Hendrik P. Barendregt. The impact of the lambda calculus on logic and computer science. Bulletin of Symbolic Logic, 3(3):181--215, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of the Vienna Circle study group and the beginning of the rise of logical positivism as a key movement in the philosophy of science. Integral to their approach was the use of logic as a framework for scienti c reasoning. The movement was See [Cor eld 1997] See [Gillies 2001] and [Barendregt 1997] for further insights into this interaction. extremely important half way through the twentieth century when Turing put forward his vision of learning machines, and the early machine learning systems of the 1960s were quick to put the learning problem into the logical framework. By the end of ....

Henk Barendregt: `The impact of the lambda calculus in logic and computer science', Bulletin of Symbolic Logic 3(2), pages 181-215.

....into a jump with arguments to the callee such that one of these is a continuation that enables the callee to jump back to the caller. This idea has been formalised into a standard CPS transformation for lambda calculus. Definition 2.2.1. The pure untyped lambda calculus # is defined by [1]: A set of terms, M , inductively generated over an infinite set of variables V ars, Terms M : V M M ; Values V : x #x.M , x in V ars. The standards CPS translation for # in denotational semantics is given by the map [ F : # # originally described by Fisher: Definition ....

Hendrik P. Barendregt, The impact of the lambda calculus on logic and computer science, Bulletin of Symbolic Logic 3 (1997), no. 3, 181--215.

....If a fi reduction changes the shape of the defining term in such a way that the retranslation step corresponding to the label becomes impossible, it will also consume the label together with the operator. Using (refined) representation mappings similar to the ones given here, it 1 cf. also [Bar96b] for further structure preserving encodings of data types as terms. 8M;M 1 ; M 2 ; N; P 2 term; M 2 term ; v 2 var; v 2 var ; k; i 2 Nat : Let p; f; g; x; y; n; l; h; t 2 var (pairwise different) Then Y = ae bf: x: f (x x) x: f (x x) c Y I = ae bx:xc I K = ae bxy:xc K (M ffi ....

Henk Barendregt. The impact of the lambda calculus in logic and computer science. ftp://ftp.cs.kun.nl/pub/CompMath.Found/ church.ps.Z, October 1996.

....and study the properties of a simply typed calculus with record types and datatypes, and which supports record subtyping and constructor subtyping. We show that the calculus is con uent and strongly normalizing. We also show that the type checking is decidable. 1 Introduction Type systems [3, 8] lie at the core of modern functional programming languages, such as Haskell [26] or ML [24] and proof assistants, such as Coq [4] or PVS [30] In order to improve the usability of these languages, it is important to devise exible (and safe) type systems, in which programs and proofs may be ....

H. Barendregt. The impact of the lambda calculus in logic and computer science. Bulletin of Symbolic Logic, 3(2):181-215, June 1997.

....provided one adopts expansive extensionality rules, including j expansion, surjective pairing, and a suitable expansion rule for datatypes. Finally, in the third part of the paper, we extend our calculus with unbounded recursion and show that confluence is preserved. 1 Introduction Type systems [3, 8] lie at the core of modern functional programming languages, such as Haskell [28] or ML [26] and proof assistants, such as Coq [4] or PVS [32] In order to improve the usability of these languages, it is important to devise flexible (and safe) type systems, in which programs and proofs may be ....

H. Barendregt. The impact of the lambda calculus in logic and computer science. Bulletin of Symbolic Logic, 3(2):181--215, June 1997.

....provided one adopts expansive extensionality rules, including j expansion, surjective pairing, and a suitable expansion rule for datatypes. Finally, in the third part of the paper, we extend our calculus with unbounded recursion and show that confluence is preserved. 1 Introduction Type systems [3, 8] lie at the core of modern functional programming languages, such as Haskell [28] or ML [26] and proof assistants, such as Coq [4] or PVS [32] In order to improve the usability of these languages, it is important to devise flexible (and safe) type systems, in which programs and proofs may be ....

H. Barendregt. The impact of the lambda calculus in logic and computer science. Bulletin of Symbolic Logic, 3(2):181--215, June 1997.

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Hendrik P. Barendregt. The impact of the lambda calculus on logic and computer science. Bulletin of Symbolic Logic, 3(3):181--215, 1997.

No context found.

Henk Barendregt. The Impact of the Lambda Calculus in Logic and Computer Science. In The Bulletin of Symbolic Logic Vol. 3, No. 2, June 1997.

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