Algebraic and Coalgebraic Methods in the Mathematics of Program Construction: International Summer School and Workshop, Oxford, UK, April 10-14, 2000, Revised LecturesRoland Backhouse, Roy Crole, Jeremy Gibbons Springer Science & Business Media, 17/04/2002 - 390 من الصفحات 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. |
المحتوى
Chapter 1 Introduction | 1 |
Chapter 2 Ordered Sets and Complete Lattices | 21 |
Chapter 3 Algebras and Coalgebras | 79 |
Chapter 4 Galois Connections and Fixed Point Calculus | 89 |
Chapter 5 Calculating Functional Programs | 149 |
Chapter 6 Algebra of Program Termination | 202 |
Chapter 7 Exercises in Coalgebraic Specification | 237 |
Chapter 8 Algebraic Methods for Optimization Problems | 281 |
Chapter 9 Temporal Algebra | 309 |
| 386 | |
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عبارات ومصطلحات مألوفة
admits induction Algebraic and Coalgebraic algorithm apply arbitrary arrows axioms binary relation binary trees Boolean algebra category theory Chapter closure operator coalgebra coalgebraic specification complete lattice composition Computer Science concat cons constructors coreflexive datatype defined definition denote domain dual element ENDCASES equivalent example Exercise expressions F-algebra finite fixed point equation fold foldL foldT fork function f functional programming functor fusion Galois algebra Galois connection given homomorphism hylo infinite initial algebra integers invariant Kleene algebra laws least fixed point least prefix point Lemma linear List lower adjoint mathematical Mini-exercise monotonic natural numbers non-empty notation notion pair partial order PList polynomial functor poset powerset predicate preorder problem programming languages Proof Proposition prove recursion relation algebra rule satisfies semantics sequential algebra solution structure subset temporal logic Theorem tion Tsym unfold unique universal property upper adjoint well-founded