2010/9/2 Stewart, Robert <Robert.Stewart@sig.com>
David Sankel wrote:
I've been working on an alternate bind syntax based on De Bruijn indices[1].
I started to look at the Wikipedia page, but realized there was way too much for me to learn to even begin to understand what you mean. Therefore, this reference is of no value to anyone without your background.
It requires someone casually familiar with lambda calculus. Lambda calculus involves the creation of anonymous functions. λv.e declares a new function. v is the identifier bound to the argument and e is an expression that can use v. For example λx.x+1 creates a new function that returns its argument plus 1. Expressions can include other lambdas (called abstractions) and function applications. Consider the function λx.λy.x+y. This function actually returns another function which can be applied yet again. Here it is being called with some values. ((λx.λy.x+y)(22))(14) ← here x is being substituted by 22 => (λy.22+y)(14) ← now y is being substituted by 14. => 22+14 => 36 De Bruijn indices are a way to remove the need for binding a name to the variable in our function declaration. So, instead of λv.e, where e can use v, we say λe where e uses "1" to refer to the argument. The reason for using 1 is to distinguish between between nested lambdas. λx.λy.x(y) becomes λλ2(1). Note that 1 and 2 aren't the normal arithmetic variants, these are De Bruijn indices. The 2 refers to the outer lambda and the 1 refers to the inner lambda.
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. auto const_ = abs<1>( abs<1>( var<1,0>() ) );
Presumably, "abs" doesn't mean absolute value as it would in pretty much any other programming context. That seems unwise at best.
I disagree. We have namespaces to take care of duplicate identifiers and abs is the commonly used identifier for lambda abstractions in programming contexts you might not be aware of.
More examples, further explanation, and an implementation are
available here[2].
I found your README. The grammar section assumes I know what you mean by "abstraction" and "application," at the least, which I don't. The examples section does absolutely nothing for me as I don't understand the syntax or terminology. The result is that I can't make anything of your *bind* proposal.
Hopefully this helps. Thanks for the feedback. David -- David Sankel Sankel Software www.sankelsoftware.com 585 617 4748 (Office)