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1. 03Dxx
Computability and recursion theory for intuitionistic and similar approaches see 03F55; 03D50 Recursive equivalence types of sets and structures, isols
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Computability and recursion theory
  • 03D03 Thue and Post systems, etc. 03D05 Automata and formal grammars in connection with logical questions [See also 03D10 Turing machines and related notions [See also 03D15 Complexity of computation [See also 03D20 Recursive functions and relations, subrecursive hierarchies 03D25 Recursively (computably) enumerable sets and degrees 03D28 Other Turing degree structures 03D30 Other degrees and reducibilities 03D35 Undecidability and degrees of sets of sentences 03D40 Word problems, etc. [See also 03D45 Theory of numerations, effectively presented structures [See also ; for intuitionistic and similar approaches see 03D50 Recursive equivalence types of sets and structures, isols 03D55 Hierarchies 03D60 Computability and recursion theory on ordinals, admissible sets, etc. 03D65 Higher-type and set recursion theory 03D70 Inductive definability 03D75 Abstract and axiomatic computability and recursion theory 03D80 Applications of computability and recursion theory 03D99 None of the above, but in this section

2. 03Dxx
03D50, Recursive equivalence types of sets and structures, isols. 03D55, Hierarchies. 03D60, Computability and recursion theory on ordinals, admissible sets
Computability and recursion theory Thue and Post systems, etc. Automata and formal grammars in connection with logical questions
[See also Turing machines and related notions
[See also Complexity of computation
[See also Recursive functions and relations, subrecursive hierarchies Recursively (computably) enumerable sets and degrees Other Turing degree structures Other degrees and reducibilities Undecidability and degrees of sets of sentences Word problems, etc.
[See also Theory of numerations, effectively presented structures
[See also ; for intuitionistic and similar approaches see Recursive equivalence types of sets and structures, isols Hierarchies Computability and recursion theory on ordinals, admissible sets, etc. Higher-type and set recursion theory Inductive definability Abstract and axiomatic computability and recursion theory Applications of computability and recursion theory None of the above, but in this section

3. Sachgebiete Der AMS-Klassifikation: 00-09
See also {03C57} 03D50 Recursive equivalence types of sets and structures, isols 03D55 Hierarchies 03D60 Recursion theory on ordinals, admissible sets,
Sachgebiete der AMS-Klassifikation: 00-09
nach 90-99 Weiter nach 10-19 Suche in allen Klassifikationen
01-XX 03-XX 04-XX 05-XX 06-XX 08-XX
nach 90-99 Weiter nach 10-19 Suche in allen Klassifikationen

4. MathNet-Mathematical Subject Classification
03D45, Theory of numerations, effectively presented structures See also 03C57. 03D50, Recursive equivalence types of sets and structures, isols

5. HeiDOK
03D45 Theory of numerations, effectively presented structures ( 0 Dok. ) 03D50 Recursive equivalence types of sets and structures, isols ( 0 Dok.

6. MSC 2000 : CC = Equivalence
Question CC = equivalence. 03XX Mathematical logic and foundations. 03D50 Recursive equivalence types of sets and structures, isols

7. List KWIC DDC22 510 And MSC+ZDM E-N Lexical Connection
isolated (locallymaximal) invariant sets gradient-like and recurrent behavior; 37B35 isols Recursive equivalence types of sets and structures, 03D50
intersection multiplicities # intersection theory, characteristic classes,
intersection representations, etc.) # graph representations (geometric and
intersection theorems) # homological conjectures (
intersection theory, characteristic classes, intersection multiplicities
intersection, equivariant, Lawson, Deligne (co)homologies) # other algebro-geometric (co)homologies (e.g.,
intersections # complete
intersections # products and
intersections and determinantal ideals # linkage, complete
interval (piecewise continuous, continuous, smooth) # maps of the
interval analysis # error analysis and
interval analysis # general methods in interval and finite arithmetic intervals # boundary values on infinite intervals # sums over arbitrary intuitionistic logic) # subsystems of classical logic (including intuitionistic mathematics invariance and symmetry properties invariance principles # functional limit theorems; invariant attracting sets # inertial manifolds and other invariant elements) # center, normalizer ( invariant manifold theory invariant manifolds invariant manifolds and their bifurcations, reduction # symmetries and conservation laws, reverse symmetries

8. General General Mathematics Mathematics For Nonmathematicians
Properties of classes of models Settheoretic model theory Effective and approaches see 03F55 Recursive equivalence types of sets and structures,

9. Table Of Contents For Discrete Structures, Logic, And Computability, Second Edit
Cartesian Products of sets. 3.2 Recursive Functions and Procedures equivalence · Truth Functions and Normal Forms · Complete sets of Connectives

10. Catalog Of Courses
Data types, control structures, concurrency, declarations, procedures. Recursion and Recursive definitions. . Recursive and Recursively enumerable sets.
Catalog of Computer Science Courses CS 111, Introduction to Computer Science and Programming, 4 cr, 3 cl hrs, 3 lab hrs Corequisite: MATH 103 or equivalent Introduction to the discipline of computer science: Computer architecture, operating systems and networks, automata and models of computation, programming languages and compilers, data structures, algorithms, databases, security and information assurance, artificial intelligence, graphics, and social/ethical issues of computing. The lab will focus on an introduction to programming in a structured language (e.g., C): problem solving, algorithm development, top-down design, modular programming, control structures including selection, iteration and recursion, data types including arrays, strings, and dynamic structures. Concepts implemented through extensive programming using good programming style. (Same as IT 111) CS 122, Algorithms and Data Structures, 3 cr, 3 cl hrs Prerequisite: CS 111 Fundamental data structures such as linked lists, trees, and hash tables. Algorithms for sorting, searching, and other fundamental operations. Introduction to recursive algorithms. (Same as IT 122) CS 209, Programming Language Practicum, 1 cr, 3 lab hrs

11. Computation Structures Group
Specification and Implementation of Resilient, Atomic Data types W. Weihl, B. Liskov . The Recursive equivalence of the Reachability Problem and the
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Nirav Dave, Michael Pellauer, Steve Gerding, Arvind Formal Methods and Models for Codesign (MEMOCODE 2006) MIT Computer Science and Artificial Intelligence Laboratory (CSAIL) Napa Valley, CA, USA. July 2006 Memo-501 From WiFI to WiMAX: Techniques for IP Reuse Across Different OFDM Protocols Man Cheuk Ng, Muralidaran Vijayaraghavan, Gopal Raghavan, Nirav Dave, Jamey Hicks, Arvind Formal Methods and Models for Codesign (MEMOCODE 2007) MIT Computer Science and Artificial Intelligence Laboratory (CSAIL) Nice, France. May 2007 Memo-500 Scheduling as Rule Composition Nirav Dave, Arvind, Michael Pellauer Formal Methods and Models for Codesign (MEMOCODE 2007) MIT Computer Science and Artificial Intelligence Laboratory (CSAIL) Nice, France. May 2007

12. Intro To Programming Languages
1.3.1 Data types and type equivalence 12. 1.3.2 Type checking and type conversion 13 . 2.7.1 Loop structures versus Recursive structures 95
Introduction to Programming Languages Programming in C, C++, Scheme, Prolog, C#, and SOA Yinong Chen and Wei-Tek Tsai Arizona State University Contents Preface (Second Edition) ix Preface (First Edition) xi ... Index

13. Anil Nerode-Bibliography
1990 Nerode, A.; Remmel, J. B. Polynomially isolated sets. Recursion . 1966 Nerode, A. Combinatorial series and Recursive equivalence types. Fund.
Nerode Bibliography This bibliography contains papers, books, books edited, and a few abstracts and unpublished reports. Though sorted by year, it remains to be sorted by subject and alphabetic order. I never used the system in which the order of authors is an order based on seniority or purported size of contribution, so joint authors are listed usually in alphabetical order. 2001: Ganesh, M., Nerode., A , Srivastava, J., Wijesekera, D., Normal Forms and Syntactic Completeness Proofs for Functional Independencies , J. Theoretical Computer Science, December 2001. 2001: Kohn, W.; Nerode, A.; Agent Control, Enterprise Models, and Supply Chain Systems (book in prep.) 2000: Khoussainov, B.; Nerode, A., Automata Theory and Its Applications,Birkhauser, 2001, 430pp.ISBN 3-7643-4207-2 2000: Nerode, A.; Odifreddi, G.; Constructive Logics and Lambda Calculi, 500pp. (book in prep.) 2000: Nerode, A.; Foreword to Principles of Modeling and Asynchronous Distributed Simulation of Complex Systems, by Sumit Ghosh, IEEE Press. To appear early 2000. 2000: Ge, X.; Ghosh, S.; Kohn, W.; Lee, T.; Lu, J.; Nerode, A.; A mathematical framework for asynchronous, distributed, decision-making systems with semi-autonomous entities: algorithm synthesis, simulation, and evaluation, IEICE Transactions on Fundamentals, to appear.

14. JSTOR Recursive Equivalence Types And Groups
Recursive equivalence types and GROUPS 15 The following proposition shows that the notion of the group of all finite permutations of a set of RET A is<13:RETAG>2.0.CO;2-U

15. Finite Sets: Counting, Recursion, And Logic, Next Steps
We examine three ways to define sets. The first is by Recursive definition, the second is by Discrete Mathematics and Computational structures, Part 2
This Microworld is the second half of a 12-week course in Discrete Mathematics. The term "Discrete Mathematics" in this Microworld will refer loosely to the collection of techniques, ideas, and constructions that have evolved over the years to describe artificial systems, and in particular, those systems from which the modern theories of computing have evolved. So, for example, an excellent model for our subject is the Turing Machine, or, equivalently, the lambda-calculus of Alonzo Church. In fact, the lambda-calculus is the conceptual basis for the computer language, LISP , which is the language in which this Microworld is written. We recommend that you follow the 9 readings of this Microworld in the order in which they appear below, beginning with "Iteration and Recursion." You may read the 72-page collection of lectures either within the Microworld, or as a Word 2000 document. To download the Lectures as Word Document, click here , then extract the file to your disk. Also, to download the Laboratory Instructions as Word Document, click

16. Springer Online Reference Works
Those types of Recursive equivalences that do not contain sets with infinite 7, J.C.E. Dekker, J. Myhill, Recursive equivalence types Publ. Math.

Encyclopaedia of Mathematics
Article referred from
Article refers to
Recursive set theory
A branch of the theory of recursive functions (cf. Recursive function ) that examines and classifies subsets of natural numbers from the point of view of algorithms, and also studies the structures arising as a result of such a classification. For each subset of the set of all natural numbers , the following decision problem can be formulated: Is there an algorithm that permits one to decide, for any , whether or not is a member of The mathematical posing of problems of this kind, and the development of recursive set theory, only became possible in the 's after the successful formalization of the intuitive concept of an (algorithmically) computable function . The range of values of such functions forms the family of recursively-enumerable sets (cf. also Enumerable set ). Sets for which the problem formulated above is solvable are called recursive. In fact, is recursive if and only if and are both recursively enumerable. The first examples of non-recursive recursively-enumerable sets turned out to be the so-called creative sets: a recursively-enumerable set is called creative (cf. also

17. Re: Type Names Vs Type Structure
Is it possible to use something similar in a programming language so that equivalence of Recursive types is based on structure and not on name?
[Prev] [Next] [Index] [Thread]
Re: Type names vs type structure

18. Courses Offered By CSE Department, IIT Kanpur
Recursive and Recursively enumerable sets models turing machines, grammars, Recursive functions, their equivalence. Church s thesis.
Course Descriptions
ESc 101: Fundamentals of Computing
This is a compulsory course for ALL undergraduate students. For course description, please see the undergraduate bulletin. Back to list of courses
CS 100: Introduction to Profession
Course Contents:
Books and References:
Back to list of courses
CS 201: Discrete Mathematics
Structure: 3-0-0-0 Academic Load=9 Weightage=3
Course Contents:
Notion of proof: proof by counter-example, the contrapositive, proof by contradiction, inductive proofs. Algebra: Motivation of algebraic structures; review of basic group theory with emphasis to finite groups: subgroups and group homomorphism, Lagrange's theorem. Commutative rings, ideals. Finite fields and their elementary properties. Some CS applications (e.g., RSA, error correcting codes). Combinatorics: Basic counting techniques, pigeon-hole principle, recurrence relations, generating functions, Polya's counting theorem. Basics of graph theory. Introduction to probabilistic method in combinatorics. Formal logic: Propositional logic: proof system, semantics, completeness, compactness. Length of proofs, polynomial size proofs, efficiency of proof systems. First order logic: models, proof system, compactness. Examples of formal proofs in, say, number theory or group theory. Some advanced topics. E.g., CS application of logic, introduction to modal and temporal logics, Or, formal number theory including incompleteness theorem, Or, elements of proof theory including cut elimination, Or zero-one law for first order logic.

19. Computer Science
Basic concepts of data types (strings, arrays, records, sets, files); . CSC 7300 or equivalent. Data structures and algorithm design techniques for
Dept - RUBRIC General education courses are marked with stars ( 1100 Computers in Society (3) Prereq.: credit in MATH 1020/1021 or registration in MATH 1023. 2 hrs. lecture; 2 hrs. lab . Introduction to computers, their applications, and impact on people and social institutions; the Internet, E-mail, news groups, ftp, telnet, World Wide Web, multimedia, word processing, spreadsheets, databases. 1248 Introduction to Programming With Applications in Statistics (3) Prereq.: MATH 1020/1021 or sufficiently high score on the mathematics placement examination to qualify for MATH 1022 or 1431. Credit will not be given for both this course and CSC 1250. Not for degree credit for computer science majors . Computer programming using the Pascal language with applications in elementary statistics. 1250 Introduction to Computer Science I (3) Prereq.: credit or registration in MATH 1022 or 1023. Credit will not be given for this course and CSC 1248 or 1253 . Fundamentals of problem solving, program design, algorithms, and programming using a high-level language. 1251 Introduction to Computer Science II (3) Prereq.: CSC 1250 and credit or registration in MATH 1550

20. Data Structures And Programming Lecture 1
Data types vs. Data structures. A data type is a welldefined collection of data of a set with such operations as intersection, union, and equivalence.
Next: About this document Up: My Home Page
Data Structures and Programming
Lecture 1
Steven S. Skiena Why Data Structures? In my opinion, there are only three important ideas which must be mastered to write interesting programs.
  • Iteration - Do, While, Repeat, If
  • Data Representation - variables and pointers
  • Subprograms and Recursion - modular design and abstraction
At this point, I expect that you have mastered about 1.5 of these 3. It is the purpose of Computer Science II to finish the job. Data types vs. Data Structures A data type is a well-defined collection of data with a well-defined set of operations on it. A data structure is an actual implementation of a particular abstract data type. Example: The abstract data type Set has the operations EmptySet(S), Insert(x,S), Delete(x,S), Intersection(S1,S2), Union(S1,S2), MemberQ(x,S), EqualQ(S1,S2), SubsetQ(S1,S2). This semester, we will learn to implement such abstract data types by building data structures from arrays, linked lists, etc. Modula-3 Programming Control Structures: IF-THEN-ELSE, CASE-OF

21. TLCA 2003 - Abstracts Of Accepted Papers
Observational equivalence and program extraction in the Coq proof assistant . We analyze the interpretation of inductive and coinductive types as sets of
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... Internet TLCA'03 6th International Conference on Typed Lambda Calculi and Applications Valencia, Spain, June 10-12, 2003 ABSTRACTS OF PAPERS ACCEPTED FOR PRESENTATION
    Parameterizations and Fixed-Point Operators on Control Categories Y. Kakutani (Kyoto University, Japan) M. Hasegawa (Kyoto University, Japan) The lambda-mu-calculus features both variables and names, together with their binding mechanisms. This means that constructions on open terms are necessarily parameterized in two different ways for both variables and names. Semantically, such a construction must be modeled by a bi-parameterized family of operators. In this paper, we study these bi-parameterized operators on Selinger's categorical models of the lambda-mu-calculus called control categories. The overall development is analogous to that of Lambek's functional completeness of cartesian closed categories via polynomial categories. As a particular and important case, we study parameterizations of uniform fixed-point operators on control categories, and show bijective correspondences between parameterized fixed-point operators and non-parameterized ones under uniformity conditions. Inductive types in the Calculus of Algebraic Constructions F. Blanqui

22. Joy: Forth's Functional Cousin
The aggregate types comprise sets, strings, lists and files. Literals of any type cause a . As in other languages, definitions can be Recursive in Joy.
Global Utilities Search: Global Navigation Presented at the 17-th EuroForth Conference (23-26 November 2001, Schloss Dagstuhl, Saarbruecken, Germany) by Reuben Thomas, on my behalf and with my thanks.
Synopsis of the language Joy
This paper is intended as an introduction for Forth programmers.
To add two integers, say 2 and 3, and to write their sum, you type the program This is how it works internally: the first numeral causes the integer 2 to be pushed onto a stack. The second numeral causes the integer 3 to be pushed on top of that. Then the addition operator pops the two integers off the stack and pushes their sum, 5. So the notation looks like ordinary postfix. The Joy processor reads programs like the above until they are terminated by a period. Only then are they executed. In the default mode the item on the top of the stack (5 in the example) is then written to the output file, which normally is the screen. To compute the square of an integer, it has to be multiplied by itself. To compute the square of the sum of two integers, the sum has to be multiplied by itself. Preferably this should be done without computing the sum twice. The following is a program to compute the square of the sum of 2 and 3:

23. Course Descriptions, Computer Science And Computer Information Sciences, Miami,
Data types, control structures, subprograms, scope, and recursion. . Instruction sets. CPU structure. The control unit and microprogramming.
@import url(css/BarryGlobal.css); /* IE styles */ School of Arts and Sciences Computer Science (CS) and Computer Information Sciences (CIS) Programs Barry Home
Barry University Search About the Programs Faculty Admissions Financial Aid ... About the Program
Course Descriptions
CAT 102 Basic Computer Applications (3)
This course provides students with basic computer applications training. Hands-on training will be provided in a Windows-based operating environment, electronic mail, the World Wide Web, computerized library skills, word processing and electronic spreadsheets. This course will provide the necessary introductory level training for students who have never used microcomputers and/or applications software. It is a hands-on lab course. No prerequisites. Not acceptable for Computer Science and Mathematics majors. CS 121 Foundations of Computer Science (3)
Historical, logical and mathematical foundations of computer science at an introductory level. Number systems, representation of information, elements of symbolic logic, problem-solving techniques, and models of computing machines. Prerequisites: none. CS 180 Introduction to Computers (3)
An introduction to the main concepts and applications of computers from a liberal arts approach: how everyday ideas can be meaningfully represented by electrical currents which are manipulated inside a computer, computer design and construction, and an introduction to computer languages. This is a first course about computers: what they are, what they can do, what they cannot do, and their history. Ethical-social issues involving computers. Students will be exposed to the use of a variety of computer hardware and software. Not acceptable for the Computer Science major. No prerequisites.

24. Faculty Research And Selected Publications
Associate Professor; Recursive function theory with an emphasis in the theory of Recursive equivalence types, software verification and specification theory
Faculty Research and Selected Publications
Department of Mathematics and Statistics
Bowling Green State University
An expanded listing for the Department's Probabilty and Statistics Faculty is on a separate page. Albert, James H.
Ph.D., Purdue University. Professor; Bayesian analysis, statistical computing and graphics, contingency tables, exploratory data analysis, teaching of statistics, analysis of sports data.
  • Answering questions about baseball using statistics (with B. James and H. Stern), Chance, Bayesian Regression Analysis of Binary and Polychotomous Response Data (with S. Chib), Journal of the American Statistical Association, Teaching Bayesian Statistics Using Sampling Methods and MINITAB, The American Statistician, Bayesian residual analysis for binary response regression models (with S. Chib), Biometrika Bayesian estimation of normal ogive response curves using Gibbs sampling, Journal of Educational Statistics

25. VIUF Proceedings -- SPRING 1994
A VHDL Based Test Environment Including Models for equivalence Fault A Comparison of Recursive and Repetitive Models of Recursive Hardware structures
VIUF Proceedings SPRING 1994
  • A VHDL-based System-Design Methodology
  • An Automatic Test Bench Generation System
  • A VHDL Based Test Environment Including Models for Equivalence Fault Collapsing
  • A Mathematical Level/Strength Model for Synthesizing STD_LOGIC_1164 Values ...
  • VHDL Sign-off Simulation : What Future?
    A VHDL-based System-Design Methodology
    Gajski, Daniel D;
    As methodologies and tools for chip-level design mature, design effort becomes focused on increasingly higher levels of abstraction. We present a methodology and tool for system-level specification, design and refinement, based on VHDL, that results in an executable specification for each system component. The specification for each component can then be synthesized into hardware or compiled to software. We highlight advantages of the proposed methodology compared to current practice.
    An Automatic Test Bench Generation System
    Kapoor, Shekhar; Armstrong, James R; Rao, Sanat R;
    This paper presents an automatic test bench generation system for VHDL behavioral models. Modeler's Assistant, an interactive CAD tool developed at Virginia Tech, gives the graphical representation of a VHDL behavioral model, called a Process Model Graph (PMG). The Process Test Generator (PTG) is used to generate the stimulus/response test sets for individual processes of a PMG. The Hierarchical Behavioral Test Generator (HBTG) accepts the PMG and the test sets produced by PTG as inputs, and then hierarchically constructs a test sequence for the entire model. The test sequence is converted into a test bench by the Test Bench Generator (TBG), and it is then used for simulation of the model. Experimental results show that the test benches generated exercise the models thoroughly.
  • 26. ::UWC Computer Science: Undergraduate 2007::
    Syllabus Sequential structures lists, stacks, queues; Abstract data types and objects; Trees, forests, heaps, sets; Internal searching,
    Courses Undergraduate 2007 Undergraduate Courses - 2007
    1st year courses
    2nd year courses 3rd year courses
    A junior level student will have 3 contact periods per week per subject. In addition there will be 1 tutorial period per week and one practical session of 3 hours. Core Modules: Computer Science modules: COS115 Problem Solving, Algorithms and Programming COS125 Program Development and Programming Techniques MAM111 and MAM121 (first year mainstream Mathematics) Computer Literacy module (COS114) English for Educational Development modules (EED127) Electives: Applied Mathematics is strongly recommended as an elective or any other Science faculty junior modules or modules from other programmes / faculties (time table permitting) e.g. Statistics, Physics, Geology, Information Systems. To top
    Computer Literacy
    COS114 (first semester) or COS124 (second semester)
    (15 credit points) Practical Concepts: Introduction to an operating system, e-mail and the Internet; Applications software including word processing and spreadsheets; introduction to database management; introduction to presentation graphics; the integration of the above mentioned application programs Theoretical Concepts: System programs; data and data organization; Files and records, file management; Principles and usage of basic software; Systems programs; data and data organisation; Computer architecture; The computer marketplace; Local area networks and e-mail; The Internet, data security and control

    27. CCNY: Department Of Computer Science
    Physical implementation of advanced data and storage structures. Recursive and r.e. sets. Prereq CSc 30400 or CSc I2000 or equivalent. 3 hr./wk.; 3 cr.
    Department of
    Computer Science
    G9700: Report
    cr.; Satisfies non-course requirement I0000: Seminars in Computer Science
    Recent developments in computer science. Students report on assigned subjects. Topics to be announced.
    Variable cr. I0102: Database Security and Integrity
    The course will cover topics such as: database concepts, architecture, and models, plus database security and integrity in general. Specific areas include: privacy, models of database security, authorization languages and classes, data integrity, auditing and controls, and enforcement design (IMS, DB2, INGRES; distributed database systems, and object-oriented database systems).
    3 hr./wk.; 3 cr. I0400: Operating Systems
    Underlying theoretical structure of operating systems; input-output and storage systems, data management and processing; assembly and executive systems, monitors; multiprogramming. Prereq: CSc 33200 or an equivalent undergraduate course.
    3 hr./wk.; 3 cr.

    28. TAC Abstracs
    We propose a specific definition and show the equivalence with the notion of a One may show that for nonRecursive types all elements are denotable by a
    The topos of 3-colored graphs The problem of 3 coloring finite undirected graphs is NP-complete and therefore there is interest in the structure of graphs which are and are not 3 colorable. The category of undirected graphs U is a topos. A graph with a given 3 coloring is said to be 3-colored. The category C of 3-colored graphs is is a cocomplete topos, hence also complete. There is an essential geometric morphism between U and C, and the three functors involved have considerable natural appeal. These functors justify two of the heuristics used to quicken algorithms which determine whether or not a 3 coloring exists for argument finite undirected graphs. Indeed, one of these heuristics deserves to be better known. ...
    Finally, we observe that instead of B we might take any pca of the form L/T where T is a theory containing the (obvious) conversion theory for L and itself being containEd in Th(A). This may be considered as a solution of (a variant of) the Longley-Phoa Conjecture claiming that realisability over a term model of untyped lambda-calculus gives rise to a fully abstract model of PCF.

    29. Types (30 Oct. - 8 Nov. 2007) A4 Due Fri 9 Nov., 5pm; A5 To Be
    Type compatibility / type equivalence Compatibility is the more useful .. Pointers and Recursive types pointers serve two purposes efficient (and
    > won't work, because >> is a single token; you have to say pair >. Yuck.) - Some languages (e.g. Ada and C++) allow things other than types to be passed as template arguments: template S; - Implementation C# generics do run-time instantiation. When you say stack , the run-time system invokes the JIT and generates the appropriate code. Don't box native types if they don't need to more efficient. Java doesn't do run-time instantiation. Internally everything is stack " from "list ". The subtle part is conformance of argument and return types. Supose I want to be able to sort things in Java that don't implement Comparable. I could make the comparator be a constructor argument instead of a generic argument: interface Comparator comp; public Sorter(Comparator s = new Sorter s = new Sorter rather than a Comparator . This is fixed in Java using type wildcards: class Sorter comp; public Sorter(Comparator

    30. FLoC '02 - LICS Wednesday July 24th
    Observational equivalence of 3rdorder idealized Algol is decidable Computational adequacy for Recursive types in models of intuitionistic set theory
    LICS on Wednesday Detailed program
    Wednesday July 24th, 2002
    See also the unified by-slot program
    All sessions take place in auditorium 1.
    Session 9
    Chair: Samson Abramsky C.-H. L. Ong, Oxford U, UK
    Observational equivalence of 3rd-order idealized Algol is decidable
    We prove that observational equivalence of 3rd-order finitary Idealized Algol (IA) is decidable using Game Semantics. By modelling state explicitly in our games, we show that the denotation of a term M of this fragment of IA (built up from finite base types) is a compactly innocent strategy-with-state i.e. the strategy is generated by a finite view function f M . Given any such f M , we construct a real-time deterministic pushdown automata (DPDA) that recognizes the complete plays of the knowing-strategy denotation of M . Since such plays characterize observational equivalence, and there is an algorithm for deciding whether any two DPDAs recognize the same language, we obtain a procedure for deciding observational equivalence of 3rd-order finitary IA. This algorithmic representation of program meanings, which is compositional, provides a foundation for model-checking a wide range of behavioural properties of IA and other cognate programming languages. Another result concerns 2nd-order IA with full recursion: we show that observational equivalence for this fragment is undecidable. Martin Hyland, U Cambridge, UK

    31. MFCS 2001 - Invited Talks
    An equivalent definition uses algebraic (or continuous) lattices and partial for defining Recursive functions on inductive data structures such as lists
    MFCS 2001
    26th International Symposium on
    Mathematical Foundations of Computer Science
    August 27 - 31, 2001
    Marianske Lazne, Czech Republic
    Invited Speakers
    Dana S. Scott: A New Category for Semantics
    Peter Buergisser: On Implications between P-NP-Hypotheses: Decision versus Computation in Algebraic Complexity
    Erik D. Demaine: Playing Games with Algorithms: Algorithmic Combinatorial Game Theory

    32. CS 334 Lecture 8
    Why can t we have direct Recursive types in ordinary imperative languages? . Structural equivalence. Same type iff have same structure all same.
    CS 334 Lecture 8
  • Mappings
  • Arrays
  • Function abstractions ...
  • Arrays
    Encompasses functions w/ both infinite and finite domains.
    Function abstractions:
    • What if S were a record instead of an n-tuple?
    Operations: abstraction and application, sometimes composition. What is difference from an array? Efficiency, esp. w/update. update f arg result x = if x = arg then result else f x or
    set of elt_type; Typically implemented as bitset or linked list of elts Operations and relations: All typical set ops, :=, =, subset, .. in .. Why need base set to be primitive type? What if base set records?
    Recursive types:
    Examples: In most lang's built by programmer from pointer types. Sometimes supported by language (e.g. Miranda, Haskell, ML). Why can't we have direct recursive types in ordinary imperative languages? OK if use ref's: list = POINTER TO RECORD first:integer; rest: list END; Recursive types may have many sol'ns E.g. union (int x list) has following sol'ns:
  • finite sequences of integers followed by Nil : e.g.
  • 33. The Journal Of Symbolic Logic, Volume 41
    405418 BibTeX Manuel Lerman types of Simple alpha-Recursively Enumerable sets. 419-426 BibTeX F. Lowenthal equivalence of Some Definitions of
    The Journal of Symbolic Logic , Volume 41
    Volume 41, Number 1, March 1976

    34. CLHS: Glossary-Section T
    1. a binary Recursive data structure made up of conses and atoms the conses are type equivalent adj. (of two types X and Y) having the same elements;
    T t n. 1. a. the boolean representing true. b. the canonical generalized boolean representing true. (Although any object other than nil is considered true as a generalized boolean t is generally used when there is no special reason to prefer one such object over another.) 2. the name of the type to which all objects belong-the supertype of all types (including itself). 3. the name of the superclass of all classes except itself. tag n. 1. a catch tag . 2. a go tag tail n. (of a list ) an object that is the same as either some cons which makes up that list or the atom (if any) which terminates the list . ``The empty list is a tail of every proper list.'' target n. 1. (of a constructed stream ) a constituent of the constructed stream . ``The target of a synonym stream is the value of its synonym stream symbol.'' 2. (of a displaced array ) the array to which the displaced array is displaced. (In the case of a chain of constructed streams or displaced arrays , the unqualified term `` target '' always refers to the immediate target of the first item in the chain, not the immediate target of the last item.) terminal I/O n.

    35. Computing Science Modules
    A pass in Higher Mathematics (or its equivalent) is a prerequisite for all Level 2 Data structures and Algorithms 2. Aims To present the data types
    Level-2 Module descriptions
    Six modules are offered in Level 2, each one consisting of about 20-25 lectures (plus associated tutorials and practicals), running at two lectures per week. A pass in Higher Mathematics (or its equivalent) is a pre-requisite for all Level 2 modules. The modules and their additional pre- and co-requisites are: Module Semi-year Pre/co-requisites Algorithmic Foundations 2 Elementary boolean algebr;
    Functional Programming 2
    CS1P, CS1Q, Algorithmic Foundations 2 Computer Systems 2 CS1P and CS1Q Information Management 2 Intending Single Honours students will take all six modules. Combined Honours students will take at least four modules, including Data Structures and Algorithms 2 and Software Design and Implementation 2. Electronic and Software Engineering students in the Faculty of Engineering will take
    • Computer Systems 2
    • Algorithmic Foundations 2
    • Information Management 2
    Other students make pick and choose. All formal exams will take place at the end of the year. Any enquiries or comments to Michael Jamieson , Course Director or Myra Smith , Teaching Administrator
    Data Structures and Algorithms 2
    Aims: To present the data types commonly used in programming, and the various data structures and algorithms used to implement them efficiently.

    36. Data Structures / Algebraic Semantics
    Most data structure types have three classes of operations constructors, .. A directed graph is a nonRecursive data structure. It consists of a set of
    Data Structures / Algebraic Semantics
    ~ Under Construction ~
    Product Type Constructor
    Natural Numbers
    Stack[Item] List[Item] ... Directed Graph
    An ontology that claims to represent data structures should be able to model the axiomatic semantics of the commonly occurring data structures, such as stacks, arrays, queues, binary trees, trees, s-expressions, nested lists, directed graphs, etc. Most data structure types have three classes of operations: constructors, accessors and tests. When suitably expressive, data structure types should allow for the recursive definitions of functions.
    New Tags and Attributes
    For greater convenience in data structuring and algebraic semantics, we have included src and tgt referencing attributes, in addition to the previous obj referencing attribute, and we have extended the Function element to include a free-standing version. With the src and tgt attributes we can embed functions in object specifications when the ambient object is either the source or target of the function. Most container classes have a parameter type, which is the type of the contained items. In order to accomodate this, a

    37. Types
    Type equivalence. Two unnamed types (sets of objects) are the same if they the same type constructor (recursively) to structurally equivalent types.

    38. Seminars And Talks
    23November-01 (MFG) Number structures and recursion SORT OUT 30-August,10,14,18-September-01 (MFG-short course) $\Omega$-valued sets
    Seminars and talks
    Over the years I must have given hundreds of seminars, talks, and short research courses. Most of these are lost forever. In January 03 I started to keep a record of these. Here is a table of recent seminars where you can find links to the slides and relevant notes where available. Here is a brief description of the content these talks.
    List of seminars given in reverse chronological order
    27-may-07 (Manchester) Galois connections done properly and Classical rings of fractions (two separate topics)
    Slides available for first part.
    15-May-07 and 22-may-07 (Manchester) From rings of fractions to localizations
    A wander around these topics as part of a longish teaching seminar.
    Slides available
    02-May-07 (Leeds) Is the Ackermann function optimal?
    A standard construction, originally due to Ackermann, produces a recursive function that is not primitive recursive. This can be relativized to produce a jump on the poset of degrees up to primitive recursive equivalence. What is there between a degree and its jump? Quite a lot.
    Slides and a write-up available.

    39. Hacettepe University Department Of Mathematics
    Course Content Mathematical logic, sets, axiom of choose and equivalent axioms, .. Course Content Structure types, Algebraic structure of data types,
    Undergraduate Menu Courses Course Descriptions Weekly Course Schedule Undergraduate Program - Course Descriptions MTK 101 Analysis I Course Content: Basic concepts of real numbers; functions, relations, graphics, limit and continuity, properties of continuous functions, tangent and velocity of variation, differentiability, techniques of differentiation, derivatives of Trigonometric functions, chain rule , differentials, Application of derivation maxima and minima, Sketch of graph, mean value theorem, indefinite integrals, substitution methods, definite integral. First fundamental theorem Calculus, Calculus techniques, second fundamental theorem of Calculus, Area of surface of Revolution using definite integral, Volumes by cylindrical shells, length of plane curve. Course credit: MTK 102 Analysis II Course Content: Logarithms and exponential functions, inverse functions, graph of the natural logarithms and exponential functions, the hyperbolic functions, derivation, integral and integral techniques, improper integral, L' Hospital rule, infinite series, sequences, monotone sequences, convergence integral test and the other tests, alternating sequences, conditional convergence, power series, Taylor and Maclourin series, computations using Taylor series. Differentiation and integration of power series, Taylor and Maclourin series, computations using Taylor series. Differentiation and integration of power series, introduction to several variable functions, basic concepts of

    40. Joachim Lambek: The Mathematics Of Sentence Structure
    From the primitive types we form compound types, by the Recursive .. rules (a) to (e) from (1) to (5), so that the two sets of rules are equivalent.
    The mathematics of sentence structure
    The definitions [of the parts of speech] are very far from having attained the degree of exactitude found in Euclidean geometry Otto Jespersen (
  • Introduction Syntactic types Type list for a fragment of English Formal systems ... REFERENCES
  • 1. Introduction
    The aim of this paper is to obtain an effective rule (or algorithm) for distinguishing sentences from nonsentences, which works not only for the formal languages of interest to the mathematical logician, but also for natural languages such as English, or at least for fragments of such languages. An attempt to formulate such an algorithm is implicit in the work of Ajdukiewicz ( . His method, later elaborated by Bar-Hillel ( ), depends on a kind of arithmetization of the so-called parts of speech , here called syntactic types The present paper begins with a new exposition of the theory of syntactic types. It is addressed to mathematicians with at most an amateur interest in linguistics. The choice of sample languages is therefore restricted to English and mathematical logic. For the same reason, technical terms have been borrowed from the field of high school grammar. Only a fragmentary treatment of English grammar is presented here. This should not be taken too seriously, but is meant to provide familiar illustrations for our general methods. The reader should not be surprised if he discovers considerable leakage across the line dividing sentences from nonsentences. It is only fair to warn him that some authorities think that such difficulties are inherent in the present methods

    41. A Neighborhood Of Infinity: Data And Codata
    It allows so much fun variation in the structure of Recursive types. Are these ideas equivalent to recursion and corecursion, or is the similarity just
    A Neighborhood of Infinity
    Saturday, July 14, 2007
    Data and Codata
    In , Hofstadter introduces the programming language Bloop . Bloop is a little like BASIC except that it forces programmers to specify in advance how many times each loop will iterate. As a result, Bloop programs have the handy property that they are guaranteed to terminate. Unfortunately this property also makes it impossible to write something like an operating system in Bloop. To write an OS we need open-ended loops that keep running until the user explicitly chooses to shut the OS down. One solution to this is to write code in Floop . Floop allows us to write unbounded loops, the equivalent of C's . The problem with that, however, is that we can write runaway infinite loops that never terminate and never give us any output. Is there some language that lies between Bloop and Floop that can give us unbounded looping when we need it, but which never allows us to hoist ourselves by our petards by writing runaway loops?
    Wishing no disrepsect to OS writers, at first blush it might seem that the distinction between a runaway loop and an idle OS is too fine - if we can write an infinite loop that does something useful, then surely we can write a useless one too. But it turns out that there is a very elegant and well-principled way to distinguish between these kinds of loops, and this allows us to write open-ended interactive software in a programming language that nonetheless always produces a well-defined output, no matter what the input. In order to do this we need to distinguish between two kinds of data:

    42. Mathematical Structures 2006
    Set theory Transfinite recursion theorem, similarity between posets, ordinal number. Set theory Ordinal numbers, limit ordinals, equivalence of sets,
    Autumn 2006: graduate course
    Name of the course: Mathematical Structures Instructor: Jaikumar Radhakrishnan Lecture timings: Combinatorics: Mondays 9:30am to 10:30am Set Theory: Wednesdays 9:30am to 10:30am Algebra: Fridays 9:30am to 10:30am Text books: [H] Naive set theory by P Halmos, Springer-Verlag [A] Algebra by M Artin, Prentice-Hall India. [HK] K Hoffman and R Kunze, Prentice-Hall India. [An] Combinatorics of finite sets by I Anderson, Oxford Science Publications
    [S] Enumerative combinatorics (Volume I) by RP Stanley
    [B] Combinatorics
    The goal of this course is to introduce the audience to the mathematical structures and the types of reasoning that one might encounter in Computer Science. The topics will be divided into three broad streams: set theory, algebra and combinatorics. In set theory , we will be content with covering the topics given in the text. The idea is to develop familiarity with the axiomatic development of the theory and concepts (e.g., the axiom of choice, Zorn's lemma, transfinite recursion, ordinal numbers, cardinal numbers etc.

    43. Department Of Computer Science - College Of Business - SFASU
    Prerequisite Two years of high school algebra or equivalent. . subprograms, data types, control structures, and describing syntax and semantics.
    Courses In Computer Science
    A student must have a grade of C or better in all courses that are prerequisite to a computer science course before enrolling in that course. Unless otherwise indicated, each course carries three semester hours credit and meets three hours per week. Enrollment in courses numbered 300 or above requires junior standing. Please read our first. 101. Introduction to Computing - A general study of computer types, capabilities, uses, and limitations. Use of operating systems and application software on a microcomputer. Use of network environments to access online resources. Introduction to problem solving using a computer. Prerequisite: Two years of high school algebra or equivalent. Credit not available for students who have taken CSC 121. Maybe not be taken by business majors.
    Course Syllabus
    102. Computer Science Principles - Fundamental concepts of computer systems, systems software, and an overview of computer science issues. Problem solving and program development using a high-level programming language. Prerequisite: Two years of high school algebra or equivalent.
    Course Syllabus
    121. Introduction to Information Processing Systems

    44. T
    1. a binary Recursive data structure made up of conses and atoms the conses are type equivalent adj. (of two types X and Y) having the same elements;
    ToC DocOverview CGDoc RelNotes ... PermutedIndex Allegro CL version 8.0 ANSI Common Lisp 26 Glossary 26.1 Glossary
    n. 1. a. the boolean representing true. b. the canonical generalized boolean representing true. (Although any object other than nil is considered true as a generalized boolean t is generally used when there is no special reason to prefer one such object over another.) 2. the name of the type to which all objects belong - the supertype of all types (including itself). 3. the name of the superclass of all classes except itself.
    n. 1. a catch tag . 2. a go tag
    n. (of a list ) an object that is the same as either some cons which makes up that list or the atom (if any) which terminates the list . The empty list is a tail of every proper list.
    n. 1. (of a constructed stream ) a constituent of the constructed stream . The target of a synonym stream is the value of its synonym stream symbol. 2. (of a displaced array ) the array to which the displaced array is displaced. (In the case of a chain of

    45. Aldat - Wikipedia, The Free Encyclopedia
    The Aldat Project is concerned with language and data structures for SS. recursion equivalent to query languages on XMLlike semistructured data.
    var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia";
    From Wikipedia, the free encyclopedia
    Jump to: navigation search
    • Aldat
      edit Aldat
      edit Motivation
      Computer memory comes in a variety of forms, two principle ones being primary memory ("RAM"), and secondary memory ("SS") which includes hard and floppy disks and CD-ROM. Data structures and languages for RAM are core computer science. The Aldat Project is concerned with language and data structures for SS.
      Secondary storage is distinguished from RAM primarily by the long times required to find data, relative to the times required to transfer it for processing. Different memory organization needs different data structures, algorithms and languages.
      There are many general-purpose languages for RAM and it is unusual to encounter languages specialized for individual applications. Languages for SS are usually query languages rather than full programming languages, and they are specialized both to particular data structures (hierarchies, linked lists, tables, etc.) and to particular applications (administrative data, spatio-temporal data, logic data, semistructured data, etc.) For instance, RAM has no spatio-temporal dialect of FORTRAN or Java, but SS has Arc-Info while commercial relational databases (SS) do not have comparable spatial capability except as add-ons.
      Aldat is a general purpose SS programming language developed at McGill University . This development has been empirical, following and sometimes leading the main thrusts of database research (including hierarchies, data-structure-set, multiset relations, entities and relationships, object-oriented databases, logic databases, active databases, data warehousing, data mining, semistructured data, and Internet data) with the aim of including all the evolving possibilities of SS programming. The difficulties of doing this are captured in the phrase "impedance mismatch", which characterizes the gaps among applications on one hand and between querying and programming on the other.

    46. PLaneT Package Repository
    (unbox a) b)) defaultequiv-rules))) (define test (test-suite Extensible Recursive equivalence (test-suite default equivalence (test-suite mismatched
    import "/css/main.css"; import "/css/planet-browser-styles.css"; PLaneT Package Repository PLT DrScheme TeachScheme! HtDP ... package version 1.2 module test mzscheme require planet "" "schematics" "schemeunit.plt" lib "" lib "" "" ;; Transparent define-struct alpha left right #f define-struct beta left right #f ;; Opaque define-struct gamma left right define-struct delta left right define make-equiv default-equiv-rules define unbox=? make-equiv add-binary-equiv-rule lambda a b box? a lambda a b unbox a b default-equiv-rules define test test-suite "Extensible Recursive Equivalence" test-suite "default equivalence" test-suite "mismatched types" test-case "null != pair" check-false null cons null null test-case "void != box" check-false void box void test-case "boolean != vector" check-false #t vector #t #f test-case "symbol != hash table" check-false sym make-hash-table test-case "character != string" check-false "string" test-case "number != byte string" check-false bytes test-case check-false make-alpha make-beta test-case check-false make-gamma make-delta test-suite "leaf types" test-case "null" check-true null null test-case "void" check-true void void test-suite "boolean" test-case "true = true" check-true #t #t test-case "false = false" check-true #f #f test-case "false != true"

    47. Fundamenta Informaticae, Volume 30, Abstracts
    The second is that polyadic parametricities of Recursive types are equivalent to each other. The third is that the theory of parametricity for Recursive
    Abstracts of Fundamenta Informaticae Volume 33.
    Number 1
    L. CZAJA
    Minimal-Maximal Time Cause-Effect Structures pages 1-16

    It is shown that minimal-time singly-valued (counterparts of 1-safe Petri nets) cause-effect (c-e) structures are of the same expressive power as no-time singly-valued c-e structures, while maximal-time multi-valued c-e structures are of essentially greater expressive power than no-time multi-valued c-e structures.
    L. CZAJA
    Cause-Effect Structures - Structural and Semantic Properties Revisited pages 17-42

    On Scott Consequence Systems pages 43-70

    The notion of Scott consequence system (briefly, S-system) was introduced by D. Vakarelov in [32] in an analogy to a similar notion given by D. Scott in [26]. In part one of the paper we study the category SSyst
    In part two of the paper we prove that the separation theorem for S-systems is equivalent in ZF to some other separation principles, including the separation theorem for filters and ideals in Boolean algebras and separation theorem for convex sets in convexity spaces.

    48. [Abstract] Reasoning With Property Based Types
    Meaning in this representation is inherent in the Recursive structure alone (analogous to how If all copies of identical (not equivalent) types in a PBT

    49. 5. Data Structures
    Extend the list by appending all the items in the given list; equivalent to .. Python also includes a data type for sets. A set is an unordered
    Python Tutorial Previous: 4. More Control Flow Up: Python Tutorial Next: 6. Modules Subsections
    • 5.1 More on Lists

      5. Data Structures
      This chapter describes some things you've learned about already in more detail, and adds some new things as well.

      5.1 More on Lists
      The list data type has some more methods. Here are all of the methods of list objects:
      append x
      Add an item to the end of the list; equivalent to a[len(a):] = [ x
      extend L
      Extend the list by appending all the items in the given list; equivalent to a[len(a):] = L
      insert i, x
      Insert an item at a given position. The first argument is the index of the element before which to insert, so a.insert(0, x inserts at the front of the list, and a.insert(len(a), x is equivalent to a.append( x
      remove x
      Remove the first item from the list whose value is x . It is an error if there is no such item.
      pop i
      Remove the item at the given position in the list, and return it. If no index is specified, removes and returns the last item in the list. (The square brackets around the

    50. Course Information
    In the second class (Recursive types) there are equations between these freely is every uncountable subset of the reals equivalent with the whole set?
    Master Class 2006/2007 on Logic.
    Course Information
    Below, you find some preliminary descriptions of the courses. This information page is, as yet, still under construction.
    MODEL THEORY (Wim Veldman)
    In mathematics one often studies the class of structures satisfying a given set of formal axioms, for instance the class of groups, the class of fields, or the class of linear orders.
    In Model Theory one starts to study the rather general case that the axioms are formulated in a first-order or elementary language. This means that, when interpreting the formulas of such a language, one only quantifies over the domain of the structure, and not, for instance, over the power set of the domain.
    The pivotal notion of model theory is the notion of a formula being true in a mathematical structure. This notion has been given a formal definition by A. Tarski.
    Axiomatizing a structure is closely related to finding a method to decide which sentences are true in the structure. We shall discuss Tarski's quantifier elimination results. Given a formal theory, what can we say about the class of its countable models? We give a characterization, due to several mathematicians independently, of theories that have exactly one countable model.

    51. Data::Walk - Traverse Perl Data Structures -
    The equivalent of directories in FileFind(3pm) are the container data types in too, allowing you to recursively untaint data structures.

    52. Core Topics
    Review of Discrete Math; sets, set theory, set operations; Origins of Kleene star, Kleene plus; equivalence relations, equivalence classes
    Northern Arizona University
    College of Engineering and Natural Sciences
    Return to Home Quicklinks Advising (Gateway Center) Bookstore Cline Library Campus Life Campus Safety Catalogs Careers at NAU Financial Aid Give to NAU Inside NAU LOUIE online Maps MyNAU (Portal) Student Employment Student Handbook Webmail
    CS Core Topics
    The following lists define the core topics that are covered in each required course. Additional topics may be covered according to the interests and inclinations of the particular instructor. CS 122
    • Algorithms
      • Elements of an algorithm: sequencing, selection, iteration, accumulation of knowledge Solution styles: specialized linear, brute force search, convergence Specialized vs generalized problem sets and solutions Deriving generalized solutions from specialized solutions
      Programming languages
      • Matlab and C++ Commands, data types, variables, input and output Operators: arithmetic, relational, logical Conditionals: if, switch

    53. Induction, Recursion, Replacement And The Ordinals
    the equivalence between my notion of wellfoundedness (induction) and the recursion scheme due to Osius, for endofunctors of Set that preserve inverse
    Induction, recursion, replacement and the ordinals
    Paul Taylor
    My chief contribution to this subject is the notion of " well founded coalgebra ", which is described briefly in the "extended abstract" below and also Sections and of my book, Practical Foundations of Mathematics . The detailed treatment is in the full paper that is the second item below.
    In particular, this proves
    • the equivalence between my notion of well-foundedness (induction) and the recursion scheme due to Osius, for endofunctors of Set that preserve inverse images, that, if the functor has an initial algebra, a coalgebra for it is well founded iff it has a coalgebra homomorphism to the initial algebra, and that extensional well founded coalgebras behave in many ways like sets (of the set-theoretic kind), in particular their coproducts "overlap" in a similar way, and are idempotent like joins in a lattice.
    Parametric recursion is covered in the Exercises for Chapter VI of the book.
    The earlier JSL paper on Intutionistic Sets and Ordinals treats them in the normal without replacement.

    54. EF2PJ Programming Languages III 2+2+0 IV 3+2+0 Machine And
    Structure of a PASCAL program, basic data types, input/output statements, recursion. structured data types record, set, file (binary and text),
    EF2PJ Programming languages III: 2+2+0 IV: 3+2+0
    Machine and assembly language programming. Memory and symbolic addressing. Machine instructions: 3A, 2A, 1A and stack machines. A simple educational machine (picoComputer-pC): instruction set, addressing modes, machine language and assembly language with examples. Introduction to high level languages. Syntax notations (BNF, EBNF, syntax diagrams) and semantics of programming languages. Pseudolanguage. Data types: static (scalar and structured) and dynamic (with variable size and structure). Control structures: sequence, selections, loops and jumps. Program modules (subroutines and functions) - internal and independent, recursion. Data input and output. Structured programming: flow diagrams, canonical form theorem, structural theorems; transfigurations and structuring of non-structured programs. Complexity analysis of computer algorithms. PASCAL. Structure of a PASCAL program, basic data types, input/output statements, control structures. Modularization (subroutines, functions), passing arguments by value and by reference, recursion. structured data types: record, set, file (binary and text), pointers and dynamic memory allocation and deallocation with examples (lists). C. Detailed description of the language fundamentals, program structure. Data types: scalar types, new type definition, arrays. Input/output data conversions. Operators and expressions, conversions and evaluation order. Control structures: sequence, selections, loops and jumps. Pointers and arrays: addresses and pointers; address arithmetics, dynamic memory allocation. Modularization (functions), mechanism of argument passing. Recursive functions, pointers to functions, main program arguments, standard library functions. Visibility and and duration of variables. Definition and using of structures and unions. Handling of files and corresponding functions (opening, closing, input/output). Preprocessor commands.

    55. 0 Top The TOP Concept In The Hierarchy. 1 Adverbial Modification
    133 feature constraint 134 phrase structure grammar 135 Recursive language Language (set of strings) for which the question of whether some string belongs

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