Great explanation Dan,

A couple of years ago I put this video together about the adverb '~'  . 

http://bobtherriault.wordpress.com/2010/11/17/those-tricky-adverbs/ 

Let me know if you have any interest in developing your explanations into a 
more multimedia mode. I don't have huge amounts of time (and it does take some 
time), but I do enjoy doing this stuff.

Cheers, bob

On 2013-06-13, at 9:48 AM, Dan Bron wrote:

> Alexander Epifanov wrote:
>> but I did not understand what is the different, 
>> I mean how it works if it is adverb.
> 
> To understand this error, we must first discuss what adverbs are, how they
> behave, and how they differ from verbs.  So let's start there.
> 
> ----------
> Adverbs are a different class, or order, of words than verbs.  In
> particular, they have higher grammatical precedence than verbs, and so
> gobble up any suitable arguments lying around before verbs can even see
> them.  Conjunctions are in this same high-precedence class, but whereas
> adverbs only take one argument (on the left), conjunctions take two (one on
> the left, the other on the right).  You can think of adverbs and
> conjunctions as higher-order analogs to monadic and dyadic verbs
> respectively.*  
> 
> Adverbs are called adverbs because they normally modify verbs: that is, in
> typical use, they accept a verb argument and produce verb result, which is
> related in some (consistent) way to the argument.  The most famous example
> is  /  :
> 
>          +/ 2 3 4  NB.  Sum of data (Σ s[i])
>          */ 2 3 4  NB.  Product of data  (Π s[i])
>          ^/ 2 3 4  NB.  Tetration ("power tower") of data
> 
> Here, / takes a dyad (two-argument verb) as an argument, and produces a
> monad (one-argument verb)*.  The output is related to the input in the
> following sense: when the output verb is provided an noun, it inserts the
> input verb between each pair of items in the noun, such that:  
> 
>          +/ 2 3 4  is  2+3+4  
>          */ 2 3 4  is  2*3*4
>          ^/ 2 3 4  is  2^3^4  NB. Note: J executes right-to-left, so this
> is 2^(3^4)
> 
> and
> 
>          +/ 2 3 4 , 5 6 7 ,: 8 9 10 
> is:
>          2  3  4
>             +
>          5  6  7 
>             + 
>          8  9 10
> 
> which, because + is rank 0 (scalar), is:
> 
>          2  3  4
>          +  +  +
>          5  6  7
>          +  +  +
>          8  9 10
> 
> etc.  
> 
> But bear in mind that taking verb arguments and deriving (consistently)
> related verbal results is only the typical case for an adverb.  Adverbs can
> also take a noun for an argument (an "adjective"); the most common example
> is  }  , which normally takes a noun argument specifying which indices the
> derived verb should modify (when it, itself, is applied to nouns):
> 
>          putFirst        =:    0}
>          putLast         =:   _1}
>          putFirstAndLast =: 0 _1}
> 
>          '*' putFirst '12345'
>       *2345
>          '*' putLast 'ABCDE'
>       ABCD*
>          '*' putFirstAndLast 'ABCDE'
>       *BCD*
>          
> So adverbs can take verbs or nouns as inputs, and normally produce verbs as
> outputs.  But adverbs are not restricted to verbal output; they can produce
> anything, including verbs, nouns, and even other adverbs and conjunctions.
> Primitive adverbs which produce non-verb results are unusual (primitive
> conjunctions are a little more diverse in this regard), but they exist.  For
> example, when the adverb ~ is applied to a string, it treats the string in
> as a name and evokes it, such that  'someName'~  is equivalent to  someName
> . Therefore ~ can produce anything at all:
> 
>          someNoun =: 42
>          someVerb =: +
>          someAdverb =: /
>          someConjunction =: @
>       
>          'someNoun'~
>       42
>          'someVerb'~
>       +
>          'someAdverb'~
>       /
>          'someConjunction'~
>       @
>          
> 
> Of course user-defined adverbs will produce anything they're defined to
> produce, so you can't know what they'll do without reading the definition or
> documentation.  That said, user-defined adverbs tend to follow the same
> patterns as primitive adverbs: they're almost always abstractions over verbs
> which produce verb results; sometimes they take noun arguments and/or
> produce noun results, and only very rarely do they produce other adverbs or
> conjunctions.
> 
> Ok, with that as a background, we're ready to discuss write_image and the
> error you observed.  
> 
> ---------------
> 
> The word write_image falls into this "user defined adverb" category.  The
> reason it was defined as an adverb instead of a verb is so that it can
> accept up to 3 arguments (filename, data to write, and a set of options like
> image quality or scaling), whereas if it were defined as a verb, it could
> accept no more than two arguments.  Meaning if write_image had been defined
> as a verb, it would have to find some way to pack two arguments into a
> single noun, and unpack them inside the definition, which can sometimes lead
> to convoluted code.  Keeping it as an adverb with three distinct arguments
> is very clear and clean.
> 
> But it does stymie attempts to use it like a verb, as you discovered.  In
> particular, when you embedded it in
> 
>       (('small/'&, (write_image)~ ((3 3)&resize_image)@:read_image)@:>) i
> 
> , its higher grammatical priority caused the adverb to seek out an argument
> immediately, and since the verb 'small/'&, was on its left and suitable
> (because verbs are perfectly acceptable arguments for adverbs), the result
> was that write_image bound with 'small/'&, .  
> Now, the specific coding style** of write_image prevented it from being
> executed immediately (if it'd been executed, you'd know it, because you
> would have gotten an error: write_image is expecting data [a noun] as an
> argument, not a verb like 'small/'&,), but it also allowed the J interpreter
> to infer that when it is executed, it will produce a verb.
> 
> So write_image woke up, looked around for an argument, found 'small/'&, ,
> bound with it, and though it didn't actually execute, the J interpreter knew
> its product would be a verb.  Knowing this, J proceeded parsing the
> sentence, found another verb ((3 3)&resize_image)@:read_image)@:>, and hit a
> close paren.  Since it had found two verbs in isolation (nestled inside a
> cozy pair of parens), it interpreted the train as a hook.  This is really no
> different from the sentence (%~ i.) 10  where ~ immediately binds to %, the
> product of that binding and i. form a hook.
> 
> After forming the hook, the interpreter it hit the noun  i  and applied the
> hook as  ('small/'&,write_image~    3 3&resize_image@:read_image)@:>  i .
> The interpreter executed 3 3 resize_image read_image > i and got a result.
> Up to this point, everything was fine.  But now it came time to use the
> results it had calculated, and actually execute  write_image . That's where
> the problem occurred: and it was exactly the error I mentioned earlier, that
> the interpreter avoided by deferring the execution of write_image (you can
> delay the inevitable, but you can't avoid it). 
> 
> That adverb was written expecting that its argument be a noun, and refers to
> m, which is the name for the noun argument to an adverb (or conjunction).
> But given how you expressed your sentence, in this case argument to
> write_image was a verb:  'small/'&,  .  Therefore m (the name for a noun
> argument to an adverb) was undefined, yet write_image tried to use it
> anyway.
> 
> J calls the use of undefined names a "value error".   This is the same error
> as when you type
> 
>          someNameIHaventDefinedYet 
>       |value error: someNameIHaventDefinedYet
>                
> in the session manager.
> 
> But a closer analogy is the value error you'd get if you tried to use x
> (which names a left argument) in a monadic verb which only has a right
> argument:
> 
>          monad def 'x + y' 4
>       |value error: x
>       |       x+y
>          
> You get a value error because x is undefined, and x is undefined because
> monadic (valences of) verbs don't have the concept of a left argument: x is
> literally meaningless.
> 
> Similarly, when write_image referred to the noun argument m, the J
> interpreter balked: "What noun argument? Your argument is a verb, 'small/'&,
> .  I don't know what you're talking about." .  The name for the
> (non-existent) noun argument to write_image, m, was literally meaningless.
> All because adverbs have higher precedence than verbs and can accept verbs
> as well as nouns as arguments.  
> 
> Well, actually, because Cliff decided to define write_image as an adverb so
> he could have three separate arguments, without boxing.  I know that's a lot
> to digest.  I'm not known for my laconic style (cf Roger Hui), but I hope
> this helps.
> 
> -Dan
> 
> *  Technically, all verbs in J are ambivalent; that is, they can be called
> with either one argument (on the right) or two arguments (one on the right,
> and one on the left).  The words "monad"/"monadic" and "dyad"/"dyadic" are
> just shorthand for the "one-argument valence of the verb" and "the two
> argument valence of the verb" respectively.  
> 
> Note that some valences of some verbs have empty domains, such as the dyad
> ~. or the monad E. or the monad 4 : 'x + y' etc.  That doesn't mean the
> valence doesn't exist; it does exist, but it rejects all arguments (a
> generalization of the concept that e.g. + rejects any argument that's not a
> number).
> 
> Now adverbs and conjunctions (collectively called operators) are analogous
> to the monadic and dyadic valence of a verb respectively, but it is exactly
> because of their higher grammatical precedence that there is no operator
> analog to an ambivalent verb.  That is, there is no operator that can take
> either one argument or two arguments.  Operators' higher binding power
> requires that we treat these cases separately - and, incidentally, is the
> reason adverbs (monadic operators) take their argument from the left, as
> opposed to monadic verbs which take their argument from the right.
> 
> ** The specific coding style that allowed the J interpreter to conclude
> write_image would produce a verb without actually executing it was that it
> mentioned x and y - which, by definition, refer to the noun arguments to an
> explicit verb.  Therefore write_image must produce an explicit verb, and x
> and y refer to /its/ arguments.
> 
> 
> 
> 
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