Algebraic and Coalgebraic Methods in the Mathematics of Program Construction: International Summer School and Workshop, Oxford, UK, April 10-14, 2000, Revised Lectures

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Roland Backhouse, Roy Crole, Jeremy Gibbons
Springer, 31.07.2003 - 390 Seiten
Program construction is about turning specifications of computer software into implementations. Recent research aimed at improving the process of program construction exploits insights from abstract algebraic tools such as lattice theory, fixpoint calculus, universal algebra, category theory, and allegory theory.
This textbook-like tutorial presents, besides an introduction, eight coherently written chapters by leading authorities on ordered sets and complete lattices, algebras and coalgebras, Galois connections and fixed point calculus, calculating functional programs, algebra of program termination, exercises in coalgebraic specification, algebraic methods for optimization problems, and temporal algebra.
 

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Inhalt

Department of Mathematics and Computer Science
1
Mathematics in ACMMPC
13
Ordered Sets and Complete Lattices
21
Order Order Order
28
Lattices in General and Complete Lattices in Particular
39
Closure Systems and Closure Operators
47
Speaking Categorically
75
Trees
84
EverMind Westerkade 154 9718 AS Groningen
202
Hylo Equations
218
Department of Computer Science University of Nijmegen
237
Binary Trees
244
Invariants
253
Towards a μCalculus for Coalgebras
261
Refinements between Coalgebraic Specifications
275
Algebraic Methods for Optimization Problems
281

Identifying Galois Connections
100
Fixed Points
115
Fixed Point Calculus
127
Further Reading
146
Calculating Functional Programs
149
Recursive Datatypes in the Category Set
160
Recursive Datatypes in the Category Cpo
173
Applications
183
Implementation in Haskell
197
The Algebra of Relations
283
Optimization Problems
291
Optimal Bracketing
299
Temporal Algebra
309
Relational Laws of Sequential Algebra
355
Interval Calculi
364
Conclusion
382
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