{"product_id":"9783031853548","title":"Simple Type Theory A Practical Logic for Expressing and Reasoning About Mathematical Ideas","description":"\u003ch3\u003eComputer Science Foundations and Applied Logic\u003c\/h3\u003e\u003ch1\u003eSimple Type Theory\u003c\/h1\u003e\u003ch2\u003eA Practical Logic for Expressing and Reasoning About Mathematical Ideas\u003c\/h2\u003e\u003ch3\u003eWilliam M. Farmer\u003c\/h3\u003e\u003cdiv\u003e\u003cb\u003eComputers \/ Computer Science\u003c\/b\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\n\u003cp\u003eThis unique textbook, in contrast to a standard logic text, provides the reader with a logic that can be \u003cem\u003eused\u003c\/em\u003e in practice to express and reason about mathematical ideas.\u003cspan style=\"mso-spacerun: yes;\"\u003e  \u003c\/span\u003eThe book is an introduction to \u003cem\u003esimple type theory\u003c\/em\u003e, a classical higher-order version of predicate logic that extends first-order logic.\u003cspan style=\"mso-spacerun: yes;\"\u003e  \u003c\/span\u003e\u003c\/p\u003e\r\n\u003cp\u003eIt presents a practice-oriented logic called \u003cem\u003eAlonzo\u003c\/em\u003e that is based on Alonzo Church's formulation of simple type theory known as \u003cem\u003eChurch's type theory\u003c\/em\u003e. Unlike traditional predicate logics, Alonzo admits undefined expressions.\u003cspan style=\"mso-spacerun: yes;\"\u003e  \u003c\/span\u003eThe book illustrates using Alonzo how simple type theory is suited ideally for reasoning about mathematical structures and constructing libraries of mathematical knowledge.\u003cspan style=\"mso-spacerun: yes;\"\u003e  \u003c\/span\u003eFor this \u003cstrong\u003esecond edition\u003c\/strong\u003e, more than 400 additions, corrections, and improvements have been made, including a new chapter on inductive sets and types.\u003c\/p\u003e\r\n\u003cp\u003e\u003cstrong\u003eTopics and features:\u003c\/strong\u003e\u003c\/p\u003e\r\n\u003cp style=\"margin-left: .5in; text-indent: -.25in; mso-list: l0 level1 lfo1;\"\u003e\u003c!-- [if !supportLists]--\u003e\u003cspan style=\"font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol; mso-bidi-font-weight: bold;\"\u003e\u003cspan style=\"mso-list: Ignore;\"\u003e·\u003cspan style=\"font: 7.0pt 'Times New Roman';\"\u003e       \u003c\/span\u003e\u003c\/span\u003e\u003c\/span\u003e\u003c!--[endif]--\u003eOffers the first book-length introduction to simple type theory as a predicate logic\u003c\/p\u003e\r\n\u003cp style=\"margin-left: .5in; text-indent: -.25in; mso-list: l0 level1 lfo1;\"\u003e\u003c!-- [if !supportLists]--\u003e\u003cspan style=\"font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol; mso-bidi-font-weight: bold;\"\u003e\u003cspan style=\"mso-list: Ignore;\"\u003e·\u003cspan style=\"font: 7.0pt 'Times New Roman';\"\u003e       \u003c\/span\u003e\u003c\/span\u003e\u003c\/span\u003e\u003c!--[endif]--\u003eProvides the reader with a logic that is close to mathematical practice\u003c\/p\u003e\r\n\u003cp style=\"margin-left: .5in; text-indent: -.25in; mso-list: l0 level1 lfo1;\"\u003e\u003c!-- [if !supportLists]--\u003e\u003cspan style=\"font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol; mso-bidi-font-weight: bold;\"\u003e\u003cspan style=\"mso-list: Ignore;\"\u003e·\u003cspan style=\"font: 7.0pt 'Times New Roman';\"\u003e       \u003c\/span\u003e\u003c\/span\u003e\u003c\/span\u003e\u003c!--[endif]--\u003eIncludes a module system for building libraries of mathematical knowledge\u003c\/p\u003e\r\n\u003cp style=\"margin-left: .5in; text-indent: -.25in; mso-list: l0 level1 lfo1;\"\u003e\u003c!-- [if !supportLists]--\u003e\u003cspan style=\"font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol; mso-bidi-font-weight: bold;\"\u003e\u003cspan style=\"mso-list: Ignore;\"\u003e·\u003cspan style=\"font: 7.0pt 'Times New Roman';\"\u003e       \u003c\/span\u003e\u003c\/span\u003e\u003c\/span\u003e\u003c!--[endif]--\u003eEmploys two semantics, one for mathematics and one for logic\u003c\/p\u003e\r\n\u003cp style=\"margin-left: .5in; text-indent: -.25in; mso-list: l0 level1 lfo1;\"\u003e\u003c!-- [if !supportLists]--\u003e\u003cspan style=\"font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol; mso-bidi-font-weight: bold;\"\u003e\u003cspan style=\"mso-list: Ignore;\"\u003e·\u003cspan style=\"font: 7.0pt 'Times New Roman';\"\u003e       \u003c\/span\u003e\u003c\/span\u003e\u003c\/span\u003e\u003c!--[endif]--\u003eEmphasizes the model-theoretic view of predicate logic\u003c\/p\u003e\r\n\u003cp style=\"margin-left: .5in; text-indent: -.25in; mso-list: l0 level1 lfo1;\"\u003e\u003c!-- [if !supportLists]--\u003e\u003cspan style=\"font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol; mso-bidi-font-weight: bold;\"\u003e\u003cspan style=\"mso-list: Ignore;\"\u003e·\u003cspan style=\"font: 7.0pt 'Times New Roman';\"\u003e       \u003c\/span\u003e\u003c\/span\u003e\u003c\/span\u003e\u003c!--[endif]--\u003ePresents several important topics, such as definite description and theory morphisms, not usually found in standard logic textbooks\u003c\/p\u003e\r\n\u003cp\u003eAimed at students of mathematics and computing at the graduate or upper-undergraduate level, this book is well suited for mathematicians, computing professionals, engineers, and scientists who need a \u003cem\u003epractical\u003c\/em\u003e logic for expressing and reasoning about mathematical ideas.\u003c\/p\u003e\r\n\u003cp\u003e\u003cstrong\u003eWilliam M. Farmer\u003c\/strong\u003e is a Professor in the Department of Computing and Software at McMaster University in Hamilton, Ontario, Canada.\u003c\/p\u003e\r\n\u003cp class=\"MsoNormal\"\u003e \u003c\/p\u003e\r\n\u003cp class=\"MsoNormal\"\u003e \u003c\/p\u003e\r\n\u003cp class=\"MsoNormal\"\u003e \u003c\/p\u003e\r\n\u003cp class=\"MsoNormal\"\u003e \u003c\/p\u003e\r\n\u003cp class=\"MsoNormal\"\u003e \u003c\/p\u003e\r\n\u003cp class=\"MsoNormal\"\u003e \u003c\/p\u003e\r\n\u003cp class=\"MsoNormal\" style=\"text-align: center;\" align=\"center\"\u003e \u003c\/p\u003e\n\u003c\/div\u003e\u003cdiv\u003e\n\u003cp\u003eWilliam M. Farmer has 40 years of experience working in industry and\u003cbr\u003eacademia in computing and mathematics.  He received a B.A. in\u003cbr\u003emathematics from the University of Notre Dame in 1978 and an M.A. in\u003cbr\u003emathematics in 1980, an M.S. in computer sciences in 1983, and a\u003cbr\u003ePh.D. in mathematics in 1984 from the University of Wisconsin-Madison.\u003cbr\u003eHe is currently a Professor in the Department of Computing and\u003cbr\u003eSoftware at McMaster University.  Before joining McMaster in 1999, he\u003cbr\u003econducted research in computer science for twelve years at The MITRE\u003cbr\u003eCorporation in Bedford, Massachusetts, USA and taught computer\u003cbr\u003eprogramming and networking courses for two years at St. Cloud State\u003cbr\u003eUniversity.\u003c\/p\u003e\r\n\u003cp\u003eDr. Farmer's research interests are logic, mathematical knowledge\u003cbr\u003emanagement, mechanized mathematics, and formal methods.  One of his\u003cbr\u003emost significant achievements is the design and implementation of the\u003cbr\u003eIMPS proof assistant, which was done at MITRE in partnership with\u003cbr\u003eDr. Joshua Guttman and Dr. Javier Thayer.  His work on IMPS has led to\u003cbr\u003eresearch on developing practical logics based on simple type theory\u003cbr\u003eand NGB set theory and on organizing mathematical knowledge as a\u003cbr\u003enetwork of interconnected axiomatic theories.  He also has\u003cbr\u003ecollaborated with Dr. Jacques Carette for several years at McMaster on\u003cbr\u003edeveloping a framework for integrating axiomatic and algorithmic\u003cbr\u003emathematics.  As part of this research, Dr. Farmer has investigated\u003cbr\u003ehow to reason about the interplay of syntax and semantics, as\u003cbr\u003eexhibited in syntax-based mathematical algorithms like symbolic\u003cbr\u003edifferentiation, within a logic equipped with global quotation and\u003cbr\u003eevaluation operators.  Dr. Farmer is currently working on developing a\u003cbr\u003ecommunication-oriented approach to formal mathematics as an\u003cbr\u003ealternative to the standard certification-oriented approach employed\u003cbr\u003eusing proof assistants.\u003c\/p\u003e\n\u003c\/div\u003e\u003cbr\u003e\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublication Date: \u003c\/td\u003e\n\u003ctd\u003e24 April 2026\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublisher: \u003c\/td\u003e\n\u003ctd\u003eSpringer Nature Switzerland\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eImprint: \u003c\/td\u003e\n\u003ctd\u003eBirkhäuser\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eISBN-13: \u003c\/td\u003e\n\u003ctd\u003e9783031853548\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eFormat: \u003c\/td\u003e\n\u003ctd\u003ePaperback \/ softback\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePage Count: \u003c\/td\u003e\n\u003ctd\u003e319\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e","brand":"Springer Nature Switzerland","offers":[{"title":"Default Title","offer_id":51027017695372,"sku":"9783031853548","price":58.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783031853548.jpg?v=1782431508","url":"https:\/\/lateknightbooks.com\/products\/9783031853548","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}