000 04343nam a22004935i 4500
001 978-1-4020-2335-4
003 DE-He213
005 20251006084448.0
007 cr nn 008mamaa
008 100301s2005 ne | s |||| 0|eng d
020 _a9781402023354
020 _a99781402023354
024 7 _a10.1007/1-4020-2335-9
_2doi
082 0 4 _a511.3
_223
100 1 _aKamareddine, Fairouz.
_eauthor.
245 1 2 _aA Modern Perspective on Type Theory
_h[electronic resource] :
_bFrom its Origins until Today /
_cby Fairouz Kamareddine, Twan Laan, Rob Nederpelt.
264 1 _aDordrecht :
_bSpringer Netherlands,
_c2005.
300 _aXIV, 360 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aApplied Logic Series,
_x1386-2790 ;
_v29
505 0 _aThe Evolution of Type Theory until the 1940s -- Prehistory -- Type theory in Principia Mathematica -- Deramification -- Propositions as Types, Pure Type Systems, AUTOMATH -- Propositions as Types and Pure Type Systems -- The pre-PAT RTT and STT in PAT-style -- A Correspondence between RTT and the system Nuprl -- Automath -- Extensions of Pure Type Systems -- Pure Type Systems with definitions -- The Barendregt cube with parameters -- Pure Type Systems with parameters and definitions.
520 _a`Towards the end of the nineteenth century, Frege gave us the abstraction principles and the general notion of functions. Self-application of functions was at the heart of Russell's paradox. This led Russell to introduce type theory in order to avoid the paradox. Since, the twentieth century has seen an amazing number of theories concerned with types and functions and many applications. Progress in computer science also meant more and more emphasis on the use of logic, types and functions to study the syntax, semantics, design and implementation of programming languages and theorem provers, and the correctness of proofs and programs. The authors of this book have themselves been leading the way by providing various extensions of type theory which have been shown to bring many advantages. This book gathers much of their influential work and is highly recommended for anyone interested in type theory. The main emphasis is on: - Types: from Russell to Ramsey, to Church, to the modern Pure Type Systems and some of their extensions. - Functions: from Frege, to Russell to Church, to Automath and the use of functions in mathematics, programming languages and theorem provers. - The role of types in logic: Kripke's notion of truth, the evolution and role of the propositions as types concept and its use in logical frameworks. - The role of types in computation: extensions of type theories which can better model proof checkers and programming languages are given. The first part of the book is historical, yet at the same time, places historical systems (like Russell's RTT) in the modern setting. The second part deals with modern type theory as it developed since the 1940s, and with the role of propositions as types (or proofs as terms), but at the same time, places another historical system (the proof checker Automath) in the modern setting. The third part uses this bridging in the first two parts between historical and modern systems to propose new systems that bring more advantages together. This book has much to offer to mathematicians, logicians and to computer scientists in general. It will have considerable influence for many years to come.' - Henk Barendregt
650 0 _aMATHEMATICS.
650 0 _aLOGIC.
650 0 _aCOMPUTER SCIENCE.
650 0 _aLOGIC, SYMBOLIC AND MATHEMATICAL.
650 1 4 _aMATHEMATICS.
650 2 4 _aMATHEMATICAL LOGIC AND FOUNDATIONS.
650 2 4 _aMATHEMATICS OF COMPUTING.
650 2 4 _aLOGIC.
700 1 _aLaan, Twan.
_eauthor.
700 1 _aNederpelt, Rob.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781402023347
830 0 _aApplied Logic Series,
_x1386-2790 ;
_v29
856 4 0 _uhttp://dx.doi.org/10.1007/1-4020-2335-9
_zVer el texto completo en las instalaciones del CICY
912 _aZDB-2-SMA
942 _2ddc
_cER
999 _c60225
_d60225