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PROSE〔(PROSE – A General Purpose Higher Level Language, Procedure Manual, Control Data Corp. Pub No. 840003000 Rev. B (Jan 1977) )〕〔(PROSE – A general Purpose Higher Level Language, Calculus Operations Manual, Control Data Corp. Pub. No 840003200 Rev B (Jan. 1977) )〕〔(PROSE – A general Purpose Higher Level Language, Calculus Applications Guide, Control Data Corp. Pub No. 84000170 Rev. A (Jan 1977) )〕〔(PROSE – A general Purpose Higher Level Language, Time Sharing System Guide, Control Data Corp. Pub. No 84000160 Rev A (Jan. 1977) )〕 was the mathematical 4GL virtual machine which established the holistic modeling paradigm known as Synthetic Calculus〔(J.M. Thames, The Evolution of Synthetic Calculus: A Mathematical Technology for Advanced Architecture, in Proc. of the International Workshop on High-Level Language Computer Architecture, University of Maryland, 1982 )〕〔(B. Krinsky and J. Thames, The Structure of Synthetic Calculus, A Programming Paradigm of Mathematical Design, in Proc. of the International Workshop on High Level Computer Architecture, University of Maryland, 1984 )〕〔(J.M. Thames, Synthetic Calculus – A Paradigm of Mathematical Program Synthesis, in A. Griewank and G.F. Corliss, eds., Automatic Differentiation of Algorithms: Theory, Implementations, and Applications, SIAM, Philadelphia (1991) )〕 (AKA MetaCalculus). A successor to the SLANG〔(J.M. Thames, “SLANG—A Problem-Solving Language of Continuous Model Simulation and Optimization", ACM National Conference, San Francisco, 1969. )〕/CUE〔(J.D. McCully, “The Q Approach to Problem Solving”, Proceedings of the Fall Joint Computer Conference, 1969. )〕 simulation and optimization language developed at TRW Systems, it was introduced in 1974 on Control Data supercomputers. It was the first commercial language〔(R.N. Nilsen and W.J. Karplus, "Continuous-System Simulation Languages: State of the Art Survey" Annales de l'Association Internationale pour le Calcul analogique - No 1, Jan, 1974 ), p. 20〕〔(J.M. Thames, Computing in calculus, Research/Development, (1975), pp. 24–30 )〕〔F.W. Pfeiffer, (Some Advances Related to Nonlinear Programming ), (ACM Sigmap Bulletin, Issue 28, Jan 1980, pp. 15-21 )〕〔(F.W. Pfeiffer, Automatic differentiation in PROSE ), (ACM SIGNUM Newsletter, 22 (1987), pp. 1–8 )〕 to employ automatic differentiation (AD), which was optimized to loop in the instruction-stack of the CDC 6600 CPU. Although PROSE was a rich block-structured procedural language, its focus was the blending of simultaneous-variable ''mathematical systems'' such as: * implicit non-linear equations systems, * ordinary differential-equations systems, and * multidimensional optimization. Each of these kinds of system models were distinct and had operator templates to automate and solve them, added to the procedural syntax. These automated system problems were considered "holistic" because their unknowns were simultaneous, and they could not be reduced in formulation to solve piecewise, or by algebra manipulation (e.g. substitution), but had to be solved as wholes. And wholeness also pertained to algorithmic determinacy or mathematical "closure", which made solution convergence possible and certain in principle, if not corrupted by numerical instability. == Holarchies of Differential Propagation == Since these holistic problem models could be independently automated and solved due to this closure, they could be ''blended'' into higher wholes by nesting one inside of another, in the manner of subroutines. And users could regard them as if they were ordinary subroutines. Yet semantically, this mathematical blending was considerably more complex than the mechanics of subroutines, because an iterative solution engine was attached to each problem model by its ''calling'' operator template above it in the program hierarchy. In its numerical solution process, this engine would take control and would call the problem model subroutine iteratively, not returning to the calling template until its system problem was solved. During some or maybe all of the iterative model-subroutine calls the engine would invoke automatic differentiation of the formulas in the model holarchy with respect to the model's input-unknowns (arguments) defined in the calling template. Additional mechanisms were performed in the semantics to accommodate ubiquitous nesting of these holistic models. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「PROSE modeling language」の詳細全文を読む スポンサード リンク
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