Filters








423 Hits in 6.7 sec

Benchmarks for reasoning with syntax trees containing binders and contexts of assumptions

AMY FELTY, ALBERTO MOMIGLIANO, BRIGITTE PIENTKA
2017 Mathematical Structures in Computer Science  
benchmarks, which highlight a variety of different aspects of reasoning within a context of assumptions.  ...  Our contributions in this paper are two-fold: (1) We develop a common infrastructure and language for describing benchmarks for systems supporting reasoning with binders, and (2) we present several concrete  ...  We thank Kaustuv Chaudhuri, Andrew Gacek, Nada Habli, and Dale Miller for discussing some aspects of this work with us.  ... 
doi:10.1017/s0960129517000093 fatcat:v5d5zsrpkbgnlgtej246bwk75a

The Next 700 Challenge Problems for Reasoning with Higher-Order Abstract Syntax Representations: Part 1-A Common Infrastructure for Benchmarks [article]

Amy P. Felty, Alberto Momigliano, Brigitte Pientka
2015 arXiv   pre-print
Our contributions in this paper are three-fold: 1) we develop a common infrastructure for representing benchmarks for systems supporting reasoning with binders, 2) we present several concrete benchmarks  ...  , which highlight a variety of different aspects of reasoning within a context of assumptions, and 3) we design an open repository ORBI, (Open challenge problem Repository for systems supporting reasoning  ...  We thank Kaustuv Chaudhuri, Andrew Gacek, Nada Habli, and Dale Miller for discussing some aspects of this work with us.  ... 
arXiv:1503.06095v1 fatcat:a2hwfzvgrjdnbcme6hdngetpcy

Mechanized Metatheory Revisited

Dale Miller
2018 Journal of automated reasoning  
We will also illustrate how that framework provides a direct and semantically clean treatment of computation and reasoning with syntax containing bindings.  ...  Since most mature proof assistants do not have built-in methods to treat bindings, they have been extended with various packages and libraries that allow them to encode such syntax using, for example,  ...  I thank Gopalan Nadathur and the anonymous reviewers for their many helpful comments on an earlier draft of this paper. This work was funded in part by the ERC Advanced Grant ProofCert.  ... 
doi:10.1007/s10817-018-9483-3 fatcat:sgmm2r4hn5ab3mgpvvzwhcjs5i

Relating System F and Lambda2: A Case Study in Coq, Abella and Beluga

Jonas Kaiser, Brigitte Pientka, Gert Smolka, Marc Herbstritt
2017 International Conference on Rewriting Techniques and Applications  
In Abella, we use higher-order abstract syntax (HOAS) and nominal constants of the ambient reasoning logic. In Beluga, we also use HOAS but within contextual modal type theory.  ...  We give three formalisations of a proof of the equivalence of the usual, two-sorted presentation of System F and its single-sorted pure type system (PTS) variant λ2.  ...  We observe that our proof contains a number of challenges that, taken as a whole, constitute a nice benchmark for systems designed to reason about type systems.  ... 
doi:10.4230/lipics.fscd.2017.21 dblp:conf/rta/KaiserPS17 fatcat:k3z3uux2grd4jnrzac7rpdtahu

Reasoning with Higher-Order Abstract Syntax and Contexts: A Comparison [chapter]

Amy Felty, Brigitte Pientka
2010 Lecture Notes in Computer Science  
A variety of logical frameworks support the use of higherorder abstract syntax (HOAS) in representing formal systems given via axioms and inference rules and reasoning about them.  ...  Although these systems seem superficially the same, they differ in a variety of ways; for example, in how they handle a context of assumptions and in what theorems about a given formal system can be expressed  ...  Conclusion We presented several benchmark problems together with a general set of criteria for comparing reasoning systems which support the mechanization of formal systems.  ... 
doi:10.1007/978-3-642-14052-5_17 fatcat:lfoojniwxvanjdrz2lnjmgektm

Accelerating Verified-Compiler Development with a Verified Rewriting Engine [article]

Jason Gross and Andres Erbsen and Jade Philipoom and Miraya Poddar-Agrawal and Adam Chlipala
2022 arXiv   pre-print
Now each rewrite rule can be proved separately, with no need to revisit past proofs for other parts of the compiler.  ...  Our new Coq command takes normal proved theorems and combines them automatically into fast compilers with proofs.  ...  We claimed to allow reduction that mixes rules of the definitional equality with equalities proven explicitly as theorems; the "rules of the definitional equality" are, for example, β reduction, and we  ... 
arXiv:2205.00862v2 fatcat:wzu43zd35zffjfu4akpuwsrqky

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

Olivier Savary-Belanger, Stefan Monnier, Brigitte Pientka
2013 Lecture Notes in Computer Science  
This can be particularly challenging for languages containing binding constructs, and often leads to subtle, hard to find errors.  ...  Compiling syntax to native code requires complex code transformations which rearrange the abstract syntax tree.  ...  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

Functional programming with λ-tree syntax

Ulysse Gérard, Dale Miller, Gabriel Scherer
2019 Proceedings of the 21st International Symposium on Principles and Practice of Programming Languages 2019 - PPDP '19  
In order to formally define the language's operational semantics, we present an abstract syntax for MLTS and a natural semantics for its evaluation.  ...  We present the design of a new functional programming language, MLTS, that uses the lambda-tree syntax approach to encoding bindings appearing within data structures.  ...  Functional programming with λ-tree syntax  ... 
doi:10.1145/3354166.3354177 dblp:conf/ppdp/Gerard0S19 fatcat:qtkdac7eizhv5abtuelor33rwi

Type-and-example-directed program synthesis

Peter-Michael Osera, Steve Zdancewic
2015 Proceedings of the 36th ACM SIGPLAN Conference on Programming Language Design and Implementation - PLDI 2015  
We evaluate the algorithm by using a prototype implementation to synthesize more than 40 benchmarks and several non-trivial larger examples.  ...  The algorithm uses refinement trees, a data structure that succinctly represents constraints on the shape of generated code.  ...  Acknowledgments We would like to thank Jonathan Frankle, Rohan Shah, David Walker, the members of the UPenn PL Club, and the anonymous reviewers for their comments and feedback on our work.  ... 
doi:10.1145/2737924.2738007 dblp:conf/pldi/OseraZ15 fatcat:ob64pziw5bdgjk2geie4yj2ibi

Type-and-example-directed program synthesis

Peter-Michael Osera, Steve Zdancewic
2015 SIGPLAN notices  
We evaluate the algorithm by using a prototype implementation to synthesize more than 40 benchmarks and several non-trivial larger examples.  ...  The algorithm uses refinement trees, a data structure that succinctly represents constraints on the shape of generated code.  ...  Acknowledgments We would like to thank Jonathan Frankle, Rohan Shah, David Walker, the members of the UPenn PL Club, and the anonymous reviewers for their comments and feedback on our work.  ... 
doi:10.1145/2813885.2738007 fatcat:iblupvzp3jcrpcdxs5idmrzhou

Mechanizing proofs with logical relations – Kripke-style

ANDREW CAVE, BRIGITTE PIENTKA
2018 Mathematical Structures in Computer Science  
higher order abstract syntax (HOAS) thereby avoiding the need to manipulate and deal with binders, renaming and substitutions, (2) we take advantage of Beluga'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 exploit Beluga's rich equational theory for simultaneous substitutions  ...  If they are not closed, how can we characterize their free variables and reason about them? How should we represent the abstract syntax tree for lambda-terms and enforce the scope of bound variables?  ... 
doi:10.1017/s0960129518000154 fatcat:uhyfqoacjfdido2zdg3pijayha

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.  ...  Approaches representing lambda-terms using higher-order abstract syntax (HOAS) trees (also called λ -tree syntax) model binders in the object language (i.e. in our case the simply typed lambda-calculus  ... 
doi:10.4204/eptcs.185.3 fatcat:andya4unorcqxi26lcat6dfz3m

User-Defined Operators Including Name Binding for New Language Constructs

Kazuhiro Ichikawa, Shigeru Chiba
2017 The Art, Science, and Engineering of Programming  
A contribution of this paper is that we reveal we can integrate a system for managing names and their scopes with a module and type system of an object-oriented language like Java.  ...  To show the practicality of our proposal, we have conducted two micro benchmarks to see the performance of our compiler.  ...  A method or an operator with the requires clause becomes available if all the specified types in the required clause are assumptions (i.e., within a context-sensitive expression of a turnstile type containing  ... 
doi:10.22152/programming-journal.org/2017/1/15 fatcat:wvfkjhcbu5divhinqksipskh4e

Graph Representations for Higher-Order Logic and Theorem Proving [article]

Aditya Paliwal, Sarah Loos, Markus Rabe, Kshitij Bansal, Christian Szegedy
2019 arXiv   pre-print
In this paper, we consider several graphical representations of higher-order logic and evaluate them against the HOList benchmark for higher-order theorem proving.  ...  This paper presents the first use of graph neural networks (GNNs) for higher-order proof search and demonstrates that GNNs can improve upon state-of-the-art results in this domain.  ...  In this work, we explore the use of the tree structure (e.g. the abstract syntax tree) of logic expressions for learning representations.  ... 
arXiv:1905.10006v2 fatcat:kokjdqbvpvgvbfl4blxmbrafpe

Satisfiability Modulo Recursive Programs [chapter]

Philippe Suter, Ali Sinan Köksal, Viktor Kuncak
2011 Lecture Notes in Computer Science  
Using our system, Leon, we verified detailed correctness properties for functional data structure implementations, as well as syntax tree manipulations.  ...  Our procedure is sound for counterexamples and for proofs of terminating functions.  ...  We thank Nikolaj Bjørner and Leonardo de Moura for their help with Z3. We thank Mirco Dotta and Swen Jacobs for preliminary versions of some of the benchmarks.  ... 
doi:10.1007/978-3-642-23702-7_23 fatcat:msorndfrk5d4zj7pbcvxtssoxu
« Previous Showing results 1 — 15 out of 423 results