holonic math workbenches?
Yes, in contrast to PROSE, Mathematica and Maple were designed, like Macsyma before them, to automate the pre-computer reductionistic paradigm of symbolic manipulation. In terms of calculus, for example, one of their main early usages was deriving derivative formulas before automatic differentiation trumped this card. In essence this is a mathematical mechanics focusdesigning how to solve rather than what to solvean algorithmic focus. Whereas PROSE completely hid calculus under the hood, leaving only algebraic (not algebra) modeling like Fortran or Basic as the only skill required, these tools immerse the user in the world-view of the numerical analyst, which is what many of their users are. Within these reductionistic frameworks, which were already in existence before the Breckenridge AD symposium in 1991, they have incorporated AD as an afterthought. Holonic nesting, like PROSE, requires a complete departure from the symbolic paradigm of Mathematica and Maple, and though Matlab and M
