scholarly journals Types for Complexity of Parallel Computation in Pi-Calculus

2021 ◽  
pp. 59-86
Author(s):  
Patrick Baillot ◽  
Alexis Ghyselen
Keyword(s):  
Programming Languages ◽  
Parallel Computation ◽  
Time Complexity ◽  
Operational Semantics ◽  
Computation Time ◽  
Type Systems ◽  
Complexity Bound ◽  
Functional Programming Languages ◽  
Control Programs ◽  
Pi Calculus

AbstractType systems as a technique to analyse or control programs have been extensively studied for functional programming languages. In particular some systems allow to extract from a typing derivation a complexity bound on the program. We explore how to extend such results to parallel complexity in the setting of the pi-calculus, considered as a communication-based model for parallel computation. Two notions of time complexity are given: the total computation time without parallelism (the work) and the computation time under maximal parallelism (the span). We define operational semantics to capture those two notions, and present two type systems from which one can extract a complexity bound on a process. The type systems are inspired both by size types and by input/output types, with additional temporal information about communications.

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.

Principal signatures for higher-order program modules

1994 ◽  
Vol 4 (3) ◽  
pp. 285-335 ◽  
Author(s):  
Mads Tofte
Keyword(s):  
Programming Languages ◽  
Functional Programming ◽  
Operational Semantics ◽  
Higher Order ◽  
Principal Type ◽  
Functional Programming Languages ◽  
Standard Ml ◽  
Static Semantics ◽  
Program Modules

AbstractIn this paper we present a language for programming with higher-order modules. The language HML is based on Standard ML in that it provides structures, signatures and functors. In HML, functors can be declared inside structures and specified inside signatures; this is not possible in Standard ML. We present an operational semantics for the static semantics of HML signature expressions, with particular emphasis on the handling of sharing. As a justification for the semantics, we prove a theorem about the existence of principal signatures. This result is closely related to the existence of principal type schemes for functional programming languages with polymorphism.

Linearization of the lambda-calculus and its relation with intersection type systems

2004 ◽  
Vol 14 (5) ◽  
pp. 519-546 ◽  
Author(s):  
MÁRIO FLORIDO ◽  
LUÍS DAMAS
Keyword(s):  
Programming Languages ◽  
Functional Programming ◽  
Type System ◽  
Lambda Calculus ◽  
Type Systems ◽  
Functional Programming Languages

In this paper we present a notion of expansion of a term in the lambda-calculus which transforms terms into linear terms. This transformation replaces each occurrence of a variable in the original term by a fresh variable taking into account non-trivial implications in the structure of the term caused by these simple replacements. We prove that the class of terms which can be expanded is the same of terms typable in an Intersection Type System, i.e. the strongly normalizable terms. We then show that expansion is preserved by weak-head reduction, the reduction considered by functional programming languages.

A formalism for the specification of essentially-algebraic structures in 2-categories

1992 ◽  
Vol 2 (1) ◽  
pp. 1-28 ◽  
Author(s):  
A. J. Power ◽  
Charles Wells
Keyword(s):  
Programming Languages ◽  
Functional Programming ◽  
Operational Semantics ◽  
Higher Order ◽  
Two Dimensional ◽  
Functional Programming Languages ◽  
One Dimensional ◽  
Special Cases ◽  
Rewrite Rules ◽  
Definition Of

A type of higher-order two-dimensional sketch is defined which has models in suitable 2-categories. It has as special cases the ordinary sketches of Ehresmann and certain previously defined generalizations of one-dimensional sketches. These sketches allow the specification of constructions in 2-categories such as weighted limits, as well as higher-order constructions such as exponential objects and subobject classifiers, that cannot be sketched by limits and colimits. These sketches are designed to be the basis of a category-based methodology for the description of functional programming languages, complete with rewrite rules giving the operational semantics, that is independent of the usual specification methods based on formal languages and symbolic logic. A definition of ‘path grammar’, generalizing the usual notion of grammar, is given as a step towards this goal.

Uniqueness typing for functional languages with graph rewriting semantics

1996 ◽  
Vol 6 (6) ◽  
pp. 579-612 ◽  
Author(s):  
Erik Barendsen ◽  
Sjaak Smetsers
Keyword(s):  
Programming Languages ◽  
Functional Programming ◽  
Natural Deduction ◽  
Natural Extension ◽  
Type Systems ◽  
Higher Order ◽  
Functional Languages ◽  
Conventional System ◽  
Functional Programming Languages ◽  
Graph Rewriting

We present two type systems for term graph rewriting: conventional typing and (polymorphic) uniqueness typing. The latter is introduced as a natural extension of simple algebraic and higher-order uniqueness typing. The systems are given in natural deduction style using an inductive syntax of graph denotations with familiar constructs such as let and case.The conventional system resembles traditional Curry-style typing systems in functional programming languages. Uniqueness typing extends this with reference count information. In both type systems, typing is preserved during evaluation, and types can be determined effectively. Moreover, with respect to a graph rewriting semantics, both type systems turn out to be sound.

Production management of standardized products using electronic process automation — single window

2020 ◽  
Keyword(s):  
Programming Languages ◽  
Production Management ◽  
Work Place ◽  
Web Interface ◽  
Process Automation ◽  
Control Programs ◽  
New Information ◽  
Shift Report ◽  
Planning Problems ◽  
Registration Card

A non-standard approach to solving the activation planning problems of the standardized products in a multinomenclature workshop is considered. This approach is caused by writing control programs and developing new information systems without changing previously developed workstations, which were created by using an outdated programming languages, in particular Clipper applications. The concept of creating a single information space — a set of databases and software tools integrated at the software level is proposed. Keywords standardized product; normal; software; web interface; single window; automatic work place; production task; shift task; order-shift report; control and registration card

Real-time MLton: A Standard ML runtime for real-time functional programs

2021 ◽  
Vol 31 ◽  
Author(s):  
BHARGAV SHIVKUMAR ◽  
JEFFREY MURPHY ◽  
LUKASZ ZIAREK
Keyword(s):  
Programming Languages ◽  
Real Time ◽  
Concurrency Control ◽  
General Purpose ◽  
Functional Languages ◽  
Control Mechanisms ◽  
Real Time Systems ◽  
Functional Programming Languages ◽  
Standard Ml ◽  
Time Systems

Abstract There is a growing interest in leveraging functional programming languages in real-time and embedded contexts. Functional languages are appealing as many are strictly typed, amenable to formal methods, have limited mutation, and have simple but powerful concurrency control mechanisms. Although there have been many recent proposals for specialized domain-specific languages for embedded and real-time systems, there has been relatively little progress on adapting more general purpose functional languages for programming embedded and real-time systems. In this paper, we present our current work on leveraging Standard ML (SML) in the embedded and real-time domains. Specifically, we detail our experiences in modifying MLton, a whole-program optimizing compiler for SML, for use in such contexts. We focus primarily on the language runtime, reworking the threading subsystem, object model, and garbage collector. We provide preliminary results over a radar-based aircraft collision detector ported to SML.

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