[Om3] homework, describing a definition for n-ary plus

[Lars Hellström]

Jan Willem Knopper skrev 2014-06-05 17.47:
> <!--
>    NOTATION: arith1.plus is<OMS cd='arith1' name='plus'/>
>
>    This is a example description of an n-ary plus, defined based on a
> binary plus (for which I use homework2.plus2).
>
>    homework1.function_with_arguments describes an n-ary function which
> can be defined by allowing access to the arguments in a single variable
> (by an OMBIND).

OK, so that's essentially a sibling of fns1.lambda, which gives you the list 
of the arguments as one object (that can then be decomposed), instead of 
binding a separate variable to each argument.

This will let you define many n-ary functions, so it's useful, but it 
doesn't get very far with other forms of stating properties of them. I.e., 
it lets you define a plus such that it will be n-associative, but can you 
state as an FMP that it is n-associative?

> Several computer languages have a keyword or accessor to
> get to an array of arguments (Javascript, GAP).
>
>    homework1.length returns the length of an argument sequence/list
>
>    homework1.first returns the first argument of an argument sequence/list
>
>    homework1.rest returns a new argument sequence/list containing all but
> the first argument.
>
>    homework1.argument_sequence is implied (argument list)

Duplicates stuff from list1 and list2.

> -->
> <--
>    real question
>
>    is the idea that I describe an n-ary function with a new cd good
> enough for all applications ?

I believe you can handle at least 98% of all such situations with just a few 
new symbols, i.e., no change needed to the standard. The area where this 
would get into trouble is saying things about binders that bind a variable 
number of variables, since binding a variable is syntactically special.

>    regardless of whether we need it for this definition it might be good
> to have some new kind of apply function that calls a function with the
> arguments in a list (list1.list ?).

Yes. That is essentially my take on the subject. I intend to submit such a 
CD for OM2014, so I'd like to polish it for a few days more.

>    will it be good enough to do this in a cd as well,
>
>    homework1.apply_with_arguments:
>
>
> @(homework1.apply_with_arguments,arith1.plus,@(homework1.argument_sequence,1,2,3))

My preferred style is rather

  @(list4.eval,@(list1.list,arith1.plus,1,2,3))


>    is it possible to do correct types for this, or will this run into
> problems ?

I don't really care. Types are overrated, and often thrown around in a 
frighteningly naive manner.  :-)


Lars Hellström