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9783031853517

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William M. Farmer has 40 years of experience working in industry and academia in computing and mathematics.  He received a B.A. in mathematics from the University of Notre Dame in 1978 and an M.A. in mathematics in 1980, an M.S. in computer sciences in 1983, and a Ph.D. in mathematics in 1984 from the University of Wisconsin-Madison. He is currently a Professor in the Department of Computing and Software at McMaster University.  Before joining McMaster in 1999, he conducted research in computer science for twelve years at The MITRE Corporation in Bedford, Massachusetts, USA and taught computer programming and networking courses for two years at St. Cloud State University. Dr. Farmer's research interests are logic, mathematical knowledge management, mechanized mathematics, and formal methods.  One of his most significant achievements is the design and implementation of the IMPS proof assistant, which was done at MITRE in partnership with Dr. Joshua Guttman and Dr. Javier Thayer.  His work on IMPS has led to research on developing practical logics based on simple type theory and NGB set theory and on organizing mathematical knowledge as a network of interconnected axiomatic theories.  He also has collaborated with Dr. Jacques Carette for several years at McMaster on developing a framework for integrating axiomatic and algorithmic mathematics.  As part of this research, Dr. Farmer has investigated how to reason about the interplay of syntax and semantics, as exhibited in syntax-based mathematical algorithms like symbolic differentiation, within a logic equipped with global quotation and evaluation operators.  Dr. Farmer is currently working on developing a communication-oriented approach to formal mathematics as an alternative to the standard certification-oriented approach employed using proof assistants.

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