72,674 research outputs found
Proof-relevant logical relations for name generation
Pitts and Stark's nu-calculus is a paradigmatic total language for studying the problem of contextual equivalence in higher-order languages with name generation. Models for the nu-calculus that validate basic equivalences concerning names may be constructed using functor categories or nominal sets, with a dynamic allocation monad used to model computations that may allocate fresh names. If recursion is added to the language and one attempts to adapt the models from (nominal) sets to(nominal)domains, however, the direct-style construction of the allocation monad no longer works. This issue has previously been addressed by using a monad that combines dynamic allocation with continuations, at some cost to abstraction. This paper presents a direct-style model of a nu-calculus-like language with recursion using the novel framework of proof-relevant logical relations, in which logical relations also contain objects (or proofs) demonstrating the equivalence of (the semantic counterparts of) programs. Apart from providing a fresh solution to an old problem, this work provides an accessible setting in which to introduce the use of proof-relevant logical relations, free of the additional complexities associated with their use for more sophisticated languages
Towards an Intelligent Tutor for Mathematical Proofs
Computer-supported learning is an increasingly important form of study since
it allows for independent learning and individualized instruction. In this
paper, we discuss a novel approach to developing an intelligent tutoring system
for teaching textbook-style mathematical proofs. We characterize the
particularities of the domain and discuss common ITS design models. Our
approach is motivated by phenomena found in a corpus of tutorial dialogs that
were collected in a Wizard-of-Oz experiment. We show how an intelligent tutor
for textbook-style mathematical proofs can be built on top of an adapted
assertion-level proof assistant by reusing representations and proof search
strategies originally developed for automated and interactive theorem proving.
The resulting prototype was successfully evaluated on a corpus of tutorial
dialogs and yields good results.Comment: In Proceedings THedu'11, arXiv:1202.453
An Improved Algorithm for Generating Database Transactions from Relational Algebra Specifications
Alloy is a lightweight modeling formalism based on relational algebra. In
prior work with Fisler, Giannakopoulos, Krishnamurthi, and Yoo, we have
presented a tool, Alchemy, that compiles Alloy specifications into
implementations that execute against persistent databases. The foundation of
Alchemy is an algorithm for rewriting relational algebra formulas into code for
database transactions. In this paper we report on recent progress in improving
the robustness and efficiency of this transformation
LangPro: Natural Language Theorem Prover
LangPro is an automated theorem prover for natural language
(https://github.com/kovvalsky/LangPro). Given a set of premises and a
hypothesis, it is able to prove semantic relations between them. The prover is
based on a version of analytic tableau method specially designed for natural
logic. The proof procedure operates on logical forms that preserve linguistic
expressions to a large extent. %This property makes the logical forms easily
obtainable from syntactic trees. %, in particular, Combinatory Categorial
Grammar derivation trees. The nature of proofs is deductive and transparent. On
the FraCaS and SICK textual entailment datasets, the prover achieves high
results comparable to state-of-the-art.Comment: 6 pages, 8 figures, Conference on Empirical Methods in Natural
Language Processing (EMNLP) 201
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