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A Dependent Type Theory with Names and Binding [chapter]

Ulrich Schöpp, Ian Stark
2004 Lecture Notes in Computer Science  
Gabbay and Pitts have shown in their work on Fraenkel-Mostowski (FM) set theory how to address this through first-class names: in this paper we present a dependent type theory for programming and reasoning  ...  An associated adjunction captures constructions known from FM theory: the freshness quantifier AE, name-binding, and unique choice of fresh names.  ...  We would like to thank Alex Simpson and John Power for interesting discussions on this work.  ... 
doi:10.1007/978-3-540-30124-0_20 fatcat:domoc26smvgxzdebijb5zt5pwm

Preface: Theory and Applications of Abstraction, Substitution and Naming

Maribel Fernández, Christian Urban
2011 Journal of automated reasoning  
The first International Workshop on Theory and Applications of Abstraction, Substitution and Naming (TASSN) took place in Edinburgh in 2007, followed by a second workshop in York in 2009, associated to  ...  Formal treatments of abstract syntax have proved harder to develop, especially those addressing properties related to substituting structures for variables, binding of names and fresh name generation.  ...  Categorical Theories of Names and Binding Denotational semantics is one method of specifying meaning of languages.  ... 
doi:10.1007/s10817-011-9217-2 fatcat:p7pu4z5be5grng44bmhnsueks4

Locales: A Module System for Mathematical Theories

Clemens Ballarin
2013 Journal of automated reasoning  
Locales are a module system for managing theory hierarchies in a theorem prover through theory interpretation. They are available for the theorem prover Isabelle.  ...  The discussed mechanisms include ML-style functors, type classes and mixins (the latter are found in modern object-oriented languages).  ...  Wenzel integrated locales with the Isar proof language and provided means for constructing locale hierarchies [2] .  ... 
doi:10.1007/s10817-013-9284-7 fatcat:mnyomn2ttvfp7fqwnluuu7vfuq

An Axiomatic Value Model for Isabelle/UTP [chapter]

Frank Zeyda, Simon Foster, Leo Freitas
2017 Lecture Notes in Computer Science  
A deep and unified value model via a universal (data)type incurs restrictions on permissible value types and adds complexity; a value model directly instantiating HOL types for UTP values retains simplicity  ...  The Unifying Theories of Programming (UTP) is a mathematical framework to define, examine and link program semantics for a large variety of computational paradigms.  ...  Acknowledgement We would like to thank the anonymous reviewers for their helpful suggestions and conscientious reading of the paper.  ... 
doi:10.1007/978-3-319-52228-9_8 fatcat:attpodbcbjfg7cxrsghgif5tny

A Simple Nominal Type Theory

James Cheney
2009 Electronical Notes in Theoretical Computer Science  
In this paper we show how this difficulty can be overcome, and present a simple nominal type theory that enjoys properties such as type soundness and strong normalization, and that can be soundly interpreted  ...  This is a first step towards understanding the constructive content of nominal logic and incorporating it into existing constructive logics and type theories.  ...  Thanks are also due to Andrew Pitts, Christian Urban and the anonymous reviewers for detailed comments and suggestions.  ... 
doi:10.1016/j.entcs.2008.12.115 fatcat:x2m436r2w5hvphnptmf2cgz4ya

GKS Inquiry Functions within PROLOG [chapter]

P. Sykes, R. Krishnamurti
1987 GKS Theory and Practice  
This paper discusses the semantics of the GKS inquiry functions within a Prolog environment and illustrates the flexibility built into a proposed Prolog binding.  ...  having the same name but with differing argument lists That is, the arguments may differ in length and/or type.  ...  language functions, and to specify data types corresponding to the GKS abstract data type The rules also require the binding to observe good software engineering principles, a requirement which we have  ... 
doi:10.1007/978-3-642-72930-0_17 fatcat:exmtxglmf5a3piptt5uh26qyhy

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

2013 Journal of functional programming  
I describe the high-level language and the underlying type theory, and present a tactic-based method for elaborating concrete high-level syntax with implicit arguments and type classes into a fully explicit  ...  Many components of a dependently-typed programming language are by now well understood, for example the underlying type theory, type checking, unification and evaluation.  ...  and constructive comments.  ... 
doi:10.1017/s095679681300018x fatcat:c3h6qstkpnb3dainydfsxqzyui

A Semantics for : a Calculus with Overloading and Late-binding

T. Studer
2001 Journal of Logic and Computation  
In this paper we provide a new semantics for a stratified version of Castagna's λ {} , a λ-calculus combining overloading with late-binding.  ...  The model-construction is carried out in EETJ + (Tot) + (F-I N ), a system of explicit mathematics. We will prove the soundness of our model with respect to subtyping, type-checking and reductions.  ...  We would like to thank Giorgio Ghelli, Gerhard Jäger and Thomas Strahm for many helpful comments on earlier versions of this paper.  ... 
doi:10.1093/logcom/11.4.527 fatcat:6wnqyvktnbeknhlq6y7taob7v4

Code Generation for Higher Inductive Types [article]

Paventhan Vivekanandan
2018 arXiv   pre-print
While work proceeds on type theories with a computational interpretation of univalence and higher inductive types, it is convenient to encode these structures in more traditional type theories with mature  ...  We present a library that uses Agda's metaprogramming facilities to automate this process, allowing higher inductive types to be specified with minimal additional syntax.  ...  Acknowledgements The author is greatly indebted to David Christiansen for his contributions and advice, and the anonymous reviewers for their valuable review comments.  ... 
arXiv:1808.08330v1 fatcat:qwd4kzri6rhfxdl7naf6cfscqi

The calculus of nominal inductive constructions

Edwin Westbrook, Aaron Stump, Evan Austin
2009 Proceedings of the Fourth International Workshop on Logical Frameworks and Meta-Languages Theory and Practice - LFMTP '09  
Although name-bindings are ubiquitous in computer science, they are well-known to be cumbersome to encode and reason about in logic and type theory.  ...  CNIC supports induction over data containing bindings, comparing of names for equality, and associating meta-language types with names in a fashion similar to HOAS, features which have been shown difficult  ...  This is done by formalizing the meaning of a name-binding directly in the theory as a construct called a νabstraction. 1 We then show how the ν-abstraction can be combined with CIC to form a new theory  ... 
doi:10.1145/1577824.1577836 dblp:conf/lfmtp/WestbrookSA09 fatcat:og5cpkfqhfconkhtyqcakeooj4

First-Class Type Classes [chapter]

Matthieu Sozeau, Nicolas Oury
2008 Lecture Notes in Computer Science  
We propose an embedding of type classes into a dependent type theory that is first-class and supports some of the most popular extensions right away.  ...  Type Classes have met a large success in Haskell and Isabelle, as a solution for sharing notations by overloading and for specifying with abstract structures by quantification on contexts.  ...  Dependent Records Ample litterature exists on how to extend dependent type theories with records, e.g [3] gives a good starting point.  ... 
doi:10.1007/978-3-540-71067-7_23 fatcat:tz3zbirgrrfthmqclpog4ec2ae

Aging, Emotion, Attention, and Binding in the Taboo Stroop Task: Data and Theories

Donald MacKay, Laura Johnson, Elizabeth Graham, Deborah Burke
2015 International Journal of Environmental Research and Public Health  
We conclude that binding theory warrants further test in a range of paradigms, and that relations between aging and emotion, memory, and attention may depend on whether the task and stimuli trigger fast-reaction  ...  Binding theory also accurately predicted the interaction between consistency type and repetition for taboo words. However, one or more OPEN ACCESS Int. J. Environ. Res.  ...  Under binding theory, the binding of a taboo word's lexical node to its font color is prioritized, and interferes with the binding of font color to the color name response (see Figure 1 ).  ... 
doi:10.3390/ijerph121012803 pmid:26473909 pmcid:PMC4627001 fatcat:xcvollbarjhvvcshqtbbqck4wu

Remarks on binding theory

Carl Pollard
2005 Proceedings of the International Conference on Head-Driven Phrase Structure Grammar  
We propose some reformulations of binding principle A that build on recent work by Pollard and Xue, and by Runner et al.  ...  Another approach, which involves returning to the idea that referentially dependent expressions denote identity functions (as proposed, independently, by Pollard and Sag and by Jacobson) seerms to hold  ...  Pollard and Sag's reformulations of Principles A and B then run as follows: (2) Binding Theory for English Sag 1992, 1994) a.  ... 
doi:10.21248/hpsg.2005.32 fatcat:ajhonfv5uvbpxdzr7cqvqhtylq

A Dependent Type Theory with Abstractable Names

Andrew M. Pitts, Justus Matthiesen, Jasper Derikx
2015 Electronical Notes in Theoretical Computer Science  
This paper describes a version of Martin-Löf's dependent type theory extended with names and constructs for freshness and name-abstraction derived from the theory of nominal sets.  ...  We aim for a type theory for computing and proving (via a Curry-Howard correspondence) with syntactic structures which captures familiar, but informal, 'nameful' practices when dealing with binders.  ...  Thus abs(conc(f [p]) ν) = f ∈ Nom(X N N E) by (47). 2 Related Work The first work on a dependent type theory with features inspired by the nominal sets treatment of names and binding was by Schöpp and  ... 
doi:10.1016/j.entcs.2015.04.003 fatcat:m5ejzprd4zbjblm5jve6paathm

Inverse Indirect Binding

1988 Journal of the Linguistic Society of Japan  
Third, the interpretation of 'a Noun' is quasigeneric and it acts very much like a name or what he calls type I QPs such as any, a certain, etc. in pronoun binding.  ...  These observations lead him to the conclusion that the donkeyphrase is a name-like type I QP with respect to pronoun binding, so that it need not obey the c-command condition.  ... 
doi:10.11435/gengo1939.1988.1 fatcat:2nibw6uj75gydbupgfrinope4i
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