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Little Theories
 Automated DeductionCADE11, volume 607 of Lecture Notes in Computer Science
, 1992
"... In the "little theories" version of the axiomatic method, different portions of mathematics are developed in various different formal axiomatic theories. Axiomatic theories may be related by inclusion or by theory interpretation. We argue that the little theories approach is a desirable wa ..."
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Cited by 51 (16 self)
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In the "little theories" version of the axiomatic method, different portions of mathematics are developed in various different formal axiomatic theories. Axiomatic theories may be related by inclusion or by theory interpretation. We argue that the little theories approach is a desirable way to formalize mathematics, and we describe how imps, an Interactive Mathematical Proof System, supports it.
Theory Interpretation in Simple Type Theory
 HIGHERORDER ALGEBRA, LOGIC, AND TERM REWRITING, VOLUME 816 OF LECTURE NOTES IN COMPUTER SCIENCE
, 1993
"... Theory interpretation is a logical technique for relating one axiomatic theory to another with important applications in mathematics and computer science as well as in logic itself. This paper presents a method for theory interpretation in a version of simple type theory, called lutins, which admit ..."
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Cited by 35 (16 self)
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Theory interpretation is a logical technique for relating one axiomatic theory to another with important applications in mathematics and computer science as well as in logic itself. This paper presents a method for theory interpretation in a version of simple type theory, called lutins, which admits partial functions and subtypes. The method is patterned on the standard approach to theory interpretation in rstorder logic. Although the method is based on a nonclassical version of simple type theory, it is intended as a guide for theory interpretation in classical simple type theories as well as in predicate logics with partial functions.
Two computersupported proofs in metric space topology
 Notices of the American Mathematical Society
, 1991
"... Every mathematician will agree that the discovery, analysis, and communication ..."
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Cited by 8 (3 self)
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Every mathematician will agree that the discovery, analysis, and communication
A General Method for Safely Overwriting Theories in Mechanized Mathematics Systems
 Lecture Notes in Computer Science (Proc. Intl. Zurich Sem. Digital Comm.). Spinger
, 1994
"... We propose a general method for overwriting theories with model conservative extensions in mechanized mathematics systems. Model conservative extensions, which include the denition of new constants and the introduction of new abstract datatypes, are \safe" because they preserve models as we ..."
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Cited by 2 (1 self)
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We propose a general method for overwriting theories with model conservative extensions in mechanized mathematics systems. Model conservative extensions, which include the denition of new constants and the introduction of new abstract datatypes, are \safe" because they preserve models as well as consistency. The method employs the notions of theory interpretation and theory instantiation. It is illustrated using manysorted rstorder logic, but it works for a variety of underlying logics. Supported by the MITRESponsored Research program. 1 1 Introduction Mathematical reasoning is always performed in some mathematical context consisting of vocabulary and assumptions. The formal counterpart of a context is a theory consisting of a formal language plus a set of sentences of the language called axioms. (We will denote a theory T by the pair (L; ) where L is the formal language of T and is the set of axioms of T .) An extension of a theory T is any theory T 0 obtained by ...