Essence of generalized partial computation

Generalized partial computation (GPC) is a program optimization principle based on partial computation and theorem proving. Conventional partial computation methods (or partial evaluators) explicitly make use of only given parameter values to partially evaluate programs. However, GPC explicitly utilizes not only given values but also the following information: (1) logical structure of a program to be partially evaluated; (2) abstract data type of a programming language. The main purpose of this paper is to present comprehensible examples of GPC. Graphical notations, called GPC trees, are introduced to visibly describe GPC processes.