Lambda the Ultimate

From picking up some Arizona site docs to completely rewriting a troublesome Pascal program (used for data analysis and billing from dialup logs) was 3 days. Maintenance of the system became a breeze as well

I though it was just the bees knees at the time. I still use it for data analysis and data conversions.

SNOBOL4 was used on site to generate DNS (Distributed Network Suoervisor) configuration files for our corporate metwork in the days when X25 (and the OSI 7 layer model) was the big competition to SNA.

Pretty much all of the information about Snobol available on the Internet can be found following these links (with a great deal of overlapping):
http://www.snobol4.org
http://www.snobol4.com
ftp://ftp.snobol4.org/snobol
There are reference manuals, tutorials, implementations, and historical documents there.

It will succeed immediately with 0 = 0.

To get anything else you would need to formulate it like

if (0 | 1) = (1 | 0) ...

This would then do the following tests

0 = 1 fail
0 = 0 succeed with 0 as the result

Another example would be

if (0 | 10) = ( 1 | 2 | 3 | 4 | 10) then

results would be

0 = 1 fail
0 = 2 fail
0 = 3 fail
0 = 4 fail
0 = 10 fail
10 = 1 fail
10 = 2 fail
10 = 3 fail
10 = 4 fail
10 = 10 succeed with result as 10

Icon allows for the following kinds of tests

if i ‹ j ‹ k ‹ m then ....

This means that i ‹ j and j ‹ k and k ‹ m with the result being the value held in m.

Fixed typo above

The (0 | 1) = (1 | 0) case is what I meant, but for some reason failed to type.

But thanks for the explanation; the key bit I was wondering was whether evaluation of generators was in parallel or nested. Your second example illustrates that it's parallel.

It is actually right to left resumption, innermost to outermost with evaluation left to right with right hand side being the success value, if that makes any sense.

So 0 is tested against 1 then 0, which is LR evaluation and RL resumption, and then 1 is tested against 1 and success, no testing against 0

First, that's a wonderful obituary.

I hope a technical followup won't be inappropriate:

SL5 had a interesting generalized procedure mechanism and made use of a unique concept of "argument transmitters" which are procedures (either built-in or programmer defined) that are called when values are bound to arguments. This approach was abandoned, but may still be of some interest.

This made me think of monads. Inside a "do" block, the "bind" procedure is called whenever a monadic value is bound to a variable. The ability to abstract and hide the operations that take place during this binding is central to the functionality of monads. So rather than having been abandoned completely, the SL5 approach could perhaps be seen as an early precursor to monads.

The problem I have with that is that 'bind' is entered first (well, in Haskell at least) before bindings(*) are made.

(*) Since 'bind' is also defined for 'a' function value, could we say that it is even 'aware' of the pseudo-bindings established in the desugared lambda exp that it receives as an arg? In the quoted paragraph it appears that the argument transmitters are intimately familiar with the environment.

Actually, I wasn't reminded of monads, but maybe it's due to lack of imagination on my part. Let me give the example given in "An Overview of SL5" for AT, to make things more concrete.

positiveint:=procedure (n)
   if (n:= integer(n)) >0
     then succeed n
     else fail
end

gcd:=procedure (x:positiveint, y:positiveint)

positiveint is the user-defined procedure used as an argument transmitter. When used in the definition of gcd, only arguments that can be converted to integers (via integer(n)) will be passed to gcd. Other values will cause the call to fail.

Interestingly, the language provides three built-in transmitters: val (pass by value), ref (pass by reference) and exp (pass "by expression", similar to Algol's pass by name). Transmitters can be procedures (user defined,or built-in) or environments, which are "source-language data objects" in SL5 (i.e., they are first class).

I remind you of Wirth's opinion about pass by exression. Here's a connection between these two historical discussions. Also note that AT can be used to mimic some primitive form of AOP.

Let me give the example given in "An Overview of SL5" for AT, to make things more concrete.

positiveint:=procedure (n)
   if (n:= integer(n)) >0
     then succeed n
     else fail
end

gcd:=procedure (x:positiveint, y:positiveint)

positiveint is the user-defined procedure used as an argument transmitter. When used in the definition of gcd, only arguments that can be converted to integers (via integer(n)) will be passed to gcd. Other values will cause the call to fail.

This illustrates the comparison to monads nicely. The implementation above apparently depends on the success/failure mechanism, so the argument transmitter is acting like the bind procedure of the Maybe monad, which doesn't apply its continuation on failure.

I'll demonstrate with Scheme, since macros will come in handy to counter Koray's nitpick. The success/failure behavior can be implemented starting with a standard Maybe monad, which can be defined minimally in Scheme as:

; minimal maybe monad
(define maybe (lambda (x) x))           ; 'return' for this Maybe monad
(define fail #f)                        ; the equivalent of 'Nothing'
(define (maybe-bind m k) (and m (k m))) ; 'bind' for this Maybe monad

This monad can be transformed to implement the positive integer test, by defining another monadic bind procedure in terms of maybe-bind:

(define (positive-int m succeed)
  (maybe-bind m
    (lambda (n)
      (if (and (integer? n) (> n 0))
          (succeed n)
          fail))))

The variables are named to match the SL5 argument transmitter, but note that this is a standard 'bind' procedure which takes a monad m and a continuation succeed. The similarity to the SL5 version is strong, with the difference being the need to use maybe-bind to access the monadic value, and the inclusion of an explicit continuation argument.

To implement the GCD procedure in a way that exploits the Maybe monad, we can adapt the mplus procedure from Haskell's MonadPlus type class, which has a very simple implementation for our Maybe monad — it's just an or:

(define (maybe-mplus x y) (or x y))   ; mplus for Maybe monad

Now gcd can be implemented as follows:

(define (mygcd x y)
  (positive-int x (lambda (x)
  (positive-int y (lambda (y)
    (maybe-mplus (mygcd (maybe y) (maybe (modulo x y)))
                 (maybe y)))))))

The comparison to zero is hidden inside the positive-int bind operation, and maybe-mplus is used to express the choice between branches, so the behavior of 'bind' is integral to the gcd algorithm, just as it is with the SL5 argument transmitter.

The above code is complete and fully operational, e.g. (mygcd 18 30) produces 6.

To address Koray's nitpick, mygcd can be sweetened with a macro: a lambda/m form which accepts a bind procedure for each of its arguments. I'll also cheat slightly in the interestes of readability, and omit the maybe calls, which aren't needed with our direct implementation of the maybe monad:

(define mygcd
  (lambda/m ((x positive-int) (y positive-int))
    (maybe-mplus (mygcd y (modulo x y)) y)))

This looks quite similar to the (incomplete) definition from SL5:

gcd:=procedure (x:positiveint, y:positiveint)

It would be interesting to see how the bodies compare.

In both cases, a named procedure is called for each argument, and that procedure tests the argument for a positive integer, either invoking a success continuation or abandoning the current continuation with a failure return. In my example, the procedure in question is a typical monadic 'bind' procedure, which corresponds closely to the SL5 argument transmitter in purpose and structure.

For completeness, here are the macro definitions:

(define-syntax monad-let*
  (syntax-rules ()
    ((_ () body ...)
     (begin body ...))
    ((_ ((arg0 bind0) (arg1 bind1) ...) body ...)
     (bind0 arg0
       (lambda (arg0)
         (monad-let* ((arg1 bind1) ...) body ...))))))

(define-syntax lambda/m
  (syntax-rules ()
    ((_ ((arg0 bind0) (arg1 bind1) ...) body ...)
     (lambda (arg0 arg1 ...)
       (monad-let* ((arg0 bind0) (arg1 bind1) ...)
         body ...)))))

Of course, Griswold's focus on nondeterministic evaluation approaches made it inevitable that his work would overlap with monads. It's interesting to see a specific example of that overlap, more than a decade before the initial work on monads.

BTW, an interesting paper in this area is Backtracking, Interleaving, and Terminating Monad Transformers.

Edit: Based on my limited knowledge of Icon, and without having seen the body of the SL5 gcd example when I wrote the above, I jumped to the conclusion that it was a recursive implementation, and that it would naturally exploit its own argument transmitter to achieve termination, so I did the same in my example implementation. Turns out I was being over-imaginative. I found a 1993 issue of The Icon Analyst, an allegedly bimonthly newsletter edited by Ralph and Madge Griswold. It contains an article "Lost Languages - SL5", which gives an imperative, non-recursive GCD example, so the argument transmitter is only called once on entry. This doesn't affect the comparison between argument transmitters and monadic bind, but it does mean that my gcd example above exploits the positive-int monad in a way that wasn't being done in the SL5 gcd example. However, it still seems to me that SL5 might have been capable of such an implementation.

It is interesting that Icon does not provide a rich set of primitive pattern matching procedures, and does not support declarative pattern matching of the kind found in SNOBOL, or even in regular expression based libraries and languages. This decision seems quite radical, and indeed it may be the reason that languages such as Perl and AWK ( a language inspired heavily by SNOBOL, according to Griswold[4]) were preferred by programmers. This can be explained by appeal to the "worse is better" principle, which often refers to the Bell Labs software building approach. Both SNOBOL and AWK were Bell Labs creations, while Icon was not.

I haven't read the whole of reference [4] yet, but there's a comment about this in the issue of The Icon Analyst that I found:

In retrospect, SL5 has many interesting features. [...] Not surprisingly, on rediscovering some of the features of SL5, we thought "Gee, those would be neat things to have in Icon." But Icon has grown large. If there's anything we think language designers should do is avoid the temptation to "kitchen sink" (to coin an abominable verb from a noun).

In this context, though, I think "worse is better" is a misleading description of the forces at work. It's more like "more is better": kitchen-sinking succeeds because it appeals to a larger market, particularly in languages, where most people don't want to have to learn and use multiple languages. They want the language they use to be as widely-applicable as possible, unless they have specialized requirements.

I think that in this specific context the issue is expressiveness. Being able to express patterns declaratively is important from an expressiveness point of view. While this approach has its difficulties (namely the things that led to the creation of SL5 and later Icon), it has distinct advantages (being declarative and thus easier to read, easy compositionality etc.) that were abandoned for no good reason.

(BTW, as far as I can tell, neither SL5 nor Icon have declarative pattern matching, as found in SNOBOL, so the issue isn't SL5 vs. Icon, but rather SNOBOL4 vs. (SL5 & Icon))

There are libraries in Icon/Unicon that attempt to provide the pattern matching features of SNOBOL4.

The interesting things about Icon/Unicon is that you have the ability to write your own generators. In regards to string matching/processing functions, as long as you follow the string matching protocol, your functions are treated no differently to the system procedures. Hence you can extend the matching procedures any way you want to.

In addition, there is library functions available that do a similar job on lists as for strings. The only difference really is that you can't use ? as the pattern matching operator.

Just as an aside, in the IPL are the applications, SKEEM (a version od Scheme) and IDOL (Icon Object Language - this incorporated directly into Unicon). SKEEM is an interpreter and IDOL is a compiler to Icon. These show how to do fairly significant applications in Icon. The Programming in Unicon book (obtainable from the Unicon website) goes into details of application building in Unicon - for those who are interested.

I posted a link a while back on SNOBOL-Style Patterns for Unicon which goes into more detail on the subject.

This is a subject that is discussed on occassion on the unicon-group. It requires changes to the runtime system that requires someone to be involved with.

Currently, some suggestions for analysing unicode involve treating the stream as b-bit values.

Anyone care to be involved in internationalization efforts would best need to contact Clint Jeffery or see his homepage or the Unicon website.

I think this relates to one of my own issues. People usually think of string processing in terms of regular expressions. If we think in terms of XML we actually have a parenthesized list expression if we make some sort of conversion. Processing a list in Lisp is normally recursive and functional. Prolog offers even better pattern matching if only we start out with properly formatted data (ie predicates), and Prolog certainly doesn't use state. Why don't more programmers choose these alternative?? What am I missing?

Puzzled!

Having used prolog for parsing natural language text (in a very limited domain), I can say that it is both wonderful and terrible. DCGs are far more expressive, easier to use, and much much easier to read then regexps. The implementations that I generated however often required lots of tuning to make them efficient enough to use. From the hand optimizations that I made I came to the conclusion that most of this can be eliminated if we can know that we are dealing with strings (i.e. some notion of typing) some determinacy analysis, tabling (I wasn't using XSB) and some reordering of terms.

Prolog really is not enough out of the box to compete on the scale of simple expressions like the ones produced by regexps, and DCGs as given do not scale to serious problems easily. It would be nice to see these problems solved in the prolog style, since I think it really is infinitely better than using regexps.