I only just noticed that weinzierl did this one four hours ago.

Dr. Edsger W. Dijkstra
to John Backus
International Business Machines Corporation
5600 Cottle Road
SAN JOSE CA 95193
U.S.A.

Monday 29th of May, 1978

"To interrupt one's own researches in order to follow those of another is a scientific pleasure which most experts delegate to their assistants."
(Eric Temple Bell in "Development of Mathematics")

Dear John,

I do not claim to be more noble or sensible than "most experts"; perhaps it is only because I have only one assistant to whom I can delegate no more than one man can do. But when you open your letter with: "I am quite sure that you have never read any paper I've sent you before" it is my pleasure to inform you that - although "quite sure" - you were very wrong. I very well remember that you mailed me a sizeable paper on reduction languages to which I owe my introduction to the subject. I didn't only read it, parts of it were even studied. I also remember that it left me with mixed feelings.

I can very well understand your excitement, although, for lack of experience, I still cannot share it. I am far from delighted with the state of the art of programming today, and anyone suggesting an alternative has in principle my sympathy - until, of course, he loses it again, like Terry Winograd did when he suggested natural language programming - "natural descriptions"! - as an alternative -. In the long run I have more faith in any rephrasing of the programming task that makes it more amenable to mathematical treatment. But you must have lots of patience, for the run will be very long. It isn't just mental inertia - that problem can be solved generally by educating a new generation of youngsters and waiting until the old ones have died -. It is the development of a new set of techniques needed to achieve a comparable degree of proficiency.

Could you get me a copy of G. A. Mago's (not yet published) "A network of microprocessors to execute reduction languages"? That might whet my appetite! From various angles I have looked into such networks and I am not entirely pleased with what I have seen. Firstly I suspect our techniques for proving the correctness of such designs: each next proof seems to differ so much from all the previous ones, I suspect that we haven't found the general patterns yet. Secondly I discovered that all I could design were special purpose networks, which, of course, made me suspect the programming language in the Von Neumann style which, already before you have chosen your problem, seems to have set you on the wrong track.

Semantically speaking the semicolon is, of course, only a way of expressing functional composition: it imposes the same order that can also be expressed with brackets - innermost brackets first -. In combination with the distribution you can generate many innermost bracket pairs, thus expressing very honestly that it is really only a partial order that matters. I like that, it is honest.

When you write "One can transform programs [....] by the use of laws [...] which are _part of the programming language_" etc. I am somewhat hesitant. I am not convinced (yet?) that the traditional separation in fixed program, variable data and assertions is a mistake. The first and the last - program and assertions - are somewhat merged in LUCID, in which correctness proofs are carried out in (nearly) the same formalism as the program is expressed in. On the one hand that presents a tempting unification, on the other hand I thought that mathematicians separated carefully and for good reasons the language they talk about and the metalanguage in which they do so. To put it in another way: given a functional program, I feel only confident if I can do enough other significant things to it besides carrying it out. And those I don't see yet. The almost total absence of redundancy is another aspect of the same worry. In the case of a traditional program we know how to make it redundant: by inserting assertions, combination of text and assertions makes it into a logically tightly knit whole, that gives me confidence. How do we this with functional programs? By supplying two of them and an argument that demonstrates their equivalence?

What about the following example? (My notation, because I lack the fluency in yours.)

(1) Consider the function f defined by:
f(0)=0, f(1)=1, f(2n)=f(n), f(2n+1)=f(n)+f(n+1)

(2) Consider the following program ("peven" = "positive and even", so for "podd") [1]

{N >= 0} n,a,b := N,1,0;
do peven(n) -> a,n := a+b,n/2
| podd(n) -> b,n = b+a,(n-1)/2
od {b=f(N)}

Here (1) gives a recursive definition of f, (2) gives a repetitive program. Both definitions can be translated in a straightforward manner into functional programs. What would be involved in the demonstration of their equivalence?

The above seems to me a little example of the appropriate degree of sophistication to try your hands on. (I am not going to try it myself, as I fear that my past experience would misguide me: I am afraid that I wouldn't rise above the level of translating (2)'s traditional correctness proof - with which I am very familiar - in an unfamiliar notation. Good luck!)

With my greetings and warmest regards,

yours ever
Edsger

P.S. Please note my new postal code: 5671 AL (capitals obligatory) _in front of_ the village name.

EWD.

Transcriber's notes:

[1] This was a little difficult to transcribe cleanly into pure text. The "od" on the last line is clearly the ending delimiter for the opening "do" (both of which were lowercase and underlined). The pipe on the second-last line was, I think, meant to clearly show that the line beside it was within the do loop.

In a few places Dijkstra underlined text. With some I have not carried that over, with others I've surrounded the text with underscores.