From Semantics to Types: the Case of the Imperative lambda-Calculus

AbstractAn alternative approach is proposed to the basic definitions of the lassical lambda calculus. A proof is sketched of the equivalence of the approach with the classical case. The new formulation simplifies some aspects of the syntactic theory of the lambda calculus. In particular it provides a justification for omitting in syntactic theory discussion of changes of bound variable.

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Backpropagation in the simply typed lambda-calculus with linear negation

Proceedings of the ACM on Programming Languages ◽

10.1145/3371132 ◽

2020 ◽

Vol 4 (POPL) ◽

pp. 1-27 ◽

Cited By ~ 3

Author(s):

Aloïs Brunel ◽

Damiano Mazza ◽

Michele Pagani

Keyword(s):

Lambda Calculus ◽

Typed Lambda Calculus

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Algebras and coalgebras in the light affine Lambda calculus

ACM SIGPLAN Notices ◽

10.1145/2858949.2784759 ◽

2015 ◽

Vol 50 (9) ◽

pp. 114-126 ◽

Cited By ~ 1

Author(s):

Marco Gaboardi ◽

Romain Péchoux

Keyword(s):

Lambda Calculus

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The Limits of Computation

Axiomathes ◽

10.1007/s10516-021-09561-8 ◽

2021 ◽

Author(s):

Andrew Powell

Keyword(s):

Natural Number ◽

Set Theory ◽

Lambda Calculus ◽

Second Order ◽

Functional Interpretation ◽

Arbitrary Type ◽

Computable Functions

AbstractThis article provides a survey of key papers that characterise computable functions, but also provides some novel insights as follows. It is argued that the power of algorithms is at least as strong as functions that can be proved to be totally computable in type-theoretic translations of subsystems of second-order Zermelo Fraenkel set theory. Moreover, it is claimed that typed systems of the lambda calculus give rise naturally to a functional interpretation of rich systems of types and to a hierarchy of ordinal recursive functionals of arbitrary type that can be reduced by substitution to natural number functions.

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