The Impact of the Lambda Calculus in Logic and Computer Science

Barendregt, Henk

doi:10.2307/421013

Cited by 128 publications

(21 citation statements)

References 69 publications

(55 reference statements)

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“…At the same time we have tried to make it interesting to people that are familiar with one of these fields. This paper continues ideas presented in Cohen (2000) and Barendregt (1997).…”

Section: Introductionmentioning

confidence: 50%

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Electronic Communication of Mathematics and the Interaction of Computer Algebra Systems and Proof Assistants

Barendregt

Cohen

2001

Journal of Symbolic Computation

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Present day computer algebra systems (CASs) and proof assistants (PAs) are specialized programs that help humans with mathematical computations and deductions. Although several such systems are impressive, they all have certain limitations. In most CASs side conditions that are essential for the truth of an equality are not formulated; moreover there are bugs. The PAs have a limited power for computing and hence also for assistance with proofs. Almost all examples of both categories are stand alone special purpose systems and therefore they cannot communicate with each other.We will argue that the present state of the art in logic is such that there is a natural formal language, independent of the special purpose application in question, by which these systems can communicate mathematical statements. In this way their individual power will be enhanced.Statements received at one particular location from other sites fall into two categories: with or without the qualification "evidently impeccable", a notion that is methodologically precise and sound. For statements having this quality assessment the evidence may come from the other site or from the local site itself, but in both cases it is verified locally. In cases where there is no evidence of impeccability one has to rely on cross checking. There is a trade-off between these two kinds of statements: for impeccability one has to pay the price of obtaining less power.Some examples of communication forms are given that show how the participants benefit.

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“…At the same time we have tried to make it interesting to people that are familiar with one of these fields. This paper continues ideas presented in Cohen (2000) and Barendregt (1997).…”

Section: Introductionmentioning

confidence: 50%

“…This is what is called in Barendregt (1997) the Poincaré Principle. In Poincaré (1902) it is argued that if 2 + 2 = 4 is needed in a mathematical argument, then this part is not so much a proof in the strict sense of the word, but a "mere verification".…”

Section: Efficiencymentioning

confidence: 99%

Electronic Communication of Mathematics and the Interaction of Computer Algebra Systems and Proof Assistants

Barendregt

Cohen

2001

Journal of Symbolic Computation

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“…Barendregt (1997); Barendregt et al (2013)). One subtlety is that all variables and constants carry with them their type as part of their name: that is, constants and variable are not associated with a type which could vary with different type contexts.…”

Section: Simple Types and Typed λ-Termsmentioning

confidence: 98%

Automation of Higher-Order Logic

Benzmüller¹,

Miller²

2014

Handbook of the History of Logic

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“…Since its introduction by Alonzo Church in the 1930's the lambda calculus has been studied in many aspects, notably regarding computability. A history of lambda calculus related to computation theory can be found in Barendregt, 1997 andCardone &Hindley, 2006. For an introduction to the original lambda calculus see Hindley & Seldin, 1986, and for a more in-depth analysis see Barendregt, 2001.…”

Section: Introductionmentioning

confidence: 99%

Computability Via The Lambda Calculus with Patterns

Skulkiat¹,

Vejjajiva²,

Hall³

2010

JMR

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We introduce a concept of computability relative to a structure, which specifies which functions on the universe of a first-order structure are computable, using the lambda calculus with patterns. In doing so, we add a new congruence, ≡ A , called congruence in a structure to identify two syntactically different terms which represent the same element of the universe. We then show that, with the introduction of the new congruence, all the basic properties of the original lambda calculus with patterns still hold, including the Church-Rosser theorem.

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The Impact of the Lambda Calculus in Logic and Computer Science

Cited by 128 publications

References 69 publications

Electronic Communication of Mathematics and the Interaction of Computer Algebra Systems and Proof Assistants

Electronic Communication of Mathematics and the Interaction of Computer Algebra Systems and Proof Assistants

Automation of Higher-Order Logic

Computability Via The Lambda Calculus with Patterns

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