Lambda-Calculus and Combinators, an Introduction

Hindley, J. Roger; Seldin, Jonathan P.

doi:10.1017/cbo9780511809835

Cited by 173 publications

(106 citation statements)

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“…Turing developed the UTM as a model of processing that could be used in showing what could be processed, what could not be processed, or what could not be always shown to be produced as informative output from a process. Informative processes also may be modelled using Church's lambda calculus [9], which helps formalize operations within functions and the variables within these functions.…”

Section: Theoretical Information Sciencementioning

confidence: 99%

Information theory for information science: Antecedents, philosophy, and applications

Losee¹

2017

EFI

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This paper provides an historical overview of the theoretical antecedents leading to information theory, specifically those useful for understanding and teaching information science and systems. Information may be discussed in a philosophical manner and at the same time be measureable. This notion of information can thus be the subject of philosophical discussion and the ideas about information may be applied rigorously to a wide range of practical applications where processes are studied. Theoretical Information Science and specific Information Science applications may provide tools by which questions such as "when and what information can be produced"? can be answered, as well as how to implement a system to serve a particular commercial or other specific function. These topics are discussed, and philosophical literature that might serve as a prerequisite to learning Information Science is suggested.

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Section: Theoretical Information Sciencementioning

confidence: 99%

Information theory for information science: Antecedents, philosophy, and applications

Losee¹

2017

EFI

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“…Unless mentioned otherwise, we consider alpha-congruent terms, i.e., terms that informally speaking differ only in the names of bound variables (see e.g. [9]), as identical.…”

Section: Types and Termsmentioning

confidence: 99%

“…Note that we are unable to directly eliminate D from (9), because that would require us to eliminate D from terms of the form D($y).…”

Section: Proving User Supplied Rules Soundmentioning

confidence: 99%

Term Rewriting in Logics of Partial Functions

Schmalz¹

2011

Formal Methods and Software Engineering

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Abstract. We devise a theoretical foundation of directed rewriting, a term rewriting strategy for logics of partial functions, inspired by term rewriting in the Rodin platform. We prove that directed rewriting is sound and show how to supply new rewrite rules in a soundness preserving fashion. In the context of Rodin, we show that directed rewriting makes a significant number of conditional rewrite rules unconditional. Our work not only allows us to point out a number of concrete ways of improving directed rewriting in Rodin, but also has applications in other logics of partial functions. Additionally, we give a semantics for the logic of Event-B.

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“…Law 8, 9, 11, and 12 follows immediately from Law 3, 4, 6, and 7, respectively by epistemic bitonicity. For Law 10, suppose that Like in LiP [Kra12], the preceding 1-way K-combinator property and the following simple corollary of Theorem 1 jointly establish the important fact that our communicating agents can be viewed as combinators in the sense of Combinatory Logic viewed in turn as a (non-equational) theory of (message or proof) term reduction [HS08]. (The converse of the above K-combinator property does not hold.…”

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confidence: 95%

Logic of Non-monotonic Interactive Proofs

Kramer

2013

Lecture Notes in Computer Science

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We propose a monotonic logic of internalised non-monotonic or instant interactive proofs (LiiP) and reconstruct an existing monotonic logic of internalised monotonic or persistent interactive proofs (LiP) as a minimal conservative extension of LiiP. Instant interactive proofs effect a fragile epistemic impact in their intended communities of peer reviewers that consists in the impermanent induction of the knowledge of their proof goal by means of the knowledge of the proof with the interpreting reviewer: If my peer reviewer knew my proof then she would at least then (in that instant) know that its proof goal is true. Their impact is fragile and their induction of knowledge impermanent in the sense of being the case possibly only at the instant of learning the proof. This accounts for the important possibility of internalising proofs of statements whose truth value can vary, which, as opposed to invariant statements, cannot have persistent proofs. So instant interactive proofs effect a temporary transfer of certain propositional knowledge (knowable ephemeral facts) via the transmission of certain individual knowledge (knowable non-monotonic proofs) in distributed systems of multiple interacting agents.

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Lambda-Calculus and Combinators, an Introduction

Cited by 173 publications

References 0 publications

Information theory for information science: Antecedents, philosophy, and applications

Information theory for information science: Antecedents, philosophy, and applications

Term Rewriting in Logics of Partial Functions

Logic of Non-monotonic Interactive Proofs

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