Pascal wrote:
"The weirdness of this trick though is that the resulting verb only has one
meaningful valence (which most/great many verbs already do)."
A summary of the different combinations
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.
┌───────┬───────┬───────────────┬──────────────────────────┐
│u │u a │u form │(u a) form ( ... ) │
├───────┼───────┼───────────────┼──────────────────────────┤
│dyadic │monadic│$: │ (( ... ) : )│
├───────┼───────┼───────────────┼──────────────────────────┤
│monadic│dyadic │$: │ ( : ( ... ))│
├───────┼───────┼───────────────┼──────────────────────────┤
│monadic│monadic│$:~ │(@:]) (( ... ) : )│
├───────┼───────┼───────────────┼──────────────────────────┤
│dyadic │dyadic │$:(q=. @:(,&<))│((&>)/)( : ( ... ))│
└───────┴───────┴───────────────┴──────────────────────────┘
On Wed, Apr 20, 2016 at 5:20 PM, 'Pascal Jasmin' via Programming <
[email protected]> wrote:
> a1x1x0x1=. : (($: @: +) % ($: @: *))
> NB. (u @: +) % (u @: *)
>
> %: a1x1x0x1
> %: :($:@:+ % $:@:*)
>
>
> 4 %: :($:@:+ % $:@:*) 4
> 0.707107
>
>
> the alternative:
>
> 4 %: 1 : 'u@:+ % u@:*' 4
>
> is not that much simpler. One pretty cool use of the technique is to
> return a tacit adverb from explicit... what I call double adverbs. Say for
> example the middle % was another parameter,
>
> +: % 1 : ': (($: @: +) u ($: @: *))'
> +: :($:@:+ % $:@:*)
>
>
> 4 %: % 1 : ': (($: @: +) u ($: @: *))' 4
> 0.707107
>
> and this can also be done with a conjunction to say make the left +
> another parameter
>
> 4 %: % 2 : ': (($: @: v) u ($: @: *))' + 4
> 0.707107
>
> The weirdness of this trick though is that the resulting verb only has one
> meaningful valence (which most/great many verbs already do)
>
> +: : (+ 2 : '($: u v)' -: ) 5
> 10
>
> weirder for dyadic fork
>
> * (&>)/ ( : (+ 2 : '($:@:(,&<) u v)' - ) )
> *&>/ :($:@:(,&<) + -)
>
> 2 * (&>)/ ( : (+ 2 : '($:@:(,&<) u v)' - ) ) 4 NB. 8 + _2
> 6
>
>
> ----- Original Message -----
> From: Jose Mario Quintana <[email protected]>
> To: Programming forum <[email protected]>
> Sent: Tuesday, April 19, 2016 7:15 PM
> Subject: Re: [Jprogramming] Adverbial Tacit Jym
>
> Hints and solutions for exercise 1.1.0.1 and 1.1.0.3 are shown after the
> alerts. These complete the whole Exercise 1.1.0 because solutions for the
> item 1.1.0.2 have been shown already (see the last trailing message
> bellow). The solutions shown bellow for 1.1.0.1 and 1.1.0.3 and one
> solution for 1.1.0.2 involve multiple instances of the argument u; thus,
> there are solutions for the 1.1.0.1 item as well.
>
> Let us make the exercises concrete first by providing specific examples;
> what is left is to provide the adverbs:
>
> - 1.1.0.1 Provide the adverb a1x1x0x1 corresponding to the dyadic form (u
> @: +) % (u @: *) using a variation of the trick shown in the definition
> of a1x1 ( see
> http://www.jsoftware.com/pipermail/programming/2016-April/044935.html ).
> For example,
>
> 1 2 %: a1x1x0x1 3 4
> 1.15470054 0.866025404
>
> - 1.1.0.3 Provide the adverb a1x1x0x3 corresponding to the dyadic form
> (u @: +) % (u @: *) using, again, a variation of the trick shown in the
> definition of a1x1 . For example,
>
> 2 3 %:a1x1x0x3 4 5
> 0.577350269 0.306199553
>
>
> H i n t s f i r s t . . .
> H i n t s f i r s t . .
> H i n t s f i r s t .
> H i n t s f i r s t
> H i n t s f i r s
> H i n t s f i r
> H i n t s f i
> H i n t s f
> H i n t s
> H i n t s
> H i n t
> H i n
> H i
> H
>
> - 1.1.0.1 The adverb a1x1x0x1 is a counterpart of a1x1 swapping monadic
> and dyadic.
>
> - 1.1.0.3 Given the adverbs p=. (&>)/ and q=. @:(,&<) then one can
> assert X ((u p)q -: u) Y . For example,
>
> 1 2 ( (% p)q -: %) 3 4
> 1
>
>
> S o l u t i o n s a r e n e x t . . .
> S o l u t i o n s a r e n e x t . .
> S o l u t i o n s a r e n e x t .
> S o l u t i o n s a r e n e x t
> S o l u t i o n s a r e n e x
> S o l u t i o n s a r e n e
> S o l u t i o n s a r e n
> S o l u t i o n s a r e
> S o l u t i o n s a r e
> S o l u t i o n s a r
> S o l u t i o n s a
> S o l u t i o n s
> S o l u t i o n s
> S o l u t i o n
> S o l u t i o
> S o l u t i
> S o l u t
> S o l u
> S o l
> S o
> S
>
> - 1.1.0.1
>
> a1x1x0x1=. : (($: @: +) % ($: @: *))
> NB. (u @: +) % (u @: *)
>
> %: a1x1x0x1
> %: :($:@:+ % $:@:*)
>
> 1 2 %: a1x1x0x1 3 4
> 1.15470054 0.866025404
>
>
> - 1.1.0.3
>
> a1x1x0x3=. ((&>)/) ( : (*:@:(1 -~ $:q) % %:@:(1 + $:q)))
> NB. *:@:(1 -~ u ) % %:@:(1 + u )
>
> %:a1x1x0x3
> %:&>/ :(*:@:(1 -~ $:@:(,&<)) % %:@:(1 + $:@:(,&<)))
>
> 2 3 %:a1x1x0x3 4 5
> 0.577350269 0.306199553
>
>
>
>
>
> On Wed, Apr 13, 2016 at 7:33 PM, Jose Mario Quintana <
> [email protected]> wrote:
>
> > Pascal, you are right about the example. Allow me to be more specific by
> > labeling the cases:
> >
> > Exercise 1.1.0
> >
> > - 1.1.0.0 Provide an example of the method when there are multiple
> > instances of u
> >
> > - 1.1.0.1 Provide an example of the method when u is monadic and the
> > product (u a) is dyadic
> >
> > - 1.1.0.2 Provide an example of the method when u is monadic and the
> > product is also monadic
> >
> > - 1.1.0.3 Provide an example of the method when u is dyadic and the
> > product is dyadic
> >
> > The generic form u@{. + u@{: corresponds to the case 1.1.0.2 when
> > there are two instances of u. The challenge is to exhibit an adverb,
> say,
> > a1x1x0x2 such that, for example,
> >
> > *: a1x1x0x2 3 4 5 6
> > 45
> >
> > by means of the method (i.e., using the same kind of trick).
> >
> >
> > A m i n o r h i n t f o l l o w s . . .
> > A m i n o r h i n t f o l l o w s . .
> > A m i n o r h i n t f o l l o w s .
> > A m i n o r h i n t f o l l o w s
> > A m i n o r h i n t f o l l o w
> > A m i n o r h i n t f o l l o
> > A m i n o r h i n t f o l l
> > A m i n o r h i n t f o l
> > A m i n o r h i n t f o
> > A m i n o r h i n t f
> > A m i n o r h i n t
> > A m i n o r h i n t
> > A m i n o r h i n
> > A m i n o r h i
> > A m i n o r h
> > A m i n o r
> > A m i n o r
> > A m i n o
> > A m i n
> > A m i
> > A m
> > A
> > A
> >
> >
> > #(5!:5)<'a1x1x0x1' NB. The tally of the lr of one solution...
> > 28
> >
> > Incidentally, when u is a large verb and there are multiple instances
> of
> > it, this kind of solutions produce thrifty verbs. The caveat, because
> > their reliance on $:, is that cannot be embedded in within a fixed tacit
> > verb... Unless, they are wearing a suit of armor!
> >
> >
> > On Tue, Apr 12, 2016 at 2:32 PM, 'Pascal Jasmin' via Programming <
> > [email protected]> wrote:
> >
> >>
> >>
> >> > Provide an example of the method when there are multiple instances of
> u
> >>
> >> Not sure how here, except where 1 : 'u@{. + u@{:' could be refactored
> >> into a single u, and then use $:
> >>
> >> Very interested in understanding other 3 examples.
> >>
> >>
> >> ----- Original Message -----
> >> From: Jose Mario Quintana <[email protected]>
> >> To: Programming forum <[email protected]>
> >> Sent: Tuesday, April 12, 2016 10:17 AM
> >> Subject: Re: [Jprogramming] Adverbial Tacit Jym
> >>
> >> Anyone that wants to know the answer can find the original one [0]
> written
> >> almost 10 years ago!
> >>
> >> Sorry Dan, here there are more minor hints ;)
> >>
> >> The importance of this solution is that illustrates a fairly general and
> >> straightforward method for writing of a very common form: u a where u
> is a
> >> verb and its product (u a) is also a verb.
> >>
> >> This a bonus exercise:
> >>
> >> Exercise 1.1.0
> >>
> >> - Provide an example of the method when there are multiple instances
> of u
> >>
> >> - Provide an example of the method when u is monadic and the product
> (u
> >> a) is dyadic
> >>
> >> - Provide an example of the method when u is monadic and the product is
> >> also monadic
> >>
> >> - Provide an example of the method when u is dyadic and the product is
> >> dyadic
> >>
> >>
> >>
> >> [0] [Jprogramming] Tacit adverb definitions?
> >> http://www.jsoftware.com/pipermail/programming/2006-July/002627.html
> >>
> >> On Tue, Apr 12, 2016 at 8:50 AM, Dan Bron <[email protected]> wrote:
> >>
> >> > Pascal wrote:
> >> > > for clarity, the answer is,
> >> >
> >> > No hints, please! Anyone who wants to know the answer can just scroll
> >> down
> >> > in Raul’s original message.
> >> >
> >> > -Dan
> >> > ----------------------------------------------------------------------
> >> > For information about J forums see
> http://www.jsoftware.com/forums.htm
> >>
> >> >
> >> ----------------------------------------------------------------------
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> >>
> >
> >
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