Re: [boost] De Bruijn Bind (alternate bind syntax) Interest?

Subject: Re: [boost] De Bruijn Bind (alternate bind syntax) Interest?
From: Larry Evans (cppljevans_at_[hidden])
Date: 2010-09-04 07:39:00

On 09/04/10 06:09, Larry Evans wrote:
> On 09/03/10 10:33, David Sankel wrote:
>> On Fri, Sep 3, 2010 at 8:04 AM, Stewart, Robert <Robert.Stewart_at_[hidden]>wrote:
>>
>>> Larry Evans wrote:
>>>> On 09/03/10 06:33, Stefan Strasser wrote:
>>>>
>>>> In:
>>>>
>>>>   lam<I>
>>>>
>>>> I is arity, not nesting, of the lambda expression:
>>>>
>>>>   http://bitbucket.org/camior/de-bruijn-bind/src#cl-45
>>>>
>>>> IOW:
>>>>
>>>>     \(x1,x2,x3).x1+x2+x3
>>>> =>
>>>>     lam<3>(arg<0,1>+arg<0,2>+arg<0,3>)
>>>
>>>    lam<3>(_0_1 + _0_2 + _0_3) (using zero-based indices)
>>>
>>> So much more readable, don't you think? ;-)
>>>
>>
>> Yes. I've added the following syntactic enhancements to the code (and
>> updated README) at http://bitbucket.org/camior/de-bruijn-bind
>>
>>    - abs -> lam
>>    - var -> arg
>>    - some _x_y shorthands for arg<x,y>()
>>
> 
> Since most of the time the user will be referring to the
> arg<0,I>, why not switch args to arg to allow defaulting
> the 2nd arg for the common case?  IOW, something like:
> 
>   template
>   < unsigned ArgIndex
>   , unsigned NestingLevel=0
>   >
> struct arg
> ;
> 
> instead of:
> 
>   template
>   < unsigned NestingLevel
>   , unsigned ArgIndex
>   >
> struct arg
> ;
> 
> This would allow:
> 
>   typedef arg<1> _1;
>   typedef arg<2> _2;
>   ...

Also, if:

  template
  < unsigned Arity=1
  >
struct lam
;

then:

  \(x1,x2,x3).x1+x2+x3

=curry=>

  \x1\x2\x3.x1+x2+x3

=deBruijn=>

  lam(lam(lam(arg<1,2>+arg<1,1>+arg<1,0>)))

which illustrates that only a single argument arg template
is needed.

I also illustrates that the nesting level is the
reverse of the argument order.  I wonder why
DeBruijn preferred that way?

OTOH, how would you express a nullary function?
IOW, is the following possible with current code?

  lam<0>(9)