----- Original Message -----
From: "Don Watson" <[email protected]>
To: "General forum" <[email protected]>
Sent: Sunday, March 15, 2009 8:26 PM
Subject: Re: [Jgeneral] Teaching
> If we use F to represent +/ , G to represent # and H1 and H2 to
> represent
> % . F and G are monadic as F(x) and G(x) and H is normally dyadic as H
> (x,y). In tacit programming we are replacing H1 [ F(x), G(x) ] by [
> H2 (F, G) ] (x) In which case H1 and H2 are not the same kind of
> mathematical function - are they?
>
> Don
It would be easier to understand what you are wanting to know if you used
standard mathematical notation in one expression and J in the other. I know
you are wanting to find some way of maintaining consistency but Ken and
Roger and many others who have pondered the problem have found the
simplicity of the parsing rules of J too valuable to compromise. Perhaps
the way of tackling this problem should be to show to those writing
mathematical expressions that they can rewrite many of them in a way
consistent with J's parsing rules without any loss of clarity. Indeed often
it clarifies features since commonly you use the negative number instead of
subtraction, and many expressions simply become sums. I have just looked
at a simple example -
deriving the value of the integral of (sin x)^5 as a series in (cos x) and
the whole argument transfers very readily. It would be great if someone
wrote some simple introductions to algebra, and to calculus where the J
syntax is used for derivations as well as calculation.
In your post
F(x) = sum (x)
G(x) = count (x)
H1(x,y) = x/y
In J H1(F(x),G(x)) just becomes (F H1 G)
or writing it out explicitly (F x)H1 G x
If your H1[F(x),G(x)] is mean to represent an expression in J I do not
know whether you mean H1(F(x),G(x)) where H1 is a monadic fucntion with
argument (F,G)x or using H1 dyadically (F H1 G) x
If one tries to interpret the [ and ] as in J then perhaps you might be
thinking of (H1 [ F,G ]) x
However that would require that F and G would be dyadic functions. The
expression would parse as
(H1 ([ F (, G ]))) x
Noting this is a hook in J it can be expressed in conventional terms as
H1( x , F(x , (G (ravel (x), x) )))
In several posts you have wanted to include 'explicit' expressions in tacit
ones. There are good reasons for not doing so. While some members of the
forum try to use tacit for everything, or nearly everything, others find
that writing explicit functions is the quickest way to complete tasks they
want. It can of course be very useful to include powerful tacit functions
in explicit code.
I would sugget you teach the use of J sentences as an explicit form in
introductory material. In that way you can use the powerful structures of J
and very frequently give a very clear left to right description of the
algorithm you are using.
sd_of_x =: sqrt sum square deviations x
As Brian suggested you can then use the explicit to tacit converter if you
wish. the following carries this through
sd =: 13 : 'sqrt sum square deviations y'
5!:5 <'sd'
[: sqrt [: sum [: square deviations
To make this operational you need
sqrt =: %:
sum =: +/
square =: *:
deviations =: - mean
mean =: sum % #
To apply to general arrays you might modify deviations to
deviations =: - "_ _1 mean
If you enter load 'primitives' sqrt and square are defined with
dictionary names for all the primitives. I am afraid that goes in an
alternative direction to your aim of simple one character symbols, but for
some of your users it may work well.
Fraser
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