What is the computational notion of "implementation"? It is not individuation, instantiation, reduction, or supervenience. It is, I suggest, semantic interpretation. This document is Technical Report 97-15 (Buffalo: SUNY Buffalo Department of Computer Science) and Technical Report 97-5 (Buffalo: SUNY Buffalo Center for Cognitive Science). 1 INTRODUCTION Consider the relationships among algorithms, computer programs, and the computers that execute them. An algorithm is (roughly) a procedure for computing a function (for more details, see Soare 1996; Rapaport, forthcoming). A program is a more specific and detailed textual expression of an algorithm, expressed in a programming language. Often, it is said that the program "implements" the algorithm. A computer process is an algorithm being executed (see Rapaport 1988, 1995; Smith 1997). It is a physical device (a computer) behaving in a certain way ; the way is described (or specified) by the program, and the physical device running the ...