This thesis deals with the relation between computer languages and computer architecture. In particular, it deals with SETL, a very high level set oriented language, and its implementation on a machine suitable for executing it. Architectural features which aid in implementing SETL are discussed. A machine which directly executes a pre-processed version of SETL source code is described and microprograms for the execution of a few typical SETL operators are presented. This machine is a stack machine with tags which enable the hardware to distinguish between the data types of SETL. The preprocessing required for this machine consists of rearranging the tokens of the source program into Polish form. Three different representations of sets on this machine are compared. Simplified versions of the SETL machine which are comparable to some microprogrammed systems in existence today are also described. The problem of implementing SETL on the R-2 is discussed and a method for effectively utilizing the hierarchical memory segmentation provided by the R-2 addressing system is presented.