Hi,
I have watched the Julia 1.0 video where Stefan briefly mentions new multiple dispatch algorithm. I don't have much insight into this so I would like to ask: What is the cost of multiple dispatch? ( What is the complexity of naive implementation? What is the complexity of current implementation in julia? ) Could you briefly highlight the difficulties of creating an efficient implementation? Thank you 
Have a read of:
https://github.com/JeffBezanson/phdthesis/blob/master/main.pdf (Note that multiple dispatch is not a 1.0 thing, it was there from the beginning.) On Fri, 20161104 at 16:22, Ford O. <[hidden email]> wrote: > Hi, > > I have watched the Julia 1.0 video where Stefan briefly mentions new > multiple dispatch algorithm. I don't have much insight into this so I would > like to ask: > > What is the cost of multiple dispatch? ( What is the complexity of naive > implementation? What is the complexity of current implementation in julia? ) > > Could you briefly highlight the difficulties of creating an efficient > implementation? > > Thank you 
I posted an answer to this a year ago on Stack Overflow: http://stackoverflow.com/a/32148113/176071
The internal implementation of the method caches has since changed, but the concepts should still apply. If I remember right, Stefan's remarks were about the addition of triangular subtyping, which will plug into the dispatch system seamlessly since it's "just" an extension to the type system. On Friday, November 4, 2016 at 10:44:28 AM UTC5, Mauro wrote: Have a read of: 
On Friday, November 4, 2016 at 8:05:30 PM UTC, Matt Bauman wrote:
Thanks. I see "so it's just a linear search to check if the type of the argument tuple is a subtype of the signature. So that's just O(n), right? The trouble is that checking subtypes with full generality (including Unions and TypeVars, etc) is hard. Very hard, in fact. Worse than NPcomplete [..] that is, even if P=NP, this problem would still take nonpolynomial time! It might even be PSPACE or worse." That sounds bad.. I'm not to worried about PSPACE, only "worse" and/or nonpolynomial time. But I assume that is also only a problem with functions with many arguments, and if you hit it you know.. You'll never be surprised at runtime. [This kind of reminds me, SQL query tuning is exponential in general, not a problem in practice, or you just deal with it by simplifying your query or give hints; and PostgreSQL at least has genetic algorithm as a fallback: https://www.postgresql.org/docs/9.1/static/geqopgintro.html ] And thankfully you add "But, really, your question was about the runtime complexity of dispatch. In that case, the answer is quite often "what dispatch?" — because it has been entirely eliminated!" as I expected. If Julia would need: https://en.wikipedia.org/wiki/EXPSPACE I would get a little worried, not for: https://en.wikipedia.org/wiki/PSPACE "PSPACE is also equal to P_{CTC}, problems solvable by classical computers using closed timelike curves,^{[6]} as well as to BQP_{CTC}, problems solvable by quantum computers using closed timelike curves.^{[7]"https://en.wikipedia.org/wiki/Closed_timelike_curve"}^{who discovered a solution to the equations of general relativity (GR) allowing CTCs known as the Gödel metric; and since then other GR solutions containing CTCs have been found, such as the Tipler cylinder and traversable wormholes. [..] } ^{Some physicists speculate that the CTCs which appear in certain GR solutions might be ruled out by a future theory of quantum gravity which would replace GR, an idea which Stephen Hawking has labeled the chronology protection conjecture. Others note that if every closed timelike curve in a given spacetime passes through an event horizon, a property which can be called chronological censorship, then that spacetime with event horizons excised would still be causally well behaved and an observer might not be able to detect the causal violation.[2]}

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