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Classical Combinatory Logic [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 Combinatory logic shows that bound variables can be eliminated without loss of expressiveness. It has applications both in the foundations of mathematics and in the implementation of functional programming languages.
Karim Nour
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Are there Hilbert-style Pure Type Systems? [PDF]
Logical Methods in Computer Science, 2008 For many a natural deduction style logic there is a Hilbert-style logic that is equivalent to it in that it has the same theorems (i.e. valid judgements with empty contexts).
M. W. Bunder, W. M. J. Dekkers
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Using Inhabitation in Bounded Combinatory Logic with Intersection Types for Composition Synthesis [PDF]
Electronic Proceedings in Theoretical Computer Science, 2013 We describe ongoing work on a framework for automatic composition synthesis from a repository of software components. This work is based on combinatory logic with intersection types.
Boris Düdder +4 more
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Asymptotically almost all \lambda-terms are strongly normalizing [PDF]
Logical Methods in Computer Science, 2013 We present quantitative analysis of various (syntactic and behavioral) properties of random \lambda-terms. Our main results are that asymptotically all the terms are strongly normalizing and that any fixed closed term almost never appears in a random ...
René David +5 more
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Semantics for Combinatory Logic With Intersection Types
Frontiers in Computer Science, 2022 There is a plethora of semantics of computational models, nevertheless, the semantics of combinatory logic are among the less investigated ones. In this paper, we propose semantics for the computational system of combinatory logic with intersection types.
Silvia Ghilezan +2 more
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Mixin Composition Synthesis based on Intersection Types [PDF]
Logical Methods in Computer Science, 2018 We present a method for synthesizing compositions of mixins using type inhabitation in intersection types. First, recursively defined classes and mixins, which are functions over classes, are expressed as terms in a lambda calculus with records ...
Jan Bessai +5 more
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Adapting Logic to Physics: The Quantum-Like Eigenlogic Program [PDF]
Entropy, 2020 Considering links between logic and physics is important because of the fast development of quantum information technologies in our everyday life. This paper discusses a new method in logic inspired from quantum theory using operators, named Eigenlogic ...
Zeno Toffano, François Dubois
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Bounded Combinatory Logic [PDF]
, 2012 In combinatory logic one usually assumes a fixed set of basic combinators (axiom schemes), usually K and S. In this setting the set of provable formulas (inhabited types) is PSPACE-complete in simple types and undecidable in intersection types.
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Undecidability of Equality in the Free Locally Cartesian Closed Category (Extended version) [PDF]
Logical Methods in Computer Science, 2017 We show that a version of Martin-L\"of type theory with an extensional identity type former I, a unit type N1 , Sigma-types, Pi-types, and a base type is a free category with families (supporting these type formers) both in a 1- and a 2-categorical sense.
Simon Castellan +2 more
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How Combinatory Logic Can Limit Computing Complexity [PDF]
EPJ Web of Conferences, 2020 As computing capabilities are extending, the amount of source code to manage is inevitably becoming larger and more complex. No matter how hard we try, the bewildering complexity of the source code always ends up overwhelming its own creator, to the ...
Bergier Hugolin
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