CS 611 Lecture 34 Curry - Howard Isomorphism November 15 , 2000

نویسنده

  • Andrew Myers
چکیده

The Curry-Howard isomorphism is a correspondence between logical formulas and types. The central idea is that each type τ corresponds to a logical formula φ, and that a proof that some expression e is well-formed with respect to type τ , (i.e., e : τ) corresponds to a proof that the logical formula φ is logically valid. Many variations of classical logic have been developed, especially in the last century. We’re most interested in establishing an isomorphism between types and logical formulas in constructive, or intuitionistic logic. In constructive logic, formulas of the form φ ∨ ¬φ and ¬¬φ ⇔ φ, for example, are not valid. To demonstrate that a formula is valid in constructive logic, it is not enough to demonstrate that its negation is not valid.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Constructive Classical Logic as CPS-Calculus

We establish the Curry-Howard isomorphism between constructive classical logic and CPS-calculus. CPS-calculus exactly means the target language of Continuation Passing Style(CPS) transforms. Constructive classical logic we refer to are LKT and LKQ introduced by Danos et al.(1993).

متن کامل

Lecture notes on the lambda calculus

This is a set of lecture notes that developed out of courses on the lambda calculus that I taught at the University of Ottawa in 2001 and at Dalhousie University in 2007. Topics covered in these notes include the untyped lambda calculus, the Church-Rosser theorem, combinatory algebras, the simply-typed lambda calculus, the Curry-Howard isomorphism, weak and strong normalization, type inference,...

متن کامل

Chapter 3 Proofs as Programs

In this chapter we investigate a computational interpretation of constructive proofs and relate it to functional programming. On the propositional fragment of logic this is referred to as the Curry-Howard isomorphism [How80]. From the very outset of the development of constructive logic and mathematics, a central idea has been that proofs ought to represent constructions. The Curry-Howard isomo...

متن کامل

Towards Animation of Proofs {testing proofs by examples{

In this paper, we introduce the notion of proof animation. It is a new application of the principle of \Curry-Howard isomorphism" to formal proof developments. Logically, proof animation is merely a contrapositive of \proofs as programs," which is an application of Curry-Howard isomorphism to formal program developments. Nonetheless, the new viewpoint totally changes the scene. The motivation, ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2000