<XML><RECORDS><RECORD><REFERENCE_TYPE>3</REFERENCE_TYPE><REFNUM>7061</REFNUM><AUTHORS><AUTHOR>O'Donnell,J.T.</AUTHOR><AUTHOR>Ruenger,G.</AUTHOR></AUTHORS><YEAR>1994</YEAR><TITLE>A case study in parallel program derivation: the heat equation algorithm</TITLE><PLACE_PUBLISHED>Functional Programming, Glasgow 1994, Springer Workshops in Computing </PLACE_PUBLISHED><PUBLISHER>Springer Verlag</PUBLISHER><PAGES>167-183</PAGES><LABEL>O'Donnell:1994:7061</LABEL><KEYWORDS><KEYWORD>parallel programming</KEYWORD></KEYWORDS<ABSTRACT>We investigate the application of functional specification and program transformation in a practical setting using a simple case study: the derivation of a parallel program for solving the heat equation. The main concerns here are: (1) how to write an initial specification of the algorithm using a notation appropriate to the subject area (partial differential equations), (2)the introduction of an intermediate algorithm specification using bidirectional mapping scan, and (3) the use of equational reasoning to transform the specification.</ABSTRACT></RECORD></RECORDS></XML>