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Henk Barendregt [20]Henk P. Barendregt [1]
  1.  36
    A Filter Lambda Model and the Completeness of Type Assignment.Henk Barendregt, Mario Coppo & Mariangiola Dezani-Ciancaglini - 1983 - Journal of Symbolic Logic 48 (4):931-940.
  2.  7
    Fixed Point Theorems for Precomplete Numberings.Henk Barendregt & Sebastiaan A. Terwijn - 2019 - Annals of Pure and Applied Logic 170 (10):1151-1161.
    In the context of his theory of numberings, Ershov showed that Kleene's recursion theorem holds for any precomplete numbering. We discuss various generalizations of this result. Among other things, we show that Arslanov's completeness criterion also holds for every precomplete numbering, and we discuss the relation with Visser's ADN theorem, as well as the uniformity or nonuniformity of the various fixed point theorems. Finally, we base numberings on partial combinatory algebras and prove a generalization of Ershov's theorem in this context.
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  3.  92
    The Impact of the Lambda Calculus in Logic and Computer Science.Henk Barendregt - 1997 - Bulletin of Symbolic Logic 3 (2):181-215.
    One of the most important contributions of A. Church to logic is his invention of the lambda calculus. We present the genesis of this theory and its two major areas of application: the representation of computations and the resulting functional programming languages on the one hand and the representation of reasoning and the resulting systems of computer mathematics on the other hand.
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  4.  52
    Mindfulness Reduces Habitual Responding Based on Implicit Knowledge: Evidence From Artificial Grammar Learning.Stephen Whitmarsh, Julia Uddén, Henk Barendregt & Karl Magnus Petersson - 2013 - Consciousness and Cognition 22 (3):833-845.
    Participants were unknowingly exposed to complex regularities in a working memory task. The existence of implicit knowledge was subsequently inferred from a preference for stimuli with similar grammatical regularities. Several affective traits have been shown to influence AGL performance positively, many of which are related to a tendency for automatic responding. We therefore tested whether the mindfulness trait predicted a reduction of grammatically congruent preferences, and used emotional primes to explore the influence of affect. Mindfulness was shown to correlate negatively (...)
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  5.  27
    Pairing Without Conventional Restraints.Henk Barendregt - 1974 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 20 (19-22):289-306.
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  6.  46
    Systems of Illative Combinatory Logic Complete for First-Order Propositional and Predicate Calculus.Henk Barendregt, Martin Bunder & Wil Dekkers - 1993 - Journal of Symbolic Logic 58 (3):769-788.
    Illative combinatory logic consists of the theory of combinators or lambda calculus extended by extra constants (and corresponding axioms and rules) intended to capture inference. The paper considers systems of illative combinatory logic that are sound for first-order propositional and predicate calculus. The interpretation from ordinary logic into the illative systems can be done in two ways: following the propositions-as-types paradigm, in which derivations become combinators or, in a more direct way, in which derivations are not translated. Both translations are (...)
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  7.  25
    Typed Lambda Calculus.Henk P. Barendregt, Wil Dekkers & Richard Statman - 1977 - In Jon Barwise & H. Jerome Keisler (eds.), Handbook of Mathematical Logic. North-Holland Pub. Co.. pp. 1091--1132.
  8.  15
    Pairing Without Conventional Restraints.Henk Barendregt - 1974 - Mathematical Logic Quarterly 20 (19‐22):289-306.
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  9.  32
    Completeness of Two Systems of Illative Combinatory Logic for First-Order Propositional and Predicate Calculus.Wil Dekkers, Martin Bunder & Henk Barendregt - 1998 - Archive for Mathematical Logic 37 (5-6):327-341.
    Illative combinatory logic consists of the theory of combinators or lambda calculus extended by extra constants (and corresponding axioms and rules) intended to capture inference. The paper considers 4 systems of illative combinatory logic that are sound for first-order propositional and predicate calculus. The interpretation from ordinary logic into the illative systems can be done in two ways: following the propositions-as-types paradigm, in which derivations become combinators, or in a more direct way, in which derivations are not translated. Both translations (...)
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  10. A Characterization of Terms of the λI-Calculus Having a Normal Form.Henk Barendregt - 1973 - Journal of Symbolic Logic 38 (3):441-445.
  11. The Abidhamma Model of Consciousness and its Consequences.Henk Barendregt - forthcoming - In M.G.T. Kwee, K.J. Gergen & F. Koshikawa (eds.), Buddhist Psychology: Practice, Research & Theory. Taos Institute Publishing, Taos, New Mexico.
  12.  44
    Completeness of the Propositions-as-Types Interpretation of Intuitionistic Logic Into Illative Combinatory Logic.Wil Dekkers, Martin Bunder & Henk Barendregt - 1998 - Journal of Symbolic Logic 63 (3):869-890.
    Illative combinatory logic consists of the theory of combinators or lambda calculus extended by extra constants (and corresponding axioms and rules) intended to capture inference. In a preceding paper, [2], we considered 4 systems of illative combinatory logic that are sound for first order intuitionistic propositional and predicate logic. The interpretation from ordinary logic into the illative systems can be done in two ways: following the propositions-as-types paradigm, in which derivations become combinators, or in a more direct way, in which (...)
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  13. Wiskunde, mystiek en natuurwetenschappen.Henk Barendregt - 2009 - Filosofie En Praktijk 30 (4):50.
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  14.  13
    J. R. Hindley, B. Lercher, and J. P. Seldin. Introduction to Combinatory Logic. London Mathematical Society Lecture Note Series, No. 7, Cambridge at the University Press, London and New York1972, 170 Pp. [REVIEW]Henk Barendregt - 1973 - Journal of Symbolic Logic 38 (3):518.
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  15. Buddhist Phenomenology.Henk Barendregt - 1987
  16.  41
    Degrees of Sensible Lambda Theories.Henk Barendregt, Jan Bergstra, Jan Willem Klop & Henri Volken - 1978 - Journal of Symbolic Logic 43 (1):45-55.
    A λ-theory T is a consistent set of equations between λ-terms closed under derivability. The degree of T is the degree of the set of Godel numbers of its elements. H is the $\lamda$ -theory axiomatized by the set {M = N ∣ M, N unsolvable. A $\lamda$ -theory is sensible $\operatorname{iff} T \supset \mathscr{H}$ , for a motivation see [6] and [4]. In § it is proved that the theory H is ∑ 0 2 -complete. We present Wadsworth's proof (...)
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  17.  13
    Combinatory Logic. Haskell B. Curry, J. Roger Hindley, and Jonathan P. Seldin. Combinatory Logic. Volume II. Studies in Logic and the Foundations of Mathematics, Vol. 65. North-Holland Publishing Company, Amsterdam and London 1972, XIV + 520 Pp. [REVIEW]Henk Barendregt - 1977 - Journal of Symbolic Logic 42 (1):109-110.
  18.  14
    Review: Haskell B. Curry, J. Roger Hindley, Jonathan P. Seldin, Combinatory Logic. [REVIEW]Henk Barendregt - 1977 - Journal of Symbolic Logic 42 (1):109-110.
  19.  19
    Enumerators of Lambda Terms Are Reducing Constructively.Henk Barendregt - 1995 - Annals of Pure and Applied Logic 73 (1):3-9.
    A closed λ-term E is called an enumerator if M ε /gL/dg /gTn ε N E/drn/dl = β M. Here Λ° is the set of closed λ-terms, N is the set of natural numbers and the /drn/dl are the Church numerals λfx./tfnx. Such an E is called reducing if moreover M ε /gL/dg /gTn ε N E/drn/dl /a/gb M. In 1983 I conjectured that every enumerator is reducing. An ingenious recursion theoretic proof of this conjecture by Statman is presented in (...)
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  20.  3
    Completeness of the Propositions-as-Types Interpretation of Intuitionistic Logic Into Illative Combinatory Logic.Wil Dekkers, Martin Bunder & Henk Barendregt - 1998 - Journal of Symbolic Logic 63 (3):869-890.
    Illative combinatory logic consists of the theory of combinators or lambda calculus extended by extra constants intended to capture inference. In a preceding paper, [2], we considered 4 systems of illative combinatory logic that are sound for first order intuitionistic propositional and predicate logic. The interpretation from ordinary logic into the illative systems can be done in two ways: following the propositions-as-types paradigm, in which derivations become combinators, or in a more direct way, in which derivations are not translated. Both (...)
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