The Miser Project involves the production and use of computer software that realizes an abstract machine. Those realizations are implementations of an abstractly-specified mechanism. A successful implementation makes manifest the abstract mechanism. It is thereby a valid interpretation of the theoretical formulation.
There are always incidental characteristics that accompany implementations. Some incidental characteristics have to do with limitations on all procedures enacted in physical reality: possible mechanical/electronic failures, resource exhaustion, and failure to terminate with a definite result. Other incidental characteristics involve details necessary to achieve the manifestation, yet are absent from the abstraction and not dictated by it.
Despite the contingency that accompanies a physical realization of an abstract formulation, dependable realizations are quite practical, just as the current implementations of general-purpose computers are remarkably dependable.
Starting at the oMiser level, there are three stages to successful manifestation:
The primitive elements of the theoretical structure, ‹ob›, are represented as an abstract data type using well-known computer-programming techniques. The set, Ob, is thereby made manifest via computational procedure. The effect is to provide a means of navigating everywhere within Ob that one can express by finite, computational means. The fidelity of manifestation is such that Ob appears to be given tangible existence in reality. For oMiser, this is a very strict situation: It is as if there is only one Ob and it is accessible from any and all computational realizations.
The oMiser universal function, ob.ap, is implemented by a computational procedure on the abstract data type realization of Ob and sufficient primitive elements of ‹ob›. Given the universality of ob.ap, the fidelity of Ob manifestation, and the Church-Turing equivalence of ‹ob› as a model of effective computability, oMiser is established as a general-purpose computational mechanism.
Various formal exercises must be carried out to rigorously establish the theoretical conditions claimed for (1-2). In addition, there need to be conditions on computational realizations and how valid interpretation is to be assessed. This is an empirical determination carried out alongside the mathematical formalization of the theoretical abstraction.
It is the three together, and the provision of the oFrugal scripting language for operating oMiser realizations, that provide an opportunity to carry out computations using the oMiser model of computation.
It is the prospect of extending Miser to operation over other abstract data types that leads to practical utility beyond purely theoretical interest. The challenge is to have such extension, including situation in interactive arrangements, address some extended notion of algorithmic systems. Whether and how extensions might transcend the fundamental capabilities of oMiser is a separate consideration beyond the confirmed universality of ob.ap and ‹ob›.
-- Dennis E. Hamilton
n001000b: Miser as Theoretical Model [latest]
n001000c: Initial Notes
Hamilton, Dennis E. Abstraction: Einstein on Mathematics+Theory+Reality. Orcmid's Lair blog post, 2010-02-21. Available at <http://orcmid.com/blog/2010/02/abstraction-einstein-on-theoryreality.asp>.
Hamilton, Dennis E. Reality
Is the Model. Numbering Peano blog post, 2008-05-29.
Available at <http://miser-theory.info/astraendo/pn/2008/05/reality-is-model_29.asp>.
n001000a: Diary & Job Jar
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