture common algorithmic patterns. The paper aims at the level of an undergraduate student who has experience in reading and writing Haskell programs, and who is familiar with the concept of a priority queue.

scholarly journals Dynamic game semantics

2020 ◽  
pp. 1-60
Author(s):  
Norihiro Yamada ◽  
Samson Abramsky
Keyword(s):  
Programming Languages ◽  
Functional Programming ◽  
Operational Semantics ◽  
Dynamic Game ◽  
Standard Interpretation ◽  
Functional Programming Languages ◽  
Game Semantics ◽  
Wide Range ◽  
Cartesian Closed Categories ◽  
Cartesian Closed

Abstract The present work achieves a mathematical, in particular syntax-independent, formulation of dynamics and intensionality of computation in terms of games and strategies. Specifically, we give game semantics of a higher-order programming language that distinguishes programmes with the same value yet different algorithms (or intensionality) and the hiding operation on strategies that precisely corresponds to the (small-step) operational semantics (or dynamics) of the language. Categorically, our games and strategies give rise to a cartesian closed bicategory, and our game semantics forms an instance of a bicategorical generalisation of the standard interpretation of functional programming languages in cartesian closed categories. This work is intended to be a step towards a mathematical foundation of intensional and dynamic aspects of logic and computation; it should be applicable to a wide range of logics and computations.

ПРИМЕНЕНИЕ МОДЕЛИ СИНТАКСИЧЕСКИ УПРАВЛЯЕМОГО ПЕРЕВОДА АРИФМЕТИЧЕСКИХ ВЫРАЖЕНИЙ В ПРОЦЕССЕ ОБУЧЕНИЯ СТУДЕНТОВ

2020 ◽  
Author(s):  
Igor Oblomov ◽  
Vyacheslav Rzhavin ◽  
Natalia Pervova ◽  
Alina Gerasimova
Keyword(s):  
Programming Languages ◽  
Programming Language ◽  
Learning Process ◽  
Functional Programming ◽  
Syntactic Analysis ◽  
Simple Arithmetic ◽  
Functional Programming Languages ◽  
Source Data ◽  
Prolog Programming ◽  
Arithmetic Expressions

В статье рассматривается модель синтаксически управляемого перевода простых арифметических выражений и ее использование в процессе обучения. Атрибутно-транслируемая грамматика предполагает перевод последовательности актов в последовательность действий, которые, в свою очередь, будут являться исходными данными для следующих этапов трансляции. Раскрываются основные моменты обучения студентов декларативному языку программирования Пролог, делается упор на обработку множества символов действия. Дальнейшие исследования предполагают разработку моделей синтаксического анализа с помощью средств императивных и функциональных языков программирования с целью получения и анализа объективных оценок эффективности полученных моделей в процессе обучения будущих специалистов.This article discusses the model of syntactically controlled translation of simple arithmetic expressions and its use in the learning process. The attribute-translated grammar involves the translation of a sequence of acts into a sequence of actions, which will be the source data for the next stages of translation. The article reveals the main points of teaching students the Prolog programming language, focuses on the processing of many action symbols. Further research involves the development of models of syntactic analysis by means of imperative and functional programming languages in order to obtain and analyze the objective estimates of the effectiveness of the obtained models in the training of future specialists.

scholarly journals On the equivalence between CMC and TIM

1994 ◽  
Vol 4 (1) ◽  
pp. 47-63 ◽  
Author(s):  
Rafael D. Lins ◽  
Simon J. Thompson ◽  
Simon Peyton Jones
Keyword(s):  
Programming Languages ◽  
Functional Programming ◽  
Design Space ◽  
Functional Programming Languages ◽  
Models Of Computation ◽  
Abstract Machines ◽  
Rewriting System

AbstractIn this paper we present an equivalence between TIM, a machine developed to implement non-strict functional programming languages, and the set of Categorical Multi-Combinators, a rewriting system developed with similar aims. These two models of computation at first appear to be quite different, but we show a direct equivalence between them, thereby adding some new structure to the ‘design-space’ of abstract machines for non-strict languages.

What is a purely functional language?

1998 ◽  
Vol 8 (1) ◽  
pp. 1-22 ◽  
Author(s):  
AMR SABRY
Keyword(s):  
Programming Languages ◽  
Functional Programming ◽  
Denotational Semantics ◽  
Functional Language ◽  
Formal Definition ◽  
Functional Programming Languages ◽  
Precise Meaning ◽  
Definition Of ◽  
Parameter Passing

Functional programming languages are informally classified into pure and impure languages. The precise meaning of this distinction has been a matter of controversy. We therefore investigate a formal definition of purity. We begin by showing that some proposed definitions which rely on confluence, soundness of the beta axiom, preservation of pure observational equivalences and independence of the order of evaluation, do not withstand close scrutiny. We propose instead a definition based on parameter-passing independence. Intuitively, the definition implies that functions are pure mappings from arguments to results; the operational decision of how to pass the arguments is irrelevant. In the context of Haskell, our definition is consistent with the fact that the traditional call-by-name denotational semantics coincides with the traditional call-by-need implementation. Furthermore, our definition is compatible with the stream-based, continuation-based and monad-based integration of computational effects in Haskell. Finally, we observe that call-by-name reasoning principles are unsound in compilers for monadic Haskell.

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