Faithful Reproductions of the Automath Landau Formalization

نویسنده

Chad E. Brown

چکیده

In the 1970s van Benthem Jutting translated Landau’s book Grundlagen der Analysis into Automath. The type theory of Automath differs from modern type theories in significant ways. The most important difference is that Automath is λ-typed while most modern type theories are Π-typed. In this paper we define the notion of a faithful reproduction of an Automath signature. We describe how one can obtain a particular faithful reproduction of a signature corresponding to the Automath version of Landau’s book. We then consider what properties a Π-typed type theory must have in order for the faithful reproduction to be a correct signature. Based on this information, we can give different mappings of the reproduction into type theories such as ECC and, in particular, the system Coq.

برای دانلود رایگان 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

N.G. de Bruijn’s Contribution to the Formalization of Mathematics

N.G. de Bruijn was one of the pioneers to explore the idea of using a computer to formally check mathematical proofs. The Automath project, that started in 1967 and ran until 1980, was the first in developing computer programs to actually check mathematical proofs. But Automath is more than that: it is a language for doing mathematics and it has philosophical implications for the way we look at...

متن کامل

Exact solutions of the 2D Ginzburg-Landau equation by the first integral method

The first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. This method can be applied to non integrable equations as well as to integrable ones. In this paper, the first integral method is used to construct exact solutions of the 2D Ginzburg-Landau equation.

متن کامل

The Triumph of Types: Principia Mathematica’s Impact on Computer Science

Types now play an essential role in computer science; their ascent originates from Principia Mathematica. Type checking and type inference algorithms are used to prevent semantic errors in programs, and type theories are the native language of several major interactive theorem provers. Some of these trace key features back to Principia. This lecture examines the influence of Principia Mathemati...

متن کامل