Strachey: I should like to intervene now and try to initiate a slightly more general discussion on declarative or descriptive languages and to try to clear up some points about which there is considerable confusion. I have called the objects I am trying to discuss DLs because I don't quite know what they are. Here are some questions concerning ])Ls: (1) What are DLs? (2) What is their relationship to imperative languages? (3) Why do we need DLs? (4) How can we use them to program? (5) How can we implement them? (6) How can we do this efficiently? (7) Should we mix l)Ls with imperative languages?
It seems to me that what I mean by DLs is not exactly what other people mean. I mean, roughly, languages which do not contain assignment statements or jumps. This is, as a matter of fact, not a very clear distinction because you can always disguise the assignments and the jumps, for that matter, inside other statement forms which make them look different. The important characteristic of DLs is that it is possible to produce equivalence relations, particularly the rule for substitution which Peter Landin describes as (~) in his paper. That equivalence relation, which appears to be essential in alost every proof, does not hold if you allow assignment statements. The great advantage then of l)Ls is that they give you some hope of proving the equivalence of program transformations and to begin to have a calculus for combining and manipulating them, which at the moment we haven't got.
I suggest that an answer to the second question is that DLs form a subset of all languages. They are an interesting subset, but one which is inconvenient to use unless you are used to it. We need them because at the moment we don't know how to construct proofs with languages which include imperatives and jumps.
How should we use them to program? I think this is a matter of learning a new programming technique. I am not convinced that all problems are amenable to programming in DLs but I am not convinced that there are any which are not either; I preserve an open mind on this point. It is perfectly true that in the process of rewriting programs to avoid labels and jumps, you've gone half the way towards going into 1)Ls. When you have also avoided assignment statements, you've gone the rest of the way. With many problems yeu can, in fact, go the whole way. LisP has no assignment statements and it is remarkable what you can do with pure Lisp if you try. If you think of it in terms of the implementations that we know about, the result is generally intolerably inefficient--but then that is where we come to the later questions.
How do we implement them? There have not been many attempts to implement DLs efficiently, I think. Obviously, it can be done fairly straightforwardly by an interpretive method, but this is very slow. Methods which compile a runable program run into a lot of very interesting problems. It can be done, because DLs are a subset of ordinary programming languages; any programming language which has sufficient capabilities can cope with them. There are problems, however: we need entities whose value is a function--not the application of a function but a function--and these involve some problems.
How to implement efficiently is another very interesting and difficult problem. It means, I think, recognizing certain subsets and transforming them from, say, recursions into loops. This can certainly be done even if they have been written iu terms of recursions and not, as Peter Landin suggested, in terms of already transformed functions like iterate or while.
I think the last question, "Should DLs be nIixed with imperative languages?", clearly has the answer that they should, because at the moment we don't know how to do everything in pure DLs. If you mix declarative and imperative features like this, you may get an apparently large programming language, but the important thing is that it should be simple and easy to define a function. Any language which by mere chance of the way it is written makes it extremely difficult to write compositions of functions and very easy to write sequences of commands will, of course, in an obvious psychological way, hinder people from using descriptive rather than imperative features. In the long run, I think the effect will delay our understanding of basic similarities, which underlie different sorts of programs and different ways of solving problems.
Smith: As I understand the declarative languages, there has to be a mixture of imperative and descriptive statements or no computation will take place. If I give you a set of simultaneous equations, you may say "yes?", meaning well, what am I supposed to do about it, or you may say "yes", meaning yes I understand, but you don't do anything until I say "now find the values of the variables." In fact, in a well-developed language there is not just one question that I can ask but a number of questions. So, in effect, the declarative statements are like data which you set aside to be used later after I give you the imperatives, of which I had a choice, which get the action.
Strachey: This is a major point of confusion. There are two ideas here and I think we should try to sort them out. If you give a quadratic equation to a machine and then say "print the value of x", this is not the sort of language that I call a DL. I regard it as an implicit language--that is, one where you give the machine the data and then hope that it will be smart enough to solve the problem for you. It is very different from a language such as LisP, where you define a function explicitly and have only one imperative. which says "evaluate this expression and print the result."
Abrahams: I've clone a fair amount of programming in LISP, and there is one situation which I feel is symptomatic of the times when you really do want an imperative language. It is a situation that arises if you are planning to do programming in pure Lisp and you find that your functions accumulate a large number of arguments. This often happens when you have a number of variables and you are actually going through a process and at each stage of the process you want to change the state of the world a little bit-- say, to change one of these variables. So you have the choice of either trying to communicate them all, or trying to do some sort of essentially imperative action that changes one of them. If you try to list all of the transitions from state to state and incorporate them into one function, you'll find that this is not really a very natural kind of function because the natures of the transitions are too different.
Landin: I said in iny talk that LisP had not gone quite all the way and I think that this difficulty is connected with going all the way. If we write a function definition where the right-hand side is a listing of expressions such as
F(x) = E1 , E2, E~
thel~ we can say that this function will produce a three-list as its result. If llOW we have ~mother function G(x, y, z) = E, on some occasion we might have an expression such as G(a 2, b 2, c ~) and we often feel that we should be able to write G(F(t)), and another example which should be allowed is
G(a > b --~ E1 , E2 , E3 else E4 , E5 , E6).
l am not quite sure but I think you can get around your problem by treating every function as if it were in fact monadic and had a single argument which was the list structure you are trying to process.
Abrahams: This is a difficulty in other programming languages too; you cannot define a function of an indefinite number of arguments.
Naur: I still don't understand this distinction about an implicit language. Does it mean that whenever you have such a language there is a built-in feature for solving equations?
Abrahams: I think the point is whether you are concerned with the problem or are concerned with the method of solution of the problem.
Ingerman: I suggest that in the situation where you have specified everything that you want to know, though the exact sequence in which you evoke the various operations to cause the solution is left unspecified, then you have something which is effectively a descriptive language; if you have exactly the same pieces of information, surrounded with promises that you will do this and then this, then you have an imperative language. The significant point is that it is not all or nothing but there is a scale and while it is probably pretty simple to go all the way with imperatives, the chances of being ttble to get all the way descriptive is about zero, but there is a settle and we should recognize this scale. Smilh: I think that there is a confusion between implicit or explicit on the one hand and imperative or declarative on the other. These are two separate distinctions and can occur in all combinations. For illstance, an analog computer handles ilnplicit declaratives.
Young: I think it is fairly obvious that you've got to have the ability for sequencing imperatives in any sort of practical language. There are many, many cases in which only a certain sequence of operations will produce the logically correct results. So that we cannot have a purely declarative language, we must have a general purpose one. A possible definition of a declarative language is one in which I can make the statements (a), (b), (c) and (d) and indicate whether I mean these to be taken as a sequence or as a set; that is, must they be performed in a particular order or do I merely mean that so long as they are all performed, they may be performed in any sequence at any time and whenever convenient for efficiency.
Strachey: You can, in fact, impose an ordering on a language which doesn't have the sequencing of commands by nesting the functional applications.
Landin: The point is that when you compound functional expressions you are imposing a partial ordering, and when you decompose this into commands you are unnecessarily giving a lot of inforination about sequencing.
Strachey: One inconvenient thing about a purely imperative language is that you have to specify far too much sequencing. For example, if you wish to do a matrix multiplication, you have to do n a multiplications. If you write an ordinary program to do this, you have to specify the exact sequence which they are all to be done. Actually, it doesn't matter in what order you do the multiplications so long as you add them togcther in the right groups. Thus the ordinary sort of imperative language imposes much too much sequencing, which makes it very difficult to rearrange if you want to make things more efficient.
Monday, July 12, 2010
At the end of the Peter Ladin's "The next 700 programming languages" There is a very interesting discussion between giants (Strachey, Landin, Smith, Young, and Abrahams) of the software engineering. A definite must read...