Combining Theorem Proving and Symbolic Mathematical Computing

نویسندگان

  • Karsten Homann
  • Jacques Calmet
چکیده

An intelligent mathematical environment must enable symbolic mathematical computation and sophisticated reasoning techniques on the underlying mathematical laws. This paper disscusses diierent possible levels of interaction between a symbolic calculator based on algebraic algorithms and a theorem prover. A high level of interaction requires a common knowledge representation of the mathematical knowledge of the two systems. We describe a model for such a knowledge base mainly consisting of type and algorithm schemata, algebraic algorithms and theorems.

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

Intuition in formal proof : a novel framework for combining mathematical tools

This doctoral thesis addresses one major difficulty in formal proof: removing obstructions to intuition which hamper the proof endeavour. We investigate this in the context of formally verifying geometric algorithms using the theorem prover Isabelle, by first proving the Graham’s Scan algorithm for finding convex hulls, then using the challenges we encountered as motivations for the design of a...

متن کامل

Using Computer Algebra for Automated Reasoning in the Theorema System ABSTRACT

While most of the Automated Reasoning systems (see e.g. [8]) are based on purely logical approaches, many researchers started during the last decade to believe that solving non-trivial problems is only possible by using additionally algorithms from Computer Algebra. This is only natural, since most of human made proofs use complex computations, and in fact some researchers advocated the combina...

متن کامل

A short introduction to two approaches in formal verification of security protocols: model checking and theorem proving

In this paper, we shortly review two formal approaches in verification of security protocols; model checking and theorem proving. Model checking is based on studying the behavior of protocols via generating all different behaviors of a protocol and checking whether the desired goals are satisfied in all instances or not. We investigate Scyther operational semantics as n example of this...

متن کامل

Analytica - A Theorem Prover in Mathematica

Current automatic theorem provers, particularly those based on some variant of resolution, have concentrated on obtaining ever higher inference rates by using clever programming techniques, parallelism, etc. We believe that this approach is unlikely to lead to a useful system for actually doing mathematics. The main problem is the large amount of domain knowledge that is required for even the s...

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 1994