LEADER 04420nam 22006615 450 001 9910999687703321 005 20250423130212.0 010 $a3-031-85352-0 024 7 $a10.1007/978-3-031-85352-4 035 $a(CKB)38586596600041 035 $a(DE-He213)978-3-031-85352-4 035 $a(MiAaPQ)EBC32027700 035 $a(Au-PeEL)EBL32027700 035 $a(EXLCZ)9938586596600041 100 $a20250423d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 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 $a2nd ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Birkhäuser,$d2025. 215 $a1 online resource (XXIX, 319 p. 11 illus., 5 illus. in color.) 225 1 $aComputer Science Foundations and Applied Logic,$x2731-5762 311 08$a3-031-85351-2 327 $aChapter 1 Introduction -- Chapter 2 Answers to Readers? Questions -- Chapter 3 Preliminary Concepts -- Chapter 4 Syntax -- Chapter 5 Semantics -- Chapter 6 Additional Notation -- Chapter 7 Beta-reduction and Substitution -- Chapter 8 Proof Systems -- Chapter 9 Theories -- Chapter 10 Inductive Sets and Types -- Chapter 11 Sequences -- Chapter 12 Developments -- Chapter 13 Real Number Mathematics -- Chapter 14 Morphisms -- Chapter 15 Alonzo Variants -- Chapter 16 Software Support. 330 $aThis unique textbook, in contrast to a standard logic text, provides the reader with a logic that can be used in practice to express and reason about mathematical ideas. The book is an introduction to simple type theory, a classical higher-order version of predicate logic that extends first-order logic. It presents a practice-oriented logic called Alonzo that is based on Alonzo Church's formulation of simple type theory known as Church's type theory. Unlike traditional predicate logics, Alonzo admits undefined expressions. The book illustrates using Alonzo how simple type theory is suited ideally for reasoning about mathematical structures and constructing libraries of mathematical knowledge. For this second edition, more than 400 additions, corrections, and improvements have been made, including a new chapter on inductive sets and types. Topics and features: · Offers the first book-length introduction to simple type theory as a predicate logic · Provides the reader with a logic that is close to mathematical practice · Includes a module system for building libraries of mathematical knowledge · Employs two semantics, one for mathematics and one for logic · Emphasizes the model-theoretic view of predicate logic · Presents several important topics, such as definite description and theory morphisms, not usually found in standard logic textbooks Aimed at students of mathematics and computing at the graduate or upper-undergraduate level, this book is well suited for mathematicians, computing professionals, engineers, and scientists who need a practical logic for expressing and reasoning about mathematical ideas. William M. Farmer is a Professor in the Department of Computing and Software at McMaster University in Hamilton, Ontario, Canada. . 410 0$aComputer Science Foundations and Applied Logic,$x2731-5762 606 $aComputer science 606 $aSet theory 606 $aMathematical logic 606 $aComputational complexity 606 $aReasoning 606 $aComputer Science Logic and Foundations of Programming 606 $aSet Theory 606 $aMathematical Logic and Foundations 606 $aComputational Complexity 606 $aFormal Reasoning 615 0$aComputer science. 615 0$aSet theory. 615 0$aMathematical logic. 615 0$aComputational complexity. 615 0$aReasoning. 615 14$aComputer Science Logic and Foundations of Programming. 615 24$aSet Theory. 615 24$aMathematical Logic and Foundations. 615 24$aComputational Complexity. 615 24$aFormal Reasoning. 676 $a004.0151 700 $aFarmer$b William M$4aut$4http://id.loc.gov/vocabulary/relators/aut$01357617 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910999687703321 996 $aSimple type theory$93364018 997 $aUNINA