SDEF, a systolic array programming system, is presented. It is intended to provide ( 1) systolic algorithm researchers/developers with an executable notation, and (2) the software systems community with a target notation for the development of higherlevel systolic software tools. The design issues associated with such a programming system are identified. A spacetime representation of systolic computations is described briefly in order to motivate SDEF's program notation. The programming system

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... reats a special class of systolic computations, called atomic systolic computations, any one of which can be specified as a set of properties: the computation's ( 1) index set (S), (2) domain dependencies (D), (3) spacetime embedding (E), and nodal function ( F) . These properties are defined and illustrated. SDEF's user interface is presented. It comprises an editor, a translator, a domain type database, and a systolic array simulator used to test SDEF programs. The system currently runs on a Sun 3/50 operating under Unix and Xwindows. Key design choices affecting this implementation are described. SDEF is designed for portability. The problem of porting it to a Transputer array is discussed.