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 -- Temporal Algebra.

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.

9783540477976

10.1007/3-540-47797-7 doi

Computer science.

Software engineering.

Programming languages (Electronic computers).

Computers.

Computer logic.

Mathematical logic.

Computer Science.

Software Engineering.

Theory of Computation.

Software Engineering/Programming and Operating Systems.

Programming Languages, Compilers, Interpreters.

Logics and Meanings of Programs.

Mathematical Logic and Formal Languages.

QA76.758

005.1