Containers, monads and induction recursion

2014 ◽  
Vol 26 (1) ◽  
pp. 89-113 ◽  
Author(s):  
NEIL GHANI ◽  
PETER HANCOCK
Keyword(s):  
Programming Language ◽  
Algebraic Structure ◽  
Functional Programming ◽  
Type System ◽  
Pivotal Role ◽  
A Value ◽  
Structural Recursion ◽  
Definition Of ◽  
High Level ◽  
Original Type

Induction recursion offers the possibility of a clean, simple and yet powerful meta-language for the type system of a dependently typed programming language. At its crux, induction recursion allows us to define a universe, that is a setUofcodesand a decoding functionT : U → Dwhich assigns to every codeu : U, a valueT, uof some typeD, e.g.the large type Set of small types or sets. The name induction recursion refers to the build-up of codes inUusing inductive clauses, simultaneously with the definition of the functionT, by structural recursion on codes.Our contribution is to (i) bring out explicitly algebraic structure which is less visible in the original type-theoretic presentation – in particular showing how containers and monads play a pivotal role within induction recursion; and (ii) use these structures to present a clean and high level definition of induction recursion suitable for use in functional programming.

Modelling general recursion in type theory

2005 ◽  
Vol 15 (4) ◽  
pp. 671-708 ◽  
Author(s):  
ANA BOVE ◽  
VENANZIO CAPRETTA
Keyword(s):  
Programming Language ◽  
Type Theory ◽  
Functional Programming ◽  
Recursive Algorithm ◽  
Recursive Algorithms ◽  
Constructive Type Theory ◽  
Structural Recursion ◽  
Constructive Type ◽  
Definition Of ◽  
Theoretic Version

Constructive type theory is an expressive programming language in which both algorithms and proofs can be represented. A limitation of constructive type theory as a programming language is that only terminating programs can be defined in it. Hence, general recursive algorithms have no direct formalisation in type theory since they contain recursive calls that satisfy no syntactic condition guaranteeing termination. In this work, we present a method to formalise general recursive algorithms in type theory. Given a general recursive algorithm, our method is to define an inductive special-purpose accessibility predicate that characterises the inputs on which the algorithm terminates. The type-theoretic version of the algorithm is then defined by structural recursion on the proof that the input values satisfy this predicate. The method separates the computational and logical parts of the definitions and thus the resulting type-theoretic algorithms are clear, compact and easy to understand. They are as simple as their equivalents in a functional programming language, where there is no restriction on recursive calls. Here, we give a formal definition of the method and discuss its power and its limitations.

scholarly journals Component J: A component-based programming language with dynamic reconfiguration

2008 ◽  
Vol 5 (2) ◽  
pp. 63-86 ◽  
Author(s):  
João Seco ◽  
Ricardo Silva ◽  
Margarida Piriquito
Keyword(s):  
Structural Properties ◽  
Programming Language ◽  
Type System ◽  
Dynamic Reconfiguration ◽  
Language Design ◽  
Core Component ◽  
Language Level ◽  
Definition Of ◽  
High Level ◽  
Composition Operations

This paper describes an evolution of the ComponentJ programming language, a component-based Java-like programming language where composition is the chosen structuring mechanism. ComponentJ constructs allow for the high-level specification of component structures, which are the basis for the definition of compound objects. In this paper we present a new language design for ComponentJ which is more flexible and also allows the dynamic reconfiguration of objects. The manipulation of components and composition operations at the programming language level allows for the compile time verification, by a type system, of safety structural properties of ComponentJ programs. This work is based on earlier fundamental results where the main concepts are presented and justified in the form of a core component calculus. .

scholarly journals Learners Programming Language a Helping System for Introductory Programming Courses

2016 ◽  
Vol 35 (3) ◽  
pp. 347-358
Author(s):  
Muhammad Shumail Naveed ◽  
Muhammad Sarim ◽  
Kamran Ahsan
Keyword(s):  
Programming Languages ◽  
Programming Language ◽  
Retention Rate ◽  
Introductory Programming ◽  
Source Program ◽  
Definition Of ◽  
High Level ◽  
Novice Students ◽  
Introductory Programming Courses ◽  
Programming Courses

Programming is the core of computer science and due to this momentousness a special care is taken in designing the curriculum of programming courses. A substantial work has been conducted on the definition of programming courses, yet the introductory programming courses are still facing high attrition, low retention and lack of motivation. This paper introduced a tiny pre-programming language called LPL (Learners Programming Language) as a ZPL (Zeroth Programming Language) to illuminate novice students about elementary concepts of introductory programming before introducing the first imperative programming course. The overall objective and design philosophy of LPL is based on a hypothesis that the soft introduction of a simple and paradigm specific textual programming can increase the motivation level of novice students and reduce the congenital complexities and hardness of the first programming course and eventually improve the retention rate and may be fruitful in reducing the dropout/failure level. LPL also generates the equivalent high level programs from user source program and eventually very fruitful in understanding the syntax of introductory programming languages. To overcome the inherent complexities of unusual and rigid syntax of introductory programming languages, the LPL provide elementary programming concepts in the form of algorithmic and plain natural language based computational statements. The initial results obtained after the introduction of LPL are very encouraging in motivating novice students and improving the retention rate.

Migrating JAVA to Mobile Platforms through HAXE

2016 ◽  
pp. 240-268 ◽  
Author(s):  
Pablo Nicolás Díaz Bilotto ◽  
Liliana Favre
Keyword(s):  
Programming Language ◽  
Mobile Applications ◽  
Software Evolution ◽  
Wide Spectrum ◽  
The Other ◽  
Model Transformations ◽  
Mobile Platforms ◽  
Model Driven ◽  
Definition Of ◽  
High Level

Software developers face several challenges in deploying mobile applications. One of them is the high cost and technical complexity of targeting development to a wide spectrum of platforms. The chapter proposes to combine techniques based on MDA (Model Driven Architecture) with the HaXe language. The outstanding ideas behind MDA are separating the specification of the system functionality from its implementation on specific platforms, managing the software evolution, increasing the degree of automation of model transformations, and achieving interoperability with multiple platforms. On the other hand, HaXe is a very modern high level programming language that allows us to generate mobile applications that target all major mobile platforms. The main contributions of this chapter are the definition of a HaXe metamodel, the specification of a model-to-model transformation between Java and HaXe and, the definition of an MDA migration process from Java to mobile platforms.

Idris, a general-purpose dependently typed programming language: Design and implementation

2013 ◽  
Vol 23 (5) ◽  
pp. 552-593 ◽  
Author(s):  
EDWIN BRADY
Keyword(s):  
Programming Language ◽  
Type Theory ◽  
Functional Programming ◽  
General Purpose ◽  
High Level Language ◽  
Type Checking ◽  
Programming Language Design ◽  
Implicit Arguments ◽  
Type Classes ◽  
High Level

AbstractMany components of a dependently typed programming language are by now well understood, for example, the underlying type theory, type checking, unification and evaluation. How to combine these components into a realistic and usable high-level language is, however, folklore, discovered anew by successive language implementors. In this paper, I describe the implementation ofIdris, a new dependently typed functional programming language.Idrisis intended to be ageneral-purposeprogramming language and as such provides high-level concepts such as implicit syntax, type classes anddonotation. I describe the high-level language and the underlying type theory, and present a tactic-based method forelaboratingconcrete high-level syntax with implicit arguments and type classes into a fully explicit type theory. Furthermore, I show how this method facilitates the implementation of new high-level language constructs.

scholarly journals The ins and outs of Clean I/O

1995 ◽  
Vol 5 (1) ◽  
pp. 81-110 ◽  
Author(s):  
Peter Achten ◽  
Rinus Plasmeijer
Keyword(s):  
Programming Languages ◽  
Programming Language ◽  
Functional Programming ◽  
Data Types ◽  
Spreadsheet Program ◽  
Functional Programming Languages ◽  
Hard Time ◽  
Functional Programming Language ◽  
Algebraic Data Types ◽  
High Level

AbstractFunctional programming languages have banned assignment because of its undesirable properties. The reward of this rigorous decision is that functional programming languages are side-effect free. There is another side to the coin: because assignment plays a crucial role in Input/Output (I/O), functional languages have a hard time dealing with I/O. Functional programming languages have therefore often been stigmatised as inferior to imperative programming languages because they cannot deal with I/O very well. In this paper, we show that I/O can be incorporated in a functional programming language without loss of any of the generally accepted advantages of functional programming languages. This discussion is supported by an extensive account of the I/O system offered by the lazy, purely functional programming language Clean. Two aspects that are paramount in its I/O system make the approach novel with respect to other approaches. These aspects are the technique of explicit multiple environment passing, and the Event I/O framework to program Graphical User I/O in a highly structured and high-level way. Clean file I/O is as powerful and flexible as it is in common imperative languages (one can read, write, and seek directly in a file). Clean Event I/O provides programmers with a high-level framework to specify complex Graphical User I/O. It has been used to write applications such as a window-based text editor, an object based drawing program, a relational database, and a spreadsheet program. These graphical interactive programs are completely machine independent, but still obey the look-and-feel of the concrete window environment being used. The specifications are completely functional and make extensive use of uniqueness typing, higher-order functions, and algebraic data types. Efficient implementations are present on the Macintosh, Sun (X Windows under Open Look) and PC (OS/2).

scholarly journals Type stability in Julia: avoiding performance pathologies in JIT compilation

2021 ◽  
Vol 5 (OOPSLA) ◽  
pp. 1-26
Author(s):  
Artem Pelenitsyn ◽  
Julia Belyakova ◽  
Benjamin Chung ◽  
Ross Tate ◽  
Jan Vitek
Keyword(s):  
Programming Language ◽  
Corpus Analysis ◽  
Formal Definition ◽  
Compiler Optimizations ◽  
Definition Of ◽  
High Level ◽  
Jit Compilation

As a scientific programming language, Julia strives for performance but also provides high-level productivity features. To avoid performance pathologies, Julia users are expected to adhere to a coding discipline that enables so-called type stability. Informally, a function is type stable if the type of the output depends only on the types of the inputs, not their values. This paper provides a formal definition of type stability as well as a stronger property of type groundedness, shows that groundedness enables compiler optimizations, and proves the compiler correct. We also perform a corpus analysis to uncover how these type-related properties manifest in practice.

scholarly journals Implementing type theory in higher order constraint logic programming

2019 ◽  
Vol 29 (8) ◽  
pp. 1125-1150
Author(s):  
FERRUCCIO GUIDI ◽  
CLAUDIO SACERDOTI COEN ◽  
ENRICO TASSI
Keyword(s):  
Programming Languages ◽  
Programming Language ◽  
Type System ◽  
Theorem Prover ◽  
Type Checking ◽  
Language Extension ◽  
Order Constraint ◽  
Simple Implementation ◽  
Calculus Of Inductive Constructions ◽  
High Level

In this paper, we are interested in high-level programming languages to implement the core components of an interactive theorem prover for a dependently typed language: the kernel – responsible for type-checking closed terms – and the elaborator – that manipulates open terms, that is terms containing unresolved unification variables.In this paper, we confirm that λProlog, the language developed by Miller and Nadathur since the 80s, is extremely suitable for implementing the kernel. Indeed, we easily obtain a type checker for the Calculus of Inductive Constructions (CIC). Even more, we do so in an incremental way by escalating a checker for a pure type system to the full CIC.We then turn our attention to the elaborator with the objective to obtain a simple implementation thanks to the features of the programming language. In particular, we want to use λProlog’s unification variables to model the object language ones. In this way, scope checking, carrying of assignments and occur checking are handled by the programming language.We observe that the eager generative semantics inherited from Prolog clashes with this plan. We propose an extension to λProlog that allows to control the generative semantics, suspend goals over flexible terms turning them into constraints, and finally manipulate these constraints at the meta-meta level via constraint handling rules.We implement the proposed language extension in the Embedded Lambda Prolog Interpreter system and we discuss how it can be used to extend the kernel into an elaborator for CIC.

scholarly journals Acute: High-level programming language design for distributed computation

2007 ◽  
Vol 17 (4-5) ◽  
pp. 547-612 ◽  
Author(s):  
PETER SEWELL ◽  
JAMES J. LEIFER ◽  
KEITH WANSBROUGH ◽  
FRANCESCO ZAPPA NARDELLI ◽  
MAIR ALLEN-WILLIAMS ◽  
...  
Keyword(s):  
Programming Language ◽  
Distributed System ◽  
Operational Semantics ◽  
Module Structure ◽  
Distributed Programming ◽  
Type Safety ◽  
Programming Language Design ◽  
Local Resources ◽  
Definition Of ◽  
High Level

AbstractExisting languages provide good support for typeful programming of stand-alone programs. In a distributed system, however, there may be interaction between multiple instances of many distinct programs, sharing some (but not necessarily all) of their module structure, and with some instances rebuilt with new versions of certain modules as time goes on. In this paper, we discuss programming-language support for such systems, focussing on their typing and naming issues. We describe an experimental language, Acute, which extends an ML core to support distributed development, deployment, and execution, allowing type-safe interaction between separately built programs. The main features are (1) type-safe marshalling of arbitrary values; (2) type names that are generated (freshly and by hashing) to ensure that type equality tests suffice to protect the invariants of abstract types, across the entire distributed system; (3) expression-level names generated to ensure that name equality tests suffice for type safety of associated values, for example, values carried on named channels; (4) controlled dynamic rebinding of marshalled values to local resources; and (5) thunkification of threads and mutexes to support computation mobility. These features are a large part of what is needed for typeful distributed programming. They are a relatively lightweight extension of ML, should be efficiently implementable, and are expressive enough to enable a wide variety of distributed infrastructure layers to be written as simple library code above the byte-string network and persistent store APIs. This disentangles the language run-time from communication intricacies. This paper highlights the main design choices in Acute. It is supported by a full language definition (of typing, compilation, and operational semantics), by a prototype implementation, and by example distribution libraries.

Implementing a normalizer using sized heterogeneous types

2009 ◽  
Vol 19 (3-4) ◽  
pp. 287-310 ◽  
Author(s):  
ANDREAS ABEL
Keyword(s):  
Normal Form ◽  
Programming Language ◽  
Functional Programming ◽  
Type System ◽  
Free Variable ◽  
Functional Programming Language ◽  
Inductive Types

AbstractIn the simply typed λ-calculus, a hereditary substitution replaces a free variable in a normal formrby another normal formsof typea, removing freshly created redexes on the fly. It can be defined by lexicographic induction onaandr, thus giving rise to a structurally recursive normalizer for the simply typed λ-calculus. We implement hereditary substitutions in a functional programming language with sized heterogeneous inductive types$\Fhat$, arriving at an interpreter whose termination can be tracked by the type system of its host programming language.

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