Dana S. Scott
ABSTRACT
A very fast development in the early 1930s, following Hilbert's codification of Mathematical Logic, led to the Incompleteness Theorems, Computable Functions, Undecidability Theorems, and the general formulation of recursive Function Theory. The so-called Lambda Calculus played a key role. The history of these developments will be traced, and the much later place of Lambda Calculus in Mathematics and Programming-Language Theory will be outlined.
Supplemental Material
Recommendations
The Intensional Lambda Calculus
LFCS '07: Proceedings of the international symposium on Logical Foundations of Computer ScienceWe introduce a natural deduction formulation for the Logic of Proofs, a refinement of modal logic S4 in which the assertion □ A is replaced by [[ s ]] A whose intended reading is " s is a proof of A ". A term calculus for this formulation yields a typed ...
Linear lambda calculus with non-linear first-class continuations
ICSCA '17: Proceedings of the 6th International Conference on Software and Computer ApplicationsThe Curry-Howard isomorphism is the correspondence between propositions and types, proofs and lambda-terms, and proof normalization and evaluation. In Curry-Howard isomorphism, we find a duality between values and continuations in pure functional ...
Focused Linear Logic and the λ-calculus
Linear logic enjoys strong symmetries inherited from classical logic while providing a constructive framework comparable to intuitionistic logic. However, the computational interpretation of sequent calculus presentations of linear logic remains ...
Comments