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Extending Nunchaku to Dependent Type Theory [PDF]
Electronic Proceedings in Theoretical Computer Science, 2016 Nunchaku is a new higher-order counterexample generator based on a sequence of transformations from polymorphic higher-order logic to first-order logic. Unlike its predecessor Nitpick for Isabelle, it is designed as a stand-alone tool, with frontends for
Simon Cruanes +1 more
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First steps in synthetic guarded domain theory: step-indexing in the topos of trees [PDF]
Logical Methods in Computer Science, 2012 We present the topos S of trees as a model of guarded recursion. We study the internal dependently-typed higher-order logic of S and show that S models two modal operators, on predicates and types, which serve as guards in recursive definitions of terms,
Lars Birkedal +3 more
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The Sierpinski Object in the Scott Realizability Topos [PDF]
Logical Methods in Computer Science, 2020 We study the Sierpinski object $\Sigma$ in the realizability topos based on Scott's graph model of the $\lambda$-calculus. Our starting observation is that the object of realizers in this topos is the exponential $\Sigma ^N$, where $N$ is the natural ...
Tom de Jong, Jaap van Oosten
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Cut-Simulation and Impredicativity [PDF]
Logical Methods in Computer Science, 2009 We investigate cut-elimination and cut-simulation in impredicative (higher-order) logics. We illustrate that adding simple axioms such as Leibniz equations to a calculus for an impredicative logic -- in our case a sequent calculus for classical type ...
Christoph Benzmueller +2 more
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A Focused Sequent Calculus Framework for Proof Search in Pure Type Systems [PDF]
Logical Methods in Computer Science, 2011 Basic proof-search tactics in logic and type theory can be seen as the root-first applications of rules in an appropriate sequent calculus, preferably without the redundancies generated by permutation of rules. This paper addresses the issues of defining
Stéphane Jean Eric Lengrand +2 more
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Actris 2.0: Asynchronous Session-Type Based Reasoning in Separation Logic [PDF]
Logical Methods in Computer Science, 2022 Message passing is a useful abstraction for implementing concurrent programs. For real-world systems, however, it is often combined with other programming and concurrency paradigms, such as higher-order functions, mutable state, shared-memory concurrency,
Jonas Kastberg Hinrichsen +2 more
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Duality Theory and Categorical Universal Logic: With Emphasis on Quantum Structures [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 Categorical Universal Logic is a theory of monad-relativised hyperdoctrines (or fibred universal algebras), which in particular encompasses categorical forms of both first-order and higher-order quantum logics as well as classical, intuitionistic, and ...
Yoshihiro Maruyama
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Implementing type theory in higher order constraint logic programming [PDF]
Mathematical Structures in Computer Science, 2019 In this paper, we are interested in high-level programming languages to implement the core components of an interactive theorem prover for a dependently typed language: the kernel – responsible for type-checking closed terms – and the elaborator – that manipulates open terms, that is terms containing unresolved unification variables.In this paper, we ...
Guidi, Ferruccio +2 more
openaire +3 more sources
طب انتظامی, 2022 INTRODUCTION ... [1, 2]. Marital relationship is an essential factor in creating peace [3]. Several factors can be influential in the quality of this matter and make couples that have marital conflicts over time.
Zahra Azemnia +3 more
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Topology in the Alternative Set Theory and Rough Sets via Fuzzy Type Theory
Mathematics, 2020 In this paper, we will visit Rough Set Theory and the Alternative Set Theory (AST) and elaborate a few selected concepts of them using the means of higher-order fuzzy logic (this is usually called Fuzzy Type Theory).
Vilém Novák
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