CRT-AIDED SEMI-AUTOMATED MATHEMATICS

The report describes the status of the sixth in a series of six experiments in semi-automated mathematics. This effort extended from 1 October 1966 through 31 May 1968. These experiments culminated in large complex computer programs which allow a mathematician to prove mathematical theorems on a man-machine basis. SAM VI, the sixth program, uses a cathode ray tube as the principal interface between the mathematician and a high speed digital computer. An elaborate language and logical capability has been implemented in SAM VI. These include I/O languages for expressing mathematical statements in a form suitable for both the mathematician and the machine to recognize and handle with ease and convenience, a language for expressing and handling sorts and range of symbols, and auto-logic algorithm and matching routine. The latter constitute the capability for handling, automatically, logic with equality. This capability is particularly useful at an intermediate state of the proof when it is desired to have the machine try to verify automatically a given portion of the proof.