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

Subject: Re: [boost] De Bruijn Bind (alternate bind syntax) Interest?
From: David Sankel (camior_at_[hidden])
Date: 2013-06-23 23:43:12

On Sun, Jun 23, 2013 at 9:40 AM, Larry Evans <cppljevans_at_[hidden]>wrote:

> On 09/02/10 16:08, David Sankel wrote:> 2010/9/2 David Sankel
> <camior_at_[hidden]>
> >
> >> 2010/9/2 Dave Abrahams <dave_at_[hidden]>
> >>
> >> On Thu, Sep 2, 2010 at 11:57 AM, David Sankel <camior_at_[hidden]> wrote:
> >>>
> >>>> Hello all,
> >>>>
> >>>> I've been working on an alternate bind syntax based on De Bruijn
> >>>> indices[1].
> >>>> The syntax is very simple, yet the terms are very powerful.
> >>>>
> >>>> Here is an example of a function const that takes in an argument c and
> >>>> returns another function that, for all input, returns c:
> >>>>
> >>>>    //λx.λy.x = λλ1 with De Bruijn indices.
> >>>>
> >>>
> >>> Not according to the page you linked below.  What am I missing?
> >>>
> >>> [1] http://en.wikipedia.org/wiki/De_Bruijn_index
> >>>
> >>
> >> Sorry about that. The wikipedia page uses 1-indexed indices where I'm
> using
> >> 0-indexed indices. So, increment 1 on all my examples to get the
> wikipedia
> >> syntax.
> >>
> >
> > I'm beginning to think it is better to use 1-indexing instead of
> 0-indexing
> > all around. It will be both compatible with the Wikipedia page and
> familiar
> > to boost bind/lambda users.
> >
> > Funny thing is, I started with 1-indexing but changed it to 0-indexing
> for
> > the fallacious reasoning of the arrrrgh function that Dave A mentioned.
> >
> Hi David,
>
> I looked at the web page mentioned in your first post to this thread
> and could not understand the flip example:
>
>   For flip, I'm introducing subscripts on abstractions (λ) to indicate
>   the number of arguments. For the variables (1,2,etc.) I use a
>   subscript to indicate which argument of the abstraction it refers
>   to.
>
>     flip = λx.λ(y,z).x(z,y) = λ₁λ₂1(1₁, 2₀)
>
> which seems to have a 0 for the subscript of 2.  and 1 for the
> subscript of 1.  That's consistent with the argument indices starting
> at 0 (1₁ corresponds z {the 2nd argument in the argument list, (z,y)},
> and 2â‚€ corresponds to y {the 1st argument in the argument list,
> (z,y)}); however, subscrited numbers should be the same since both y
> and z are bound by the same lamba, the nearest one corresponding to
> number 1.  Hence, shouldn't the above be:
>
>     flip = λx.λ(y,z).x(z,y) = λ₁λ₂2₀(1₁, 1₀)
>
> ?  Also, since the abstraction indices seem to start at 1, shouldn't
> the argument indices also start at 1?  I think that would make the
> notation more consistent, and would result in:
>
>     flip = λx.λ(y,z).x(z,y) = λ₁λ₂2_1(1_2, 1_1)
>
> (where a subscript of I have been replaced with _I).
>

You are correct on both accounts. I fixed the README at de-bruijn-bind's
new home on github.

https://github.com/camio/de-bruijn-bind

Thanks for the bug report!

-- David