[Richard Suchenwirth] 2002-02-14 - Lambda is the name for the letter "L" in the Greek alphabet. Since Alonzo Church's "Lambda calculus", it is also the term for anonymous functions. Consider
 f(x) = x+1
is not much different from
 g(x) = x+1
except for the f/g difference, which are both arbitrary names. The common essence of the above functions, ignoring the name, is just
 (x) = x+1
or in other words, "given x, return x+1". In Tcl, this looks like
 lambda x {expr {$x+1}}
and it's easy to implement - see [Lambda in Tcl].

To have lambdas directly, one change to Tcl would be:
   * If a command name is a list of length three, with [lambda] as first element, bind its arguments to the second element of the list, and then evaluate the third element in that scope.

As long as we don't have this, a simple way is to make up a name for a [proc]:
 proc lambda {argl body} {
    set name [info level 0]
    proc $name $argl $body
    set name
 }
where the lambda definition is returned as command name.

A more [functional programming] way would be, using the [K] combinator:
 proc lambda {argl body} {K [info level 0] [proc [info level 0] $argl $body]}
 proc K {a b} {set a}

See also [RPN again] for "[half-lambda]s": only the body is the value of a function, arguments are popped from the stack, the result is pushed on the stack.

[MS] 2004-04-23
Although not really functionalprogramming, one might try to do
  lambda x {set ::y x}
But this fails: Tcl tries to create a proc named "y x}" in the namespace "lambda x {set ", instead of the intended proc. This may be a namespace bug though.
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It seems like it would be pretty easy for [unknown] to do this automatically...
[RS]: Yes. Good idea. [Let unknown know]. It would just miss the efficiency of C-coded Tcl, but with today's CPUs, that's less of a problem...
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[RS]: While the term ''lambda'' was coined by Alonzo Church, the concept is older. I found one instance in "Funktion und Begriff", Gottlob Frege (1848-1925), Jena 1891, where he identifies functions by their ''Werteverlauf'' (value extension?), without naming them. Instead, he first puts a Greek vowel with "spiritus lenis" (looking like a superscript comma on top of the letter), and then the function "body" in parens. He then goes to show (translated to modern ASCII, and even (almost) Tcl :) that
 lambda e {expr $e**2 - 4*$e} == lambda a {expr $a * ($a - 4)}
In other words, that the two anonymous functions are identical. To prove this, one would have to iterate over all possible values of e and a (which, even with doubles, is finite, but might take a long time...)
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[SS]: Also check [Functions as Values] and TIP-187 [http://www.tcl.tk/cgi-bin/tct/tip/186.html] that are both highly related to anonymous functions.
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