I am trying to understand the mathematical concepts behind CLIPS programming language and I am not sure how is a rule in CLIPS mathematically defined ? Is it a set ?
Does the order of the set matters? Is there any place where I can read more about theoretical concepts of CLIPS language ?
CLIPS uses the rete algorithm. Here's some links for more information:
https://en.wikipedia.org/wiki/Rete_algorithm
http://reports-archive.adm.cs.cmu.edu/anon/1995/CMU-CS-95-113.pdf
http://reports-archive.adm.cs.cmu.edu/anon/scan/CMU-CS-79-forgy.pdf
https://sourceforge.net/projects/clipsrules/files/CLIPS/Misc/CLIPS_Implementation_of_Rete.pdf/download
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What is Local Reasoning ? how does it relate to Referential Transparency, Equational Reasoning and Laziness ?
(adding the definition from the commented link, just to avoid link only answer)
From http://degoes.net/articles/fp-glossary
Local reasoning is a property of some code wherein the correctness of the code can be inferred locally under specified assumptions, without considering prior application state or all possible inputs.
I've recently started working with Isabelle and I've been trying to explore different parts of it. Is it possible to prove an integration possible in Isabelle? Such as the integrating x between [0,1], dx. If possible, please could you direct me to the relevant Isabelle .thy file, or even a brief tutorial.
I've tried looking around but no success.
Thank you.
There is also IntervalIntegral.thy from https://github.com/avigad/isabelle/blob/master/Analysis/Interval_Integral.thy. This has the advantage of a rich measure-theoretic background and will be merged into Isabelle's measure theory library soon. If you want to prove that the integral from somewhere to somewhere equals some term, you usually use the fundamental theorem of calculus (interval_integral_FTC_finite) to prove that you have an indefinite integral and then use that to compute the definite integral. Integration by substitution is also available, e.g. interval_integral_substitution_finite.
The relevant theories are in HOL-Multivariate_Analysis, in particular theory Integration and following.
Disclaimer: I have not worked with these definition at all, just know about their existence.
I have a simulation I am running where I would like to test for the collision of 2D objects. I am not interested in the physics simulation portion of Box2D but would like to leverage its collision detection features.
My initial thought was to make a bunch of static bodies but after reading the documentation I got the impression they were not included in collision testing and therefore don't make sense.
Is it worthwhile using Box2D to evaluate collision detection in my system, where the position of the elements is driven by a separate system, or does it make more sense to look elsewhere for a collision detection solution? If so, how would I start down that path with Box2D?
Although I have not tried it myself, I guess you could do it by using dynamic bodies, with the world gravity set to zero, and all bodies linear velocity set to zero (so they do not move in world Step call) and then position them using SetTransform. The regular BeginContact/EndContact events should still be sent to your contact listener.
Yes, use Box2D. Box2D has the best collision detection system I've used, compared to Chipmunk and Bullet.
I agree with iforce2d, you should use dynamic bodies with a world whose gravity is set to zero.
Good luck and happy coding.
could anyone tell me what's the background theories in The Definition of Standard ML, found very interesting and beautiful, i did learn some sml a little, but i want more while don't know how to start (to understand TDSML)
3x in advance
For the old version of the Definition (SML'90) there actually was a separate book called "Commentary on Standard ML", which explained how to interpret the Definition. Both the SML'90 Definition and the Commentary are long out of print, but fortunately, are available as free PDFs.
The SML'90 Definition had some differences to SML'97, in particular regarding the module system. Overall, it was more complicated. But much of the Commentary should still apply, and if you have both versions side by side, it shouldn't be hard to figure out what's still relevant.
This is off the top of my head: In order to understand the methods employed in The Definition of Standard ML, you should some basic understanding of:
set theory
functions
first-order logic
type theory
Additionally, you should be able to read and understand inference rules of which the book makes extensive use.
The QR code specification requires an optimal choice of mask to avoid patterns that are difficult to scan. If the rules for this choice are ignored and one of the mask patterns is chosen arbitrarily, but the scanner is not confused by the pattern while scanning it, will there be any decoding problems?
Yes, sometimes. Due ISO/IEC 18004:2000 (8.8), masking is used for:
balancing dark and light modules,
avoiding Position Detection pattern.
The first one will affect on version detection, which is made provisionaly for versions of QR code less than 7.
The second one will affect on position patterns detection.
Both these steps should be done before reading Format Information and applying mask to QR code while decoding.
No. The mask that is used is recorded in the QR code itself, in the area around the finder patterns. As long as that is read correctly, the mask will be correctly removed before decoding. It doesn't matter whether it's actually the optimal pattern or not. Any mask may be used in theory.