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:
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-lambdas": only the body is the value of a function, arguments are popped from the stack, the result is pushed on the stack.
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...
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...)
SS: Also check Function as Values and TIP-187 [L1 ] that are both highly related to anonymous functions.