On Mon, Aug 10, 2015 at 12:58 PM, Kirby Urner <kur...@oreillyschool.com> wrote:
> > > On Mon, Aug 10, 2015 at 12:02 PM, Mark Engelberg <mark.engelb...@gmail.com > > wrote: > >> >> >>> The idea of an interface has migrated to that of a "protocol" which >>> provides a ready namespace for a "record". >>> >> >> A protocol is more than just an "interface by a different name" or an >> "interface+namespace". >> > > For those not familiar with Java, it's single inheritance, so we don't > have the happy solution of injecting new functionality by adding more base > classes. > > In Java, a class is said to "extend" a base class whereas an interface, a > set of promised methods, is something a class "implements". > > Whereas on my extend only one class at a time, said class may implement > many interfaces. > > I see Clojure taps that ability too: > > http://clojure.github.io/clojure/clojure.core-api.html#clojure.core/extend > > > >> >> To understand the significance of a protocol, you need to first >> understand the "expression problem". The expression problem asks you to >> consider a set of polymorphic functions over multiple datatypes. Without >> controlling or being able to recompile the original source code, can you >> easily extend these functions to a new datatype, and can you easily create >> a new polymorphic function across those datatypes? >> > > I like to relate these concepts back to basic math and the different > number types we start with, as concentric subsets: N < Z < Q < R < C. > > Then a protocol or interface is "the operations" such as - / + * < > and > so on. What common control panel of operations works across these sets? > > Clojure, like Java, is not supportive of operator overloading right? I > can't go like: > > (defprotocol VectorOps > (__add__ [this other]) > (__sub__ [this other]) > (len [this]) > (__neg__ [this]) > (norm [this])) > > ... and then use (+ A B) to add two vectors, or (- A) to negate one. > > I think the basics of Polymorphism may be communicated without introducing > the wrinkle of not having original source code. Not wanting to change it > might be easier for a math student to understand. > > Not having the original source code sounds like a social problem, an > institutional issue, vs. a truly theoretical issue, and that's confusing to > newbies. > > The + and - operators make sense in a Group, where - is both negation and > for adding a negative inverse. > > Add * and / to the mix and we've got a field. > > Lots of datatypes participate in group and field relationships, including > numbers module N, which we may imagine as a specific type of number. > > Sorry for typos. ... numbers *modulo* N -- given "module" is a Python word, this could be confusing. Here's some source I code I wrote for that type of Number awhile back: http://www.4dsolutions.net/ocn/python/groups.py Kirby
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