scholarly journals A Semantic Framework to Debug Parallel Lazy Functional Languages

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 864
Author(s):  
Alberto de la Encina ◽  
Mercedes Hidalgo-Herrero ◽  
Luis Llana ◽  
Fernando Rubio
Keyword(s):  
Operational Semantics ◽  
Higher Order ◽  
Functional Languages ◽  
Semantic Framework ◽  
Use Of Resources ◽  
Parallel Languages ◽  
Work Done ◽  
Theoretical Foundations ◽  
Parallel Extension

It is not easy to debug lazy functional programs. The reason is that laziness and higher-order complicates basic debugging strategies. Although there exist several debuggers for sequential lazy languages, dealing with parallel languages is much harder. In this case, it is important to implement debugging platforms for parallel extensions, but it is also important to provide theoretical foundations to simplify the task of understanding the debugging process. In this work, we deal with the debugging process in two parallel languages that extend the lazy language Haskell. In particular, we provide an operational semantics that allows us to reason about our parallel extension of the sequential debugger Hood. In addition, we show how we can use it to analyze the amount of speculative work done by the processes, so that it can be used to optimize their use of resources.

Conceptual and Theoretical Foundations of Social Capital

2009 ◽  
pp. 18-42
Author(s):  
Ben Kei Daniel
Keyword(s):  
Social Sciences ◽  
Social Capital ◽  
Theoretical Framework ◽  
Analytical Tool ◽  
The Social ◽  
Scientific Legitimacy ◽  
Basic Understanding ◽  
Work Done ◽  
Conceptual Foundations ◽  
Theoretical Foundations

Social capital is a complex multifaceted and litigious theory, discussed in the Social Sciences and the Humanities. It is a theory increasingly researchers questioned its scientific legitimacy and yet paradoxically many other researchers continuously use it as a conceptual and theoretical framework to explain the structural and functional operations of communities. This Chapter discusses work done on the theory. It covers some of the theoretical controversy with a goal of aligning its conceptualization and distinguishing it from other types of capitals. The Chapter is organized first the basic theoretical and conceptual foundations of social capital are described. The aim is to present the reader with a basic understanding of what constitutes social capital, by opening discussion about various forms of capital(s)—as discussed in the disciplines of Economics and Sociology. Second, the Chapter discusses the origin of the theory as well as the work of key scholars who have contributed to the development of the theory. Furthermore, in order to identify the strengths and the weaknesses of the theory, the Chapter provides the reader with analysis of benefits and shortcomings of social capital both as a theoretical and analytical tool for studying communities.

scholarly journals Set constraints for destructive array update optimization

2001 ◽  
Vol 11 (3) ◽  
pp. 319-346 ◽  
Author(s):  
MITCHELL WAND ◽  
WILLIAM D. CLINGER
Keyword(s):  
Polynomial Time ◽  
Program Transformation ◽  
Operational Semantics ◽  
Functional Languages ◽  
Small Step ◽  
Set Constraints ◽  
Correct Program

Destructive array update optimization is critical for writing scientific codes in functional languages. We present set constraints for an interprocedural update optimization that runs in polynomial time. This is a multi-pass optimization, involving interprocedural flow analyses for aliasing and liveness. We characterize and prove the soundness of these analyses using small-step operational semantics. We also prove that any sound liveness analysis induces a correct program transformation.

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.

Mechanizing proofs with logical relations – Kripke-style

2018 ◽  
Vol 28 (9) ◽  
pp. 1606-1638 ◽  
Author(s):  
ANDREW CAVE ◽  
BRIGITTE PIENTKA
Keyword(s):  
Case Studies ◽  
Operational Semantics ◽  
Lambda Calculus ◽  
Equational Theory ◽  
Higher Order ◽  
Abstract Syntax ◽  
Completeness Proof ◽  
Typed Lambda Calculus ◽  
Contextual Equivalence ◽  
The Right

Proofs with logical relations play a key role to establish rich properties such as normalization or contextual equivalence. They are also challenging to mechanize. In this paper, we describe two case studies using the proof environmentBeluga: First, we explain the mechanization of the weak normalization proof for the simply typed lambda-calculus; second, we outline how to mechanize the completeness proof of algorithmic equality for simply typed lambda-terms where we reason about logically equivalent terms. The development of these proofs inBelugarelies on three key ingredients: (1) we encode lambda-terms together with their typing rules, operational semantics, algorithmic and declarative equality using higher order abstract syntax (HOAS) thereby avoiding the need to manipulate and deal with binders, renaming and substitutions, (2) we take advantage ofBeluga's support for representing derivations that depend on assumptions and first-class contexts to directly state inductive properties such as logical relations and inductive proofs, (3) we exploitBeluga's rich equational theory for simultaneous substitutions; as a consequence, users do not need to establish and subsequently use substitution properties, and proofs are not cluttered with references to them. We believe these examples demonstrate thatBelugaprovides the right level of abstractions and primitives to mechanize challenging proofs using HOAS encodings. It also may serve as a valuable benchmark for other proof environments.

scholarly journals HOPLA--A Higher-Order Process Language

2002 ◽  
Vol 9 (49) ◽  
Author(s):  
Mikkel Nygaard ◽  
Glynn Winskel
Keyword(s):  
Operational Semantics ◽  
Lambda Calculus ◽  
Expressive Power ◽  
Higher Order ◽  
Domain Theory ◽  
Order Process ◽  
Encode Process ◽  
Mobile Ambients ◽  
Computation Path ◽  
Congruence Properties

A small but powerful language for higher-order nondeterministic processes is introduced. Its roots in a linear domain theory for concurrency are sketched though for the most part it lends itself to a more operational account. The language can be viewed as an extension of the lambda calculus with a ``prefixed sum'', in which types express the form of computation path of which a process is capable. Its operational semantics, bisimulation, congruence properties and expressive power are explored; in particular, it is shown how it can directly encode process languages such as CCS, CCS with process passing, and mobile ambients with public names.

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