Let's Talk About Lambda Functions!

[Bryan Olson]

James J. Besemer wrote:
 > Ian Bicking wrote:
 >
 >
 >>>Decades before anyone implemented a programming language, Alonzo Church
 >>>boiled all the control structures down to just one: lambda.

Actually Ian Bicking did not write that.  I did.

 > Lambda and the Lambda Calculus have nothing to
 > do with "control structures," per se.  The lambda
 > notation itself allowed the definition of True and False,
 > predicates and a conditional expression, the value of
 > which is one of two sub expressions based on a
 > governing predicate.  Technically, however, there's
 > no 'control,' as everything was evaluated, even the
 > sub expression that was discarded.  There is no looping
 > either, only recursive applications of lambda.

That strikes me as failure to abstract.  Lambda can emulate any of the
control structures, and the control structures can all be described as
functions from states to states.

 > Smalltalk's "blocks" are more powerful than Python's
 > Lambda and even Church's Lambda notation.

The lambda calculus is equal in power to the Turing machine.  In the
important sense, no implementable language is more powerful.


--Bryan