scholarly journals Linear Dependent Type Theory for Quantum Programming Languages

2020 ◽  
Author(s):  
Peng Fu ◽  
Kohei Kishida ◽  
Peter Selinger
Keyword(s):  
Programming Languages ◽  
Type Theory ◽  
Dependent Type Theory ◽  
Quantum Programming Languages ◽  
Quantum Programming ◽  
Dependent Type

Introduction to the Special Issue on Dependent Type Theory Meets Practical Programming

2004 ◽  
Vol 14 (1) ◽  
pp. 1-2
Author(s):  
GILLES BARTHE ◽  
PETER DYBJEN ◽  
PETER THIEMANN
Keyword(s):  
Programming Languages ◽  
Type Theory ◽  
Type System ◽  
Type Systems ◽  
Special Issue ◽  
Dependent Type Theory ◽  
Dependent Type

Modern programming languages rely on advanced type systems that detect errors at compile-time. While the benefits of type systems have long been recognized, there are some areas where the standard systems in programming languages are not expressive enough. Language designers usually trade expressiveness for decidability of the type system. Some interesting programs will always be rejected (despite their semantical soundness) or be assigned uninformative types.

scholarly journals Denotational semantics of recursive types in synthetic guarded domain theory

2018 ◽  
Vol 29 (3) ◽  
pp. 465-510 ◽  
Author(s):  
RASMUS E. MØGELBERG ◽  
MARCO PAVIOTTI
Keyword(s):  
Programming Languages ◽  
Type Theory ◽  
Operational Semantics ◽  
Lambda Calculus ◽  
Denotational Semantics ◽  
Domain Theory ◽  
Logical Relation ◽  
Dependent Type Theory ◽  
Semantics Of Programming Languages ◽  
Dependent Type

Just like any other branch of mathematics, denotational semantics of programming languages should be formalised in type theory, but adapting traditional domain theoretic semantics, as originally formulated in classical set theory to type theory has proven challenging. This paper is part of a project on formulating denotational semantics in type theories with guarded recursion. This should have the benefit of not only giving simpler semantics and proofs of properties such as adequacy, but also hopefully in the future to scale to languages with advanced features, such as general references, outside the reach of traditional domain theoretic techniques.Working inGuarded Dependent Type Theory(GDTT), we develop denotational semantics for Fixed Point Calculus (FPC), the simply typed lambda calculus extended with recursive types, modelling the recursive types of FPC using the guarded recursive types ofGDTT. We prove soundness and computational adequacy of the model inGDTTusing a logical relation between syntax and semantics constructed also using guarded recursive types. The denotational semantics is intensional in the sense that it counts the number of unfold-fold reductions needed to compute the value of a term, but we construct a relation relating the denotations of extensionally equal terms, i.e., pairs of terms that compute the same value in a different number of steps. Finally, we show how the denotational semantics of terms can be executed inside type theory and prove that executing the denotation of a boolean term computes the same value as the operational semantics of FPC.

scholarly journals MiniAgda: Integrating Sized and Dependent Types

10.29007/322q ◽  
2018 ◽  
Author(s):  
Andreas Abel
Keyword(s):  
Programming Languages ◽  
Type Theory ◽  
Type System ◽  
Proof Assistants ◽  
Parametric Function ◽  
Dependent Type Theory ◽  
Essential Idea ◽  
Core Language ◽  
Higher Order Functions ◽  
Dependent Type

Sized types are a modular and theoretically well-understood tool for checking termination of recursive and productivity of corecursive definitions. The essential idea is to track structural descent and guardedness in the type system to make termination checking robust and suitable for strong abstractions like higher-order functions and polymorphism.To study the application of sized types to proof assistants and programming languages based on dependent type theory, we have implemented a core language with explicit handling of sizes. New considerations were necessary to soundly integrate sized types with dependencies and pattern matching, which was made possible by modern concepts such as inaccessible patterns and parametric function spaces.

Special issue on Dependent Type Theory Meets Programming Practice CALL FOR PAPERS

2001 ◽  
Vol 11 (4) ◽  
pp. 437-437
Author(s):  
Gilles Barthe ◽  
Peter Dybjer ◽  
Peter Thiemann
Keyword(s):  
Programming Languages ◽  
Type Theory ◽  
Type System ◽  
Type Systems ◽  
Point Of View ◽  
Theoretical Point ◽  
Special Issue ◽  
Dependent Type Theory ◽  
The Impact ◽  
Dependent Type

Modern programming languages rely on advanced type systems that detect errors at compile-time. While the benefits of type systems have long been recognized, there are some areas where the standard systems in programming languages are not expressive enough. Language designers usually trade expressiveness for decidability of the type system. Some interesting programs will always be rejected (despite their semantical soundness) or be assigned uninformative types.There are several remedies to this situation. Dependent type systems, which allow the formation of types that explicitly depend on other types or values, are one of the most promising approaches. These systems are well-investigated from a theoretical point of view by logicians and type theorists. For example, dependent types are used in proof assistants to implement various logics and there are sophisticated proof editors for developing programs in a dependently typed language.To the present day, the impact of these developments on practical programming has been small, partially because of the level of sophistication of these systems and of their type checkers. Only recently, there have been efforts to integrate dependent systems into intermediate languages in compilers and programming languages. Additional uses have been identified in high-profile applications such as mobile code security, where terms of a dependently typed lambda calculus to encode safety proofs.A special issue of the Journal of Functional Programming will be devoted to the interplay between dependent type theory and programming practice. We welcome technical contributions in the field, as well as position papers that:[bull ] make researchers in programming languages aware of new developments and research directions on the theory side;[bull ] point out to theorists practical uses of advanced type systems and urge them to address theoretical problems arising in emerging applications.Authors who are concerned about the appropriateness of a topic are welcome to contact the guest editors. Manuscripts should be unpublished works and not submitted elsewhere. Revised and enhanced versions of papers published in conference proceedings that have not appeared in archival journals are eligible for submission. All submissions will be reviewed according to the usual standards of scholarship and originality.Submissions should be sent to Gilles Barthe ([email protected]), with a copy to Nasreen Ahmad ([email protected]). Submitted articles should be sent in postscript format, preferably gzipped and uuencoded. In addition, please send, as plain text, title, abstract and contact information.The submission deadline is December 1st, 2001.

scholarly journals A relationally parametric model of dependent type theory

2014 ◽  
Vol 49 (1) ◽  
pp. 503-515 ◽  
Author(s):  
Robert Atkey ◽  
Neil Ghani ◽  
Patricia Johann
Keyword(s):  
Type Theory ◽  
Parametric Model ◽  
Dependent Type Theory ◽  
Dependent Type

scholarly journals Implementing a modal dependent type theory

2019 ◽  
Vol 3 (ICFP) ◽  
pp. 1-29 ◽  
Author(s):  
Daniel Gratzer ◽  
Jonathan Sterling ◽  
Lars Birkedal
Keyword(s):  
Type Theory ◽  
Dependent Type Theory ◽  
Dependent Type

scholarly journals Guarded Dependent Type Theory with Coinductive Types

2016 ◽  
pp. 20-35 ◽  
Author(s):  
Aleš Bizjak ◽  
Hans Bugge Grathwohl ◽  
Ranald Clouston ◽  
Rasmus E. Møgelberg ◽  
Lars Birkedal
Keyword(s):  
Type Theory ◽  
Dependent Type Theory ◽  
Dependent Type

Quingo: A Programming Framework for Heterogeneous Quantum-Classical Computing with NISQ Features

2021 ◽  
Vol 2 (4) ◽  
pp. 1-37
Author(s):  
X. Fu ◽  
Jintao Yu ◽  
Xing Su ◽  
Hanru Jiang ◽  
Hua Wu ◽  
...  
Keyword(s):  
Programming Languages ◽  
Model Matching ◽  
Domain Specific ◽  
External Domain ◽  
Quantum Programming Languages ◽  
Quantum Programming ◽  
Software And Hardware ◽  
Classical Computing ◽  
Key Techniques ◽  
Execution Models

The increasing control complexity of Noisy Intermediate-Scale Quantum (NISQ) systems underlines the necessity of integrating quantum hardware with quantum software. While mapping heterogeneous quantum-classical computing (HQCC) algorithms to NISQ hardware for execution, we observed a few dissatisfactions in quantum programming languages (QPLs), including difficult mapping to hardware, limited expressiveness, and counter-intuitive code. In addition, noisy qubits require repeatedly performed quantum experiments, which explicitly operate low-level configurations, such as pulses and timing of operations. This requirement is beyond the scope or capability of most existing QPLs. We summarize three execution models to depict the quantum-classical interaction of existing QPLs. Based on the refined HQCC model, we propose the Quingo framework to integrate and manage quantum-classical software and hardware to provide the programmability over HQCC applications and map them to NISQ hardware. We propose a six-phase quantum program life-cycle model matching the refined HQCC model, which is implemented by a runtime system. We also propose the Quingo programming language, an external domain-specific language highlighting timer-based timing control and opaque operation definition, which can be used to describe quantum experiments. We believe the Quingo framework could contribute to the clarification of key techniques in the design of future HQCC systems.

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