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Page 7145 of Mathematical Reviews Vol. , Issue 95m [page]

1995 Mathematical Reviews  
{For the entire collection see MR 95j:03003.} 95m:03031 03B40 03B15 03B70 68Q55 Kamareddine, Fairouz (4~-GLAS-CS; Glasgow); Nederpelt, Rob (NL-EIND; Eindhoven) A unified approach to type theory through  ...  a refined /-calculus.  ... 

Automated techniques for higher-order program verification

Naoki KOBAYASHI, Luke ONG, David Van HORN
2013 Progress in Informatics  
The workshop also aimed for cross-fertilization of different techniques for higher-order program verification, such as game semantics, type theories, higher-order grammars and pushdown systems, control  ...  The aim of the workshop was to bring together researchers on automated techniques for higherorder program verification and analyses, and provide them with an opportunity to exchange new research results  ...  We use dependent type summaries to verify higher-order functions modularly, and leverage concrete tests to strengthen these types through iterative refinement.  ... 
doi:10.2201/niipi.2013.10.9 fatcat:xqfyvx6m25d4jcodwl373vlxlq

Foundations of path-dependent types

Nada Amin, Tiark Rompf, Martin Odersky
2014 SIGPLAN notices  
Whereas our simple calculus enjoys many desirable and intuitive properties, we demonstrate that the theory gets much more complicated once we add another Scala feature, type refinement, or extend the subtyping  ...  So we can refer to the abstract type member type Food as a type through a type selection: a.Fooda.Food is a path-dependent type, in general, a chain, starting with an immutable variable, of immutable field  ...  Process We have tried various approaches for designing a core calculus for path-dependent types, and proving it sound. In total, we went through about 30 variations of mechanized models.  ... 
doi:10.1145/2714064.2660216 fatcat:5hs77tn3sfflljjdzh5htyn2eu

Foundations of path-dependent types

Nada Amin, Tiark Rompf, Martin Odersky
2014 Proceedings of the 2014 ACM International Conference on Object Oriented Programming Systems Languages & Applications - OOPSLA '14  
Whereas our simple calculus enjoys many desirable and intuitive properties, we demonstrate that the theory gets much more complicated once we add another Scala feature, type refinement, or extend the subtyping  ...  So we can refer to the abstract type member type Food as a type through a type selection: a.Fooda.Food is a path-dependent type, in general, a chain, starting with an immutable variable, of immutable field  ...  Process We have tried various approaches for designing a core calculus for path-dependent types, and proving it sound. In total, we went through about 30 variations of mechanized models.  ... 
doi:10.1145/2660193.2660216 dblp:conf/oopsla/AminRO14 fatcat:74ryijkmefgoxalq5nldsom624

A calculus for probabilistic languages

Sungwoo Park
2003 SIGPLAN notices  
In this paper, we develop a probabilistic calculus by extending the traditional lambda calculus. In our calculus, every expression denotes a probability distribution yet evaluates to a regular value.  ...  As a consequence, we achieve a unified representation scheme for all types of probability distributions.  ...  Acknowledgment I am grateful to Frank Pfenning, who guided me through this research and suggested many key ideas in this paper.  ... 
doi:10.1145/640136.604180 fatcat:ulzxymhtvzbntbb6glaritp7eu

A calculus for probabilistic languages

Sungwoo Park
2003 Proceedings of the 2003 ACM SIGPLAN international workshop on Types in languages design and implementation - TLDI '03  
In this paper, we develop a probabilistic calculus by extending the traditional lambda calculus. In our calculus, every expression denotes a probability distribution yet evaluates to a regular value.  ...  As a consequence, we achieve a unified representation scheme for all types of probability distributions.  ...  Acknowledgment I am grateful to Frank Pfenning, who guided me through this research and suggested many key ideas in this paper.  ... 
doi:10.1145/604178.604180 fatcat:nlqb7hxpbjhtfkcmgvdusfycoe

A calculus for probabilistic languages

Sungwoo Park
2003 Proceedings of the 2003 ACM SIGPLAN international workshop on Types in languages design and implementation - TLDI '03  
In this paper, we develop a probabilistic calculus by extending the traditional lambda calculus. In our calculus, every expression denotes a probability distribution yet evaluates to a regular value.  ...  As a consequence, we achieve a unified representation scheme for all types of probability distributions.  ...  Acknowledgment I am grateful to Frank Pfenning, who guided me through this research and suggested many key ideas in this paper.  ... 
doi:10.1145/604174.604180 dblp:conf/tldi/Park03 fatcat:g37ka5mfp5ajbltq6gpws22fwe

Functional Pearl: Dependent type inference via free higher-order unification [article]

Nikolai Kudasov
2022 arXiv   pre-print
Using the Haskell programming language, we apply this approach to simply typed lambda calculus and Martin L\"of Type Theory.  ...  Implementing a proof assistant or a programming language based on such a theory is often challenging, as type inference is notoriously hard in the presence of dependent types.  ...  We have presented an approach to abstract syntax representation with free scoped monads and demonstrated its effectiveness simply typed lambda calculus and Martin Löf Type Theory.  ... 
arXiv:2204.05653v1 fatcat:xznkynhgnbgjjolho6o4eqqfpq

Thoughts on an Unified Framework for Artificial Chemistries [article]

Janrdan Misra
2009 arXiv   pre-print
This paper presents authors thoughts towards defining a unified framework to characterize and classify symbolic artificial chemistries by devising appropriate formalism to capture semantic and organizational  ...  We present an analysis of two important notions of information, namely, Shannon's Entropy and Algorithmic Information, and discuss inductive and deductive approaches for defining the framework.  ...  Most important of those is related to the choice of lambda calculus.  ... 
arXiv:0901.0318v1 fatcat:klepc7lbjzectmgx7qgjita2ym

A unified approach to type theory through a refined λ-calculus

Fairouz Kamareddine, Rob Nederpelt
1994 Theoretical Computer Science  
Nederpelt, A unified approach to type theory through a refined 2-calculus, Theoretical Computer Science 136 (1994) 183-216.  ...  -calculus, logic and type theory, got separated due to the appearence of the paradoxes.  ...  Kamareddine is grateful to the Department of Mathematics and Computing Science, Eindhoven University of Technology, for their financial support and hospitality from October 1991 to September 1992, and  ... 
doi:10.1016/0304-3975(94)00127-5 fatcat:zl2l6whaqzdlxeyqxfgyzismia

LFTOP: An LF-Based Approach to Domain-Specific Reasoning

Jian-Min Pang, Paul Callaghan, Zhao-Hui Luo
2005 Journal of Computer Science and Technology  
Many type theorists want to extend uses of type theory to more domains, and believe that the methods, ideas, and technology of type theory can have a beneficial effect for computer assisted reasoning in  ...  LFTOP: An LF based approach to domain specic reasoning Pang, Jianmin How to cite: Pang, Jianmin (2006) LFTOP: An LF based approach to domain specic reasoning, Durham theses, Durham University.  ...  The Curry and Church approaches to typed lambda calculus correspond to two paradigms in programming.  ... 
doi:10.1007/s11390-005-0526-y fatcat:u67u3mr4jvgjfomcepekpffl5a

Optimizing Higher-Order Pattern Unification [chapter]

Brigitte Pientka, Frank Pfenning
2003 Lecture Notes in Computer Science  
We present an abstract view of existential variables in a dependently typed lambda-calculus based on modal type theory.  ...  This allows us to justify optimizations to pattern unification such as linearization, which eliminates many unnecessary occurs-checks.  ...  We present an abstract view of existential variables in the dependently typed lambda-calculus based on modal type theory.  ... 
doi:10.1007/978-3-540-45085-6_40 fatcat:t3c2cnvthrd7zfggww3kxrfsle

Extending Type Inference to Variational Programs

Sheng Chen, Martin Erwig, Eric Walkingshaw
2014 ACM Transactions on Programming Languages and Systems  
We introduce the variational lambda calculus (VLC) as a formal foundation for research on typing variational programs.  ...  Through the use of conditional compilation and related tools, many software projects can be used to generate a huge number of related programs.  ...  ACKNOWLEDGMENTS We would like to thank Christian Kästner and the anonymous reviewers for many helpful comments on earlier drafts of this article.  ... 
doi:10.1145/2518190 fatcat:7dxefivrkfbgpfjs4emjhod424

What Kind of Programming Language Best Suits Integrative AGI? [article]

Ben Goertzel
2020 arXiv   pre-print
A gradual typing approach should be used to enable mixture of rules and other metagraph nodes/links associated with various type systems, and untyped metagraph nodes/links not associated with any type  ...  What kind of programming language would be most appropriate to serve the needs of integrative, multi-paradigm, multi-software-system approaches to AGI?  ...  implement within this framework is probabilistic dependent-linear-typed lambda calculus or something similar, perhaps with a Pure IsoType approach to dependent type inheritance.  ... 
arXiv:2004.05267v1 fatcat:gv2q7n2dxvf6fffr36qlkeplbe

Hybrid Type-Logical Grammars, First-Order Linear Logic and the Descriptive Inadequacy of Lambda Grammars [article]

Richard Moot
2014 arXiv   pre-print
This embedding result has several important consequences: it not only provides a simple new proof theory for the calculus, thereby clarifying the proof-theoretic foundations of hybrid type-logical grammars  ...  In this article we show that hybrid type-logical grammars are a fragment of first-order linear logic.  ...  Acknowledgments This paper is deeply indebted to Yusuke Kubota and Robert Levine, whose ESSLLI 2013 course awoke my curiosity both about the proof theoretic aspects of hybrid type-logical grammar and about  ... 
arXiv:1405.6678v1 fatcat:2nvjvhma55ffdcalyawcisnphe
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