Propositions as types
TLDR
Connecting mathematical logic and computation, it ensures that some aspects of programming are absolute.Abstract:
Connecting mathematical logic and computation, it ensures that some aspects of programming are absolute.read more
Citations
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Book
Homotopy Type Theory: Univalent Foundations of Mathematics
TL;DR: Homotopy type theory as discussed by the authors is a branch of mathematics that combines aspects of several different fields in a surprising way and is based on a recently discovered connection between homotopy the-ory and type theory.
Journal ArticleDOI
Review of Kleene, λ-Definability and Recursiveness
Rozsa Peter,S. C. Kleene +1 more
Proceedings ArticleDOI
Type soundness proofs with definitional interpreters
Nada Amin,Tiark Rompf +1 more
TL;DR: This paper presents the first mechanized soundness proofs in this style for System F and several extensions, using only straightforward induction, which is significant, as the combination of big-step semantics, mutable references, and polymorphism is commonly believed to require coinductive proof techniques.
Journal ArticleDOI
Propositions, attitudinal objects, and the distinction between actions and products
TL;DR: This paper argued that the action-product distinction is not tied to particular terms in a particular language, but is to be understood as the more general distinction between an action and the (abstract or physically realized) artifact that it creates.
References
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Journal ArticleDOI
On Computable Numbers, with an Application to the Entscheidungsproblem
TL;DR: This chapter discusses the application of the diagonal process of the universal computing machine, which automates the calculation of circle and circle-free numbers.
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Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I
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A theory of type polymorphism in programming
TL;DR: This work presents a formal type discipline for polymorphic procedures in the context of a simple programming language, and a compile time type-checking algorithm w which enforces the discipline.
Journal ArticleDOI
Linear logic
TL;DR: This column presents an intuitive overview of linear logic, some recent theoretical results, and summarizes several applications oflinear logic to computer science.