The Calculi of Lambda Conversion. (AM-6)

Church, Alonzo

doi:10.1515/9781400881932

Cited by 124 publications

(156 citation statements)

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“…A. Church developed lambda-calculus about two decades earlier, and it was defined with rules that are similar to those of ALGOL 60 [34,Section 6]. However, McCarthy admitted that at that time he 'didn't understand' lambda-calculus besides the lambda-notation [1, p. 176, 35, p. 190], and the first implementations of LISP did not conform to its semantics [1, p. 180].…”

Section: The Consequences Of the Call By Name Mechanismmentioning

confidence: 99%

On the Origin of Recursive Procedures

Hove¹

2014

The Computer Journal

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We investigate the origin of recursive procedures in imperative programming languages. We attempt to set the record straight, and to identify the trend that led to recursive procedures, by means of an analysis of the related concepts and of the most reliable available documents, as far as known to us. We show that not all of those who were involved in defining these concepts in these documents were fully aware of the implications of their proposals. Our aim is not primarily historical, but to contribute to a clarification of some of the concepts related to recursion. In particular, we demonstrate that recursive procedure declarations and recursive procedure activations are logically disjoint concepts.

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Section: The Consequences Of the Call By Name Mechanismmentioning

confidence: 99%

On the Origin of Recursive Procedures

Hove¹

2014

The Computer Journal

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“…Lambda abstraction [3] is a pure theory of nested function definition and application. In E notation, conventional function definition and application should look familiar:…”

Section: Lambda Abstractionmentioning

confidence: 99%

Capability-Based Financial Instruments

Miller¹,

Morningstar²,

Frantz³

2001

Lecture Notes in Computer Science

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Abstract. Every novel cooperative arrangement of mutually suspicious parties interacting electronically -every smart contract -effectively requires a new cryptographic protocol. However, if every new contract requires new cryptographic protocol design, our dreams of cryptographically enabled electronic commerce would be unreachable. Cryptographic protocol design is too hard and expensive, given our unlimited need for new contracts.Just as the digital logic gate abstraction allows digital circuit designers to create large analog circuits without doing analog circuit design, we present cryptographic capabilities as an abstraction allowing a similar economy of engineering effort in creating smart contracts. We explain the E system, which embodies these principles, and show a covered-call-option as a smart contract written in a simple security formalism independent of cryptography, but automatically implemented as a cryptographic protocol coordinating five mutually suspicious parties.

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“…Equational theories over terms, such as the α, β, and η in the λ-calculus [Church, 1941], are a critical component of programming languages and formal systems. As users of logic programming languages and theorem provers, we desire such rules to be available out of the box.…”

Section: Introductionmentioning

confidence: 99%

Efficiency of a good but not linear nominal unification algorithm

Ma¹,

Siek²,

Christiansen³

et al. 2018

EasyChair Preprints

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We present a nominal unification algorithm that runs in O(n × log(n) × G(n)) time, where G is the functional inverse of Ackermann's function. Nominal unification generates a set of variable assignments if there exists one, that makes terms involving binding operations α-equivalent. We preserve names while using special representations of de Bruijn numbers to enable efficient name management. We use Martelli-Montanari style multi-equation reduction to generate these name management problems from arbitrary unification terms.

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The Calculi of Lambda Conversion. (AM-6)

Cited by 124 publications

References 0 publications

On the Origin of Recursive Procedures

On the Origin of Recursive Procedures

Capability-Based Financial Instruments

Efficiency of a good but not linear nominal unification algorithm

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