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Combinatory Logic
V.E.Wolfengagen
Combinatory
Logic
inProgramming
Library“JurInfoR”
Foundedin1994
Series:ComputerScienceandInformation
Technologies
Project:
ApplicativeComputationalSystems
ProjectLeader,Dr.
L.Yu.Ismailova
Publishedontheoccasionof60thanniversaryofMoscowEngineering
PhysicsInstitute
InstituteforContemporaryEducation
“JurInfoR-MSU”
DepartmentofAdvancedComputerStudies
andInformationTechnologies
V.E.Wolfengagen
COMBINATORY
LOGIC
inPROGRAMMING
Computationswithobjectsthroughexamplesandexercises
2ndedition
•
Moscow
“CenterJurInfoR”Ltd.
2003
•
LBC32.97
UDC004
B721
Libraryof“JurInfoR”
Foundedin1994
Series:ComputerScienceandInformation
Technologies
V.E.Wolfengagen
Combinatorylogicinprogramming.Computationswithob-
jectsthroughexamplesandexercises.
—2-nded.—Moscow.:
Center“JurInfoR”,2003.—
X
+
337
p.
ISBN5-89158-101-9
Thebookisintendedforcomputersciencestudents,programmers
andprofessionalswhohavealreadygotacquaintedwiththebasic
coursesandbackgroundondiscretemathematics.Itmaybeused
asatextbookforgraduatecourseontheoreticalcomputerscience.
Thebookintroducesareadertotheconceptualframeworkforthink-
ingaboutcomputationswiththeobjects.Theseveralareasofthe-
oreticalcomputersciencearecovered,includingthefollowing:type
freeandtyped-calculusandcombinatorylogicwithapplications,
evaluationofexpressions,computationsinacategory.Thetopics,
coveredinthebookaccumulatedmuchexperienceinteachingthese
subjectsingraduatecomputersciencecourses.
Arichsetofexamplesandexercises,includingsolutions,hasbeen
preparedtostimulatetheselfstudyingandtomakeeasierthejobof
instructor.
ISBN5-89158-101-9
c V.E.Wolfengagen,1987–2003
c Center“JurInfoR”,1997–2003
Center“JurInfoR”
InstituteforContemporaryEducation“JurInfoR-MSU”
Fax:+7(095)956-25-12.E-mail:
vew
@
jmsuice.msk.ru
Contents
Prefaceoftheeditorsoftheseries
1
SpecialPreface
3
Thespectrumofproblems
5
Prefacetothefirstedition
7
Prefacetothesecondedition
12
Introduction
18
1Preliminaries
27
1.1Thespectrumofideas
................. 29
1.2Layoutofachapter
................... 30
1.3State-of-the-artinanarea
............... 32
1.4Typicaltask
....................... 35
1.5Variantsoftask
..................... 37
1.6Arecommendedorderofsolvingthetasks
....... 44
2DerivationofObject
45
2.1Principleofcombinatorycompleteness
........ 46
2.1.1Combinatorycharacteristic
.......... 46
2.1.2Systemsofconcepts
.............. 47
V
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