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Beluga: Programming with Dependent Types, Contextual Data, and Contexts [chapter]

Brigitte Pientka
2010 Lecture Notes in Computer Science  
A distinct feature of Beluga is its direct support for reasoning with contexts and contextual objects.  ...  It supports specifying formal systems in LF and it also provides a dependently typed functional language that supports analyzing and manipulating LF data via pattern matching.  ...  The foundation for programming with contextual data objects and contexts was first described in [Pie08] and subsequently extended with dependent types in [PD08] .  ... 
doi:10.1007/978-3-642-12251-4_1 fatcat:6lfb46dwpzbgdkocnaxvngnjgm

Inductive Beluga: Programming Proofs [chapter]

Brigitte Pientka, Andrew Cave
2015 Lecture Notes in Computer Science  
In this paper we describe four significant extensions to beluga: 1) we enrich our infrastructure for modelling formal systems with first-class simultaneous substitutions, a key and common concept when  ...  are well-founded and correspond to inductive proofs 4) we describe an interactive program development environment.  ...  Contextual LF types and objects are always enclosed with [ ] when they are embedded into recursive data-type definitions in the reasoning language.  ... 
doi:10.1007/978-3-319-21401-6_18 fatcat:jrmbnek7bfbordpjvnwn7r7q6i

Beluga: A Framework for Programming and Reasoning with Deductive Systems (System Description) [chapter]

Brigitte Pientka, Jana Dunfield
2010 Lecture Notes in Computer Science  
Beluga is an environment for programming and reasoning about formal systems given by axioms and inference rules.  ...  A distinctive feature of Beluga is that it not only represents binders using higher-order abstract syntax, but directly supports reasoning with contexts.  ...  In addition, we designed and implemented a type reconstruction algorithm for dependently-typed functions on contextual data.  ... 
doi:10.1007/978-3-642-14203-1_2 fatcat:pcc5n6yoa5ajzds65jt6mhps4q

Experiencing Belugas: Action Selection for an Interactive Aquarium Exhibit

Steve DiPaola, Caitlin Akai, Bill Kraus
2007 Adaptive Behavior  
The beluga interactive exhibit uses a realistic 3D simulation system that allows the virtual belugas, in a natural pod context, to learn and alter their behavior based on contextual visitor interaction  ...  This paper presents a case study of an action selection system designed with adaptive techniques to create a virtual beluga aquarium exhibit.  ...  Lance Barrett-Lennard for providing us access to their research on beluga behavior and vocalization, and the rest of the aquarium staff for their feedback on the beluga model and simulation.  ... 
doi:10.1177/1059712306076251 fatcat:pqonxzawvfbe5csxsqz3lbqbaq

Baseline hearing abilities and variability in wild beluga whales (Delphinapterus leucas)

M. Castellote, T. A. Mooney, L. Quakenbush, R. Hobbs, C. Goertz, E. Gaglione
2014 Journal of Experimental Biology  
and released belugas in Bristol Bay, Alaska.  ...  While hearing is the primary sensory modality for odontocetes, there are few data addressing variation within a natural population.  ...  Acknowledgements Paul Nachtigall and Alexander Supin assisted with the AEP program.  ... 
doi:10.1242/jeb.093252 pmid:24829324 fatcat:nejyeipljvglriityze4lhnzpe

Programming Inductive Proofs [chapter]

Brigitte Pientka
2010 Lecture Notes in Computer Science  
In this paper, we present an overview to programming with proofs in the reasoning framework, Beluga.  ...  What distinguishes Beluga from other frameworks is that it not only represents binders using higher-order abstract syntax, but directly supports reasoning with contexts and contextual objects.  ...  Beluga is however not only a reasoning environment, but may also serve as an experimental framework for programming with dependent types and proof objects, useful for certified programming and proof-carrying  ... 
doi:10.1007/978-3-642-17172-7_1 fatcat:qgrw2gtpz5dsnnv7tctph42gzq

Compiling contextual objects

Francisco Ferreira, Stefan Monnier, Brigitte Pientka
2013 Proceedings of the 7th workshop on Programming languages meets program verification - PLPV '13  
As an important side benefit, our work clarifies the connection between programming with HOAS in Beluga and programming with first-order approaches based on names.  ...  The Beluga language addresses this expressiveness problem by providing a powerful pattern matching facility as well as explicit control over contexts.  ...  More generally, Beluga is suitable for programs that manipulate data-structures with binders.  ... 
doi:10.1145/2428116.2428121 dblp:conf/plpv/FerreiraMP13 fatcat:hvy6hjcvozdatgny4kodptdooa

Programming with binders and indexed data-types

Andrew Cave, Brigitte Pientka
2012 SIGPLAN notices  
We show how to combine a general purpose type system for an existing language with support for programming with binders and contexts by refining the type system of ML with a restricted form of dependent  ...  This allows the user to specify formal systems within the logical framework LF and index ML types with contextual LF objects.  ...  The proposed programming language with support for contextual objects and data-types is a prime candidate for programming code transformations and certified programming.  ... 
doi:10.1145/2103621.2103705 fatcat:k67r2cjk4jf5xbh77h2sd3dkkq

Programming with binders and indexed data-types

Andrew Cave, Brigitte Pientka
2012 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '12  
We show how to combine a general purpose type system for an existing language with support for programming with binders and contexts by refining the type system of ML with a restricted form of dependent  ...  This allows the user to specify formal systems within the logical framework LF and index ML types with contextual LF objects.  ...  The proposed programming language with support for contextual objects and data-types is a prime candidate for programming code transformations and certified programming.  ... 
doi:10.1145/2103656.2103705 dblp:conf/popl/CaveP12 fatcat:t4gosmfs5zb2lpk5ooi52e4iui

Proofs and Programs about Open Terms [article]

Francisco Ferreira Ruiz
2018 arXiv   pre-print
We discuss three aspects of this: the reconstruction of implicit parameters that makes writing proofs and programs with dependent types easier, the addition of contextual objects to an existing programming  ...  framework LF with the expressivity of dependent types.  ...  Our programming language supports indexed data-types, dependent pattern matching and recursion.  ... 
arXiv:1805.07176v1 fatcat:pxvtcretendzxgpq7bgnsgdhiu

Case Analysis of Higher-Order Data

Jana Dunfield, Brigitte Pientka
2009 Electronical Notes in Theoretical Computer Science  
We discuss coverage checking for data that is dependently typed and is defined using higher-order abstract syntax.  ...  Unlike previous work on coverage checking for closed data, we consider open data which may depend on some context.  ...  Our data layer closely follows contextual modal type theory [10] , extended with parameter variables and context variables [12] , and finally with Σ types.  ... 
doi:10.1016/j.entcs.2008.12.117 fatcat:locdbf3wazeylozsaerrmfgvyu

Programming Type-Safe Transformations Using Higher-Order Abstract Syntax [chapter]

Olivier Savary-Belanger, Stefan Monnier, Brigitte Pientka
2013 Lecture Notes in Computer Science  
, in the dependently-typed language Beluga.  ...  Scope and type safety of the code transformations are statically guaranteed, and our implementation directly mirrors the proofs of type preservation.  ...  We thank Mathieu Boespflug for his feedback and work on the implementation of Beluga, and anonymous referees for helpful suggestions and comments on an earlier version of this paper.  ... 
doi:10.1007/978-3-319-03545-1_16 fatcat:ldg2cszrpbfbhhdjbbjvpvmjqm

A Case Study on Logical Relations using Contextual Types

Andrew Cave, Brigitte Pientka
2015 Electronic Proceedings in Theoretical Computer Science  
logical equivalence of well-typed lambda-terms using recursive types and higher-order functions 3) we exploit Beluga's support for contexts and the equational theory of simultaneous substitutions.  ...  In this paper, we describe the completeness proof of algorithmic equality for simply typed lambda-terms by Crary where we reason about logically equivalent terms in the proof environment Beluga.  ...  Beluga allows programmers to pair LF objects together with their surrounding context and this notion is internalized as a contextual type [Ψ A] which is inhabited by term M of type A in the context Ψ  ... 
doi:10.4204/eptcs.185.3 fatcat:andya4unorcqxi26lcat6dfz3m

LINCX: A Linear Logical Framework with First-Class Contexts [chapter]

Aina Linn Georges, Agata Murawska, Shawn Otis, Brigitte Pientka
2017 Lecture Notes in Computer Science  
We present Lincx, a contextual linear logical framework with first-class mixed contexts.  ...  Lincx extends the linear logical framework LLF with firstclass (linear) contexts and an equational theory of context joins that can otherwise be very tedious and intricate to develop.  ...  Having also additive operators would allow us to for example model the meta-theory of session type systems [5] and reason about concurrent computation.  ... 
doi:10.1007/978-3-662-54434-1_20 fatcat:ecrq5g3ejza77dycjdgir7ewr4

First-class substitutions in contextual type theory

Andrew Cave, Brigitte Pientka
2013 Proceedings of the Eighth ACM SIGPLAN international workshop on Logical frameworks & meta-languages: theory & practice - LFMTP '13  
This forms the basis for extending Beluga, a dependently typed proof and programming language which already supports first-class contexts and contextual objects, with first-class substitutions.  ...  First-class substitutions in contextual type theory  ...  A preliminary prototype for programming with first-class substitution variables is under way within the dependently typed programming and proof language, Beluga.  ... 
doi:10.1145/2503887.2503889 dblp:conf/lfmtp/CaveP13 fatcat:o373olpgxfexjm5clqpu54oz2q
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