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by macintux
1746 days ago
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> Because putting this description into a doc/MATHS.md file inside the repo itself is too easy. Agreed. Even a link to Wikipedia would be useful: 𝜑-calculus is not the easiest thing to search for, and I'm certainly not going to sign up for a Telegram account just to find out what this is all about. |
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> <a 47-line XML file />
I have little idea why this is here, what on earth it's for, what 𝜑-calculus is, or anything! I don't even know if it's related to lambda-calculus, modal-µ calculus, or whatever!
So, some highly speculative google-scholaring:
> [1] This article proposes a new arithmetic for fuzzy numbers called ϕ-calculus developed at the LAMIH laboratory (D. Roger and J.-M. Lecomte, 1996). For this algebra, the modeling used for the representation of fuzzy numbers is the distribution function instead of the classical membership function. New functions (square, square root, power, exponential, Neperian logarithm and trigonometric functions) are defined in this paper. With the aim of handling simply ϕ-calculus arithmetic and of comparing it with those of the intervals theory (R.E. Moore, 1966) and the Zadeh's extension principle for fuzzy numbers (L.A. Zadeh, 1965), a toolbox for Matlab has been set up. Also, several examples and an application of automatic control illustrate this algebra.
Aha! So, maybe it's a fuzzy number system -- where you have inherent uncertainty on everything. That's cool, and useful, and something I can totally see the point of (not least in an OO context -- everything has to be an object, as a fuzzy number is a generalization of a regular, real number in the sense that it does not refer to one single value but rather to a connected set of possible values, where each possible value has its own weight between 0 and 1; and that weight is called the membership function -- and a function with some data is basically an object!). Maybe that's what it means. Maybe.
More googling.
> [2] THE φ-CALCULUS – A HYBRID EXTENSION OF THE π-CALCULUS TO EMBEDDED SYSTEMS. [...] The φ-calculus is a hybrid extension of Milner’s π-calculus [17] which allows processes to interact with continuous environments. We choose the π-calculus to extend to the hybrid setting because it has already been shown to be a rich language in which many interesting discrete concurrent phenomena can be expressed: a language for, and theory of, communicating processes which can reconfigure themselves; a language in which distributed objects and classes can be defined; and a language and theory capable not only of expressing communication, but arbitrary computation, in that the λ-calculus of Church can be translated into it. This all suggests that successful hybrid versions of the π-calculus and other process calculi will have novel and elegant ways of expressing hybrid systems – possibilities for distributed control which would be awkward, if not impossible, to express in current formalisms.
Then again, maybe not! I'd love someone to explain what this is all about, ideally relatively simply.
[1] http://dx.doi.org/10.1109/ETFA.2006.355426
[2] https://www.eecs.umich.edu/techreports/cse/02/CSE-TR-458-02....