Ebook: Thirty Five Years of Automating Mathematics
Author: Fairouz D. Kamareddine (eds.)
- Genre: Mathematics // Logic
- Tags: Mathematical Logic and Foundations, Mathematics of Computing, Optimization, Symbolic and Algebraic Manipulation
- Series: Applied Logic Series 28
- Year: 2003
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
THIRTY FIVE YEARS OF AUTOMATING MATHEMATICS: DEDICATED TO 35 YEARS OF DE BRUIJN'S AUTOMATH N. G. de Bruijn was a well established mathematician before deciding in 1967 at the age of 49 to work on a new direction related to Automating Mathematics. By then, his contributions in mathematics were numerous and extremely influential. His book on advanced asymptotic methods, North Holland 1958, was a classic and was subsequently turned into a book in the well known Dover book series. His work on combinatorics yielded influential notions and theorems of which we mention the de Bruijn-sequences of 1946 and the de Bruijn-Erdos theorem of 1948. De Bruijn's contributions to mathematics also included his work on generalized function theory, analytic number theory, optimal control, quasicrystals, the mathematical analysis of games and much more. In the 1960s de Bruijn became fascinated by the new computer technology and as a result, decided to start the new AUTOMATH project where he could check, with the help of the computer, the correctness of books of mathematics. In each area that de Bruijn approached, he shed a new light and was known for his originality and for making deep intellectual contributions. And when it came to automating mathematics, he again did it his way and introduced the highly influential AUTOMATH. In the past decade he has also been working on theories of the human brain.
This volume is a collection of papers with a personal flavour. It consists of 11 articles which propose interesting variations to or examples of mechanising mathematics and illustrate differ developments in symbolic computation in the past 35 years. The volume further includes a strong argumentation by Arnon Avron that for automated reasoning, there is an interesting logic, somewhere strictly between first and second order logic, determined essentially by an analysis of transitive closure, yielding induction; and Murdoch Gabbay presenting an interesting generalisation of Fraenkel-Mostowski (FM) set theory within higher-order logic, and applying it to model Milner's p calculus.
This volume is a collection of papers with a personal flavour. It consists of 11 articles which propose interesting variations to or examples of mechanising mathematics and illustrate differ developments in symbolic computation in the past 35 years. The volume further includes a strong argumentation by Arnon Avron that for automated reasoning, there is an interesting logic, somewhere strictly between first and second order logic, determined essentially by an analysis of transitive closure, yielding induction; and Murdoch Gabbay presenting an interesting generalisation of Fraenkel-Mostowski (FM) set theory within higher-order logic, and applying it to model Milner's p calculus.
Content:
Front Matter....Pages i-8
A Mathematical Model for Biological Memory and Consciousness....Pages 9-23
Towards an Interactive Mathematical Proof Mode....Pages 25-36
Recent Results in Type Theory and Their Relationship to Automath....Pages 37-48
Linear Contexts, Sharing Functors: Techniques for Symbolic Computation....Pages 49-69
De Bruijn’s Automath and Pure Type Systems....Pages 71-123
Hoare Logic with Explicit Contexts....Pages 125-148
Transitive Closure and the Mechanization of Mathematics....Pages 149-171
Polymorphic Type-Checking for the Ramified Theory of Types of Principia Mathematica ....Pages 173-215
Termination in ACL2 Using Multiset Relations....Pages 217-245
The ?-Calculus in FM....Pages 247-269
Proof Development with ?mega: The Irrationality of $sqrt 2$ ....Pages 271-314
Back Matter....Pages 315-320
This volume is a collection of papers with a personal flavour. It consists of 11 articles which propose interesting variations to or examples of mechanising mathematics and illustrate differ developments in symbolic computation in the past 35 years. The volume further includes a strong argumentation by Arnon Avron that for automated reasoning, there is an interesting logic, somewhere strictly between first and second order logic, determined essentially by an analysis of transitive closure, yielding induction; and Murdoch Gabbay presenting an interesting generalisation of Fraenkel-Mostowski (FM) set theory within higher-order logic, and applying it to model Milner's p calculus.
Content:
Front Matter....Pages i-8
A Mathematical Model for Biological Memory and Consciousness....Pages 9-23
Towards an Interactive Mathematical Proof Mode....Pages 25-36
Recent Results in Type Theory and Their Relationship to Automath....Pages 37-48
Linear Contexts, Sharing Functors: Techniques for Symbolic Computation....Pages 49-69
De Bruijn’s Automath and Pure Type Systems....Pages 71-123
Hoare Logic with Explicit Contexts....Pages 125-148
Transitive Closure and the Mechanization of Mathematics....Pages 149-171
Polymorphic Type-Checking for the Ramified Theory of Types of Principia Mathematica ....Pages 173-215
Termination in ACL2 Using Multiset Relations....Pages 217-245
The ?-Calculus in FM....Pages 247-269
Proof Development with ?mega: The Irrationality of $sqrt 2$ ....Pages 271-314
Back Matter....Pages 315-320
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