LEADER 04241nam 22006855 450 001 9910639881303321 005 20251202151132.0 010 $a9783031211126$b(electronic bk.) 010 $z9783031211119 024 7 $a10.1007/978-3-031-21112-6 035 $a(MiAaPQ)EBC7167772 035 $a(Au-PeEL)EBL7167772 035 $a(CKB)25936578500041 035 $a(DE-He213)978-3-031-21112-6 035 $a(PPN)26781044X 035 $a(EXLCZ)9925936578500041 100 $a20230101d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSimple Type Theory $eA Practical Logic for Expressing and Reasoning About Mathematical Ideas /$fby William M. Farmer 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2023. 215 $a1 online resource (309 pages) 225 1 $aComputer Science Foundations and Applied Logic,$x2731-5762 311 08$aPrint version: Farmer, William M. Simple Type Theory Cham : Springer International Publishing AG,c2023 9783031211119 327 $a1 Introduction -- 2 Answers to Readers? Questions -- 3 Preliminary Concepts -- 4 Syntax -- 5 Semantics -- 6 Additional Notation -- 7 Beta-reduction and Substitution -- 8 Proof Systems -- 9 Theories -- 10 Sequences -- 11 Developments -- 12 Real Number Mathematics -- 13 Morphisms 14 Alonzo Variants -- 15 Software Support. 330 $aThis unique textbook, in contrast to a standard logic text, provides the reader with a logic that actually can be used in practice to express and reason about mathematical ideas. The book is an introduction to simple type theory, a classical higher-order version of predicate logic that extends first-order logic. It presents a practice-oriented logic called Alonzo that is based on Alonzo Church's formulation of simple type theory known as Church's type theory. Unlike traditional predicate logics, Alonzo admits undefined expressions. The book illustrates, using Alonzo, how simple type theory is suited ideally for reasoning about mathematical structures and constructing libraries of mathematical knowledge. Topics and features: Offers the first book-length introduction to simple type theory as a predicate logic Provides the reader with a logic that is close to mathematical practice Presents the tools needed to build libraries of mathematical knowledge Employs two semantics, one for mathematics and one for logic Emphasizes the model-theoretic view of predicate logic Includes several important topics, such as definite description and theory morphisms, not usually found in standard logic textbooks Aimed at students of computing and mathematics at the graduate or upper-undergraduate level, this book is also well-suited for mathematicians, computing professionals, engineers, and scientists who need a practical logic for expressing and reasoning about mathematical ideas. William M. Farmer is a Professor in the Department of Computing and Software at McMaster University in Hamilton, Ontario, Canada. 410 0$aComputer Science Foundations and Applied Logic,$x2731-5762 606 $aComputer science 606 $aLogic, Symbolic and mathematical 606 $aComputational complexity 606 $aReasoning 606 $aSet theory 606 $aComputer Science Logic and Foundations of Programming 606 $aMathematical Logic and Foundations 606 $aComputational Complexity 606 $aFormal Reasoning 606 $aSet Theory 615 0$aComputer science. 615 0$aLogic, Symbolic and mathematical. 615 0$aComputational complexity. 615 0$aReasoning. 615 0$aSet theory. 615 14$aComputer Science Logic and Foundations of Programming. 615 24$aMathematical Logic and Foundations. 615 24$aComputational Complexity. 615 24$aFormal Reasoning. 615 24$aSet Theory. 676 $a004.0151 676 $a511.3 700 $aFarmer$b William Michael$01357617 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910639881303321 996 $aSimple type theory$93364018 997 $aUNINA