The SCRATCHPAD language

Abstract

SCRATCHPAD is an interactive system for symbolic mathematical computation. Its user language, originally intended as a special-purpose non-procedural language, was designed to capture the style and succinctness of common mathematical notations, and to serve as a useful, effective tool for on-line problem solving. This paper describes extensions to the language which enable it to serve also as a high-level programming language, both for the formal description of mathematical algorithms and their efficient implementation.

Hashing — the key to rapid pattern matching

“…It has the disadvantage that rules may have to be reordered, involving a considerable amount of preprocessing each time a rule is added or deleted. This is similar to the mechanism of STAGE2 [5], and to the compiled rules of REDUCE [2] or SCRATCHPAD [4].…”

“…For most applications, a large number of patterns would be needed [2,3,4]; consequently the only way to make the system practical would be through the development of new pattern matching techniques, and the examination of alternative storage (string or list) organizations that would support this pattern matcher effectively, particularly with special micro-code or hardware support.…”

Interfacing mathemagix with C++

“…The Modlisp [17] and Scratchpad II [12] systems were at the origin of yet another interesting family of computer algebra systems, especially after the introduction of domains as function return values and dependent types [18,20,30]. These developments were at the forefront of language design Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page.…”

Overview of the Mathemagix Type System

“…The Scratchpad system [21,15] was at the origin of yet another interesting family of computer algebra systems, especially after the introduction of domains and categories as function values and dependent types in Modlisp and Scratchpad II [23,36,22]. These developments were at the forefront of language design and type theory [12,29,28].…”