On the Shape of Mathematical Arguments

ISBN-13: 9783540528494 / Angielski / Miękka / 1990 / 184 str.

A. J. M. Gasteren; Antonetta J. M. Van Gasteren; Edsger W. Dijkstra

Opis

This book deals with the presentation and systematic design of mathematical proofs, including correctness proofs of algorithms. Its purpose is to show how completeness of argument, an important constraint especially for the correctness of algorithms, can be combined with brevity. The author stresses that the use of formalism is indispensible for achieving this.

Spis treści

A termination argument.- A problem on bichrome 6-graphs.- Proving the existence of the Euler line.- In adherence to symmetry.- On a proof by Arbib, Kfoury, and Moll.- Not about open and closed sets.- A monotonicity argument.- On the inverse of a function.- A calculational proof of Helly's theorem on convex figures.- The formal derivation of a proof of the invariance theorem.- Proving theorems with Euclid's algorithm.- On the deisng of an in-situ permutation algorithm.- Shiloach's algorithm.- Clarity of exposition.- On naming.- On the ue of formalism.- Epilogue.- Proof rules for guarded-command programs.- Notational conventions.