LAMBDA:

THE ULTIMATE DECLARATIVE

1.1. Primitive Operations in Programming Languages

What are the primitive operations common to all high-level programming languages? It is the data manipulation primitives which most clearly differentiate high-level languages: FORTRAN has numbers, characters, and arrays; PL/I has strings and structures as well; LISP has list cells and atomic symbols. All have, however, similar notions of control structures and of variables.

If we ignore the various data types and data manipulation primitives, we find that only a few primitive ideas are left. Some of these are:

Transfer of control may be subdivided into conditional and unconditional transfers. Environment operations include binding of variables on function entry, declaration of local variables, and so on. Side effects include not only modifications to data structures, but altering of global variables and input/output. Process synchronization includes such issues as resource allocation and passing of information between processes in a consistent manner.

Large numbers of primitive constructs are provided in contemporary programming languages for these purposes. The following short catalog is by no means complete, but only representative:

Often attempts are made to reduce the number of operations of each type to some minimal set. Thus, for example, there have been proofs that sequential blocks, IF-THEN-ELSE, and WHILE-DO form a complete set of control operations. One can even do without IF-THEN-ELSE, though the technique for eliminating it seems to produce more rather than less complexity. {Note No IF-THEN-ELSE} A minimal set should contain primitives which are not only universal but also easy to describe, simple to implement, and capable of describing more complex constructs in a straightforward manner. This is why the semaphore is still commonly used; its simplicity makes it is easy to describe as well as implement, and it can be used to describe more complex synchronization operators. The expositors of monitors and path expressions, for example, go to great lengths to describe them in terms of semaphores [Hoare 74] [Campbell 74]; but it would be difficult to describe either of these “high-level” synchronization constructs in terms of the other.

With the criteria of simplicity, universality, and expressive power in mind, let us consider some choices for sets of control and environment operators. Side effects and process synchronization will not be treated further in this paper.

1.2. Function Invocation: The Ultimate Imperative

The essential characteristic of a control operator is that it transfers control. It may do this in a more or less disciplined way, but this discipline is generally more conceptual than actual; to put it another way, “down underneath, DO, CASE, and SELECT all compile into IFs and GOTOs”. This is why many people resist the elimination of GOTO from high-level languages; just as the semaphore seems to be a fundamental synchronization primitive, so the GOTO seems to be a fundamental control primitive from which, together with IF, any more complex one can be constructed if necessary. (There has been a recent controversy over the nested IF-THEN-ELSE as well. Alternatives such as repetitions of tests or decision tables have been examined. However, there is no denying that IF-THEN-ELSE seems to be the simplest conditional control operator easily capable of expressing all others.)

One of the difficulties of using GOTO, however, is that to communicate information from the code gone from to the code gone to it is necessary to use global variables. This was a fundamental difficulty with the CONNIVER language [McDermott 74], for example; while CONNIVER allowed great flexibility in its control structures, the passing around of data was so undisciplined as to be completely unmanageable. It would be nice if we had some primitive which passed some data along while performing a GOTO.

It turns out that almost every high-level programming language already has such a primitive: the functional call! This construct is almost always completely ignored by those who catalog control constructs; whether it is because function calling is taken for granted, or because it is not considered a true control construct, I do not know. One might suspect that there is a bias again function calling because it is typically implemented as a complex, slow operation, often involving much saving of registers, allocation of temporary storage, etc. {Note Expensive Procedures}

Let us consider the claim that a function invocation is equivalent to a GOTO which passes some data. But what about the traditional view of a function call which expects a returned value? The standard scenario for a function call runs something like this:

1. Calculate the arguments and put them where the function expects to find them.
2. Call the function, saving a return address (on the PDP-10, for example, a PUSHJ instruction is used, which transfers control to the function after saving a return address on a pushdown stack).
3. The function calculates a value and puts it where its caller can get it.
4. The function returns to the saved address, throwing the saved address away (on the PDP-10, this is done with a POPJ instruction, which pops an address off the stack and jumps to that address).

It would appear that the saved return address is necessary to the scenario. If we always compile a function invocation as a pure GOTO instead, how can the function know where to return?

To answer this we must consider carefully the steps logically required in order to compute the value of a function applied to a set of arguments. Suppose we have a function BAR defined as

  (DEFINE BAR
          (LAMBDA (X Y)
                  (F (G X) (H Y))))

In a typical LISP implementation, when we arrive at the code for BAR we expect to have two computed quantities, the arguments, plus a return address, probably on the control stack. Once we have entered BAR and given the names X and Y to the arguments, we must invoke the three functions denoted by F, G, and H. When we invoke G or H, it is necessary to supply a return address, because we must eventually return to the code in BAR to complete the computation by invoking F. But we do not have to supply a return address to F; we can merely perform a GOTO, and F will inherit the return address originally supplied to BAR.

Let us simulate the behavior of a PDP-10 pushdown stack to see why this is true. If we consistently used PUSHJ for calling a function and POPJ for returning from one, then the code for BAR, F, G, and H would look something like this:

  BAR:  ...            F:  ...
        PUSHJ G            POPJ
  BAR1: ...
        PUSHJ H        G:  ...
  BAR2: ...                POPJ
        PUSHJ F
  BAR3: POPJ           H:  ...
                           POPJ

We have labeled not only the entry points to the functions, but also a few key points within BAR, for expository purposes. We are justified in putting no ellipsis between the PUSHJ F and the POPJ in BAR, because we assume that no cleanup other than the POPJ is necessary, and because the value returned by F (in the assumed RESULT register) will be returned from BAR also.

Let us depict a pushdown stack as a list growing towards the right. On arrival at BAR, the caller of BAR has left a return address on the stack.

  ..., <return address for BAR>

On executing the PUSHJ G, we enter the function G after leaving a return address BAR1 on the stack:

  ..., <return address for BAR>, BAR1

The function G may call other functions in turn, adding other return addresses to the stack, but these other functions will pop them again on exit, and so on arrival at the POPJ in G the stack is the same. The POPJ pops the address BAR1 and jumps there, leaving the stack like this:

  ..., <return address for BAR>

In a similar manner, the address BAR2 is pushed when H is called, and H pops this address on exit. The same is true of F and BAR3. On return from F, the POPJ in BAR is executed, and the return address supplied by BAR’s caller is popped and jumped to.

Notice that during the execution of F the stack looks like this:

  ..., <return address for BAR>, BAR3, ...

Suppose that at the end of BAR we replaced the PUSHJ F, POPJby GOTO F. Then on arrival at the GOTO the stack would look like this:

  ..., <return address for BAR>

The stack would look this way on arrival at the POPJ in F, and so F would pop this return address and return to BAR’s caller. The net effect is as before. The value returned by F has been returned to BAR’s caller, and the stack was left the same. The only different was that one fewer stack slot was consumed during the execution of F, because we did not push the address BAR3.

Thus we see that F may be invoked in a manner different from the way in which G and H are invoked. This fact is somewhat disturbing. We would like our function invocation mechanism to be uniform, not only for aesthetic reasons, but so that functions may be compiled separately and linked up at run time with a minimum of special-case interfacing. Uniformity is achieved in some LISPs by always using PUSHJ and never GOTO, but this is at the expense of using more stack space than logically necessary. At the end of every function X the sequence “PUSHJ Y; POPJ” will occur, where Y is the last function invoked by X, requiring a logically unnecessary return address pointing to a POPJ. {Note Debugging}

An alternate approach is suggested by the implementation of the SCHEME interpreter. [Sussman 75] We note that the textual difference between the calls on F and G is that the call on G is nested as an argument to another function call, whereas the call to F is not. This suggests that we save a return address on the stack when we begin to evaluate a form (function call) which is to provide an argument for another function, rather than when we invoke the function. (The SCHEME interpreter works in exactly this way.) This discipline produces a rather elegant symmetry: evaluation of forms (function invocation) pushes additional control stack, and application of functions (function entry and the consequent binding of variables) pushes additional environment stack. Thus for BAR we would compile approximately the following code:

  BAR:    PUSH [BAR1]             ;save return address for (G X)
          <set up arguments for G>
          GOTO G                  ;call function G
  BAR1:   <save result of G>
          PUSH [BAR2]             ;save return address for (H Y)
          <set up arguments for H>
          GOTO H                  ;call function H
  BAR2:   <set up arguments for F>
          GOTO F                  ;call function F

The instruction PUSH [X] pushes the address X on the stack. Note that no code appears in BAR which ever pops a return address off the stack; it pushes return addresses for G and H, but G and H are responsible for popping them, and BAR passes its own return address implicitly to F without popping it. This point is extremely important, and we shall return to it later.

Those familiar with the MacLISP compiler will recognize the code of the previous example as being similar to the “LSUBR” calling convention. Under this convention, more than just return addresses are kept on the control stack; a function receives its arguments on the stack, above the return address. Thus, when BAR is entered, there are (at least) three items on the stack: the last argument, Y, is on top; below that, the previous (and in fact first) one, X; and below that, the return address. The complete code for BAR might look like this:

  BAR:    PUSH [BAR1]           ;save return address for (G X)
          PUSH -2(P)            ;push a copy of X
          GOTO G                ;call function G
  BAR1:   PUSH RESULT           ;result of G is in RESULT register
          PUSH [BAR2]           ;save return address for (H Y)
          PUSH -2(P)            ;push a copy of Y
          GOTO H                ;call function H
  BAR2:   POP -2(P)             ;clobber X with result of G
          MOVEM RESULT,(P)      ;clobber Y with result of H
          GOTO F                ;call function F

There is some tricky code at point BAR2: on return from H the stack looks like:

  ..., <return address for BAR>, X, Y, <result from G>

After the POP instruction, the stack looks like:

  ..., <return address for BAR>, result from G>, Y

That is, the top item of the stack has replaced the one two below it. After the MOVEM (move to memory) instruction:

  ..., <return address for BAR>, <result from G>, <result from H>

which is exactly the correct setup for calling F. Let us not here go into the issue of how such clever code might be generated, but merely recognize the fact that it gets the stack into the necessary condition for calling F.)

Suppose that the saving of a return address and the setting up of arguments were commutative operations. (This is not true of the LSUBR calling convention, because both operations use the stack; but it is true of the SUBR convention, where the arguments are “spread” [McCarthy 62] [Moon 74] in registers, and the return address on the stack.) Then we may permute the code as follows (from the original example):

  BAR:    <set up arguments for G in registers>
          PUSH [BAR1]             ;save return address for (G X)
          GOTO G                  ;call function G
  BAR1:   <save result of G>
          <set up arguments for H in registers>
          PUSH [BAR2]             ;save return address for (H Y)
          GOTO H                  ;call function H
  BAR2:   <set up arguments for F in registers>
          GOTO F                  ;call function F

As it happens, the PDP-10 provides an instruction, PUSHJ, defined as follows:

          PUSH [L1]
          GOTO G           is the same as              PUSHJ G
  L1:                                          L1:

except that the PUSHJ takes less code. Thus we may write the code as:

  BAR:     <set up arguments for G in registers>
           PUSHJ G                 ;save return address, call G
           <save result of G>
           <set up arguments for H in registers>
           PUSHJ H                 ;save return address, call H
           <set up arguments for F in registers>
           GOTO F                  ;call function F

This is why PUSHJ (and similar instructions on other machines, whether they save the return adress on a stack, in a register, or in a memory location) works on a subroutine call, and, by extension, why up to now many people have thought of pushing the return address at function call time rather than at form evaluation time. The use of GOTO to call a function “tail-recursively” (known around MIT as the “JRST hack”, from the PDP-10 instruction for GOTO, though the hack itself dates back to the PDP-1) is in fact not just a hack, but rather the most uniform method for invoking functions. PUSHJ is not a function calling primitive per se, therefore, but rather than optimization of this general approach.

1.3. LAMBDA as a Renaming Operator

Environment operators also take various forms. The most common are assignment to local variables and binding of arguments to functions, but there are others, such as pattern-matching operators (as in COMIT [MITRLE 62] [Yngve 72], SNOBOL [Forte 67], MICRO-PLANNER [Sussman 71], CONNIVER [McDermott 74], and PLASMA [Smith 75]). It is usual to think of these operators as altering the contents of a named location, or of causing the value associated with a name to be changed.

In understanding the action of an environment operator it may be more fruitful to take a different point of view, which is that the value involved is given a new (additional) name. If the name had previously been used to denote another quantity, then that former use is shadowed; but this is not necessarily an essential property of an environment operator, for we can often use alpha-conversion (“uniquization” of variable names) to avoid such shadowing. It is not the names which are important to the computation, but rather the quantities; hence it is appropriate to focus on the quantities and think of them as having one or more names over time, rather than thinking of a name as having one or more values over time.

Consider our previous example involving BAR. On entry to BAR two quantities are passed, either in registers or on the stack. Within BAR these quantities are known as X and Y, and may be referred to by those names. In other environments these quantities may be know by other names; if the code in BAR’s caller were (BAR W (+ X 3)), then the first quantity is known as W and the second has no explicit name. {Note Return Address} On entry to BAR, however, the LAMBDA assigns the names X and Y to those two quantities. The fact that X means something else to BAR’s caller is of no significance, since these names are for BAR’s use only. Thus the LAMBDA not only assigns names, but determines the extent of their significance (their scope). Note an interesting symmetry here: control constructs determine constraints in time (sequencing) in a program, while environment operators determine constraints in space (textual extent, or scope).

One way in which the renaming view of LAMBDA may be useful is in allocation of temporaries in a compiler. Suppose that we use a targeting and preferencing scheme similar to that described by in [Wulf 75] and [Johnsson 75]. Under such a scheme, the names used in a program are partitioned by the compiler into sets called “preference classes”. The grouping of several names into the same set indicates that it is preferable, other things being equal, to have the quantities referred to by those names reside in the same memory location at run time; this may occur because the names refer to the same quantity or to related quantities (such as X and X+1). A set may also have a specified target, a particular memory location which is preferable to any other for holding quantities named by members of the set.

As an example, consider the following code skeleton:

  ((LAMBDA (A B) <body>) (+ X Y) (* Z W))

Suppose that within the compiler the names T1 and T2 have been assigned to the temporary quantities resulting from the addition and multiplication. Then to process the “binding” of A and B we need only add A to the preference class of T1, and B to the preference class of T2. This will have the effect of causing A and T1 to refer to the same location, wherever that may be; similarly B and T2 will refer to the same location. If T1 is saved on a stack and T2 winds up in a register, fine; references to A and B within the <body> will automatically have this information.

On the other hand, suppose that <body> is (FOO 1 A B), where FOO is a built-in function which takes its arguments in registers 1, 2, and 3. Then A’s preference class will be targeted on register 2, and B’s on register 3 (since these are the only uses of A and B within <body>); this will cause T1 and T2 to have the same respective targets, and at the outer level an attempt will be made to perform the addition in register 2 and the multiplication in register 3. This general scheme will produce much better code than a scheme which says that all LAMBDA expressions must, like the function FOO, take their arguments in certain registers. Note too that no code whatsoever is generated for the variable bindings as such; the fact that we assign names to the results of the expressions (+ X Y) and (* Z W) rather than writing

  (FOO 1 (* Z W) (+ X Y))

makes no difference at all, which is as it should be. Thus, compiler temporaries and simple user variables are treated on a completely equal basis. This idea was used in [Johnsson 75], but without any explanation of why such equal treatment is justified. Here we have some indication that there is conceptually no difference between a user variable and a compiler-generated temporary. This claim will be made more explicit later in the discussion of continuation-passing. Names are merely a convenient textual device for indicating the various places in a program where a computed quantity is referred to. If we could, say, draw arrows instead, as in a data flow diagram, we would not need to write names. In any case, names are eliminated at compile time, and so by run time the distinction between user names and the compiler’s generated names has been lost.

Thus, at the low level, we may view LAMBDA as a renaming operation which has more to do with the internal workings of the compiler (or the interpreter), and with a notation for indicating where quantities are referred to, than with the semantics as such of the computation to be performed by the program.

1.4. An Example: Compiling a Simple Function

One of the important consequences of the view of LAMBDA and function calls presented above is that programs written in a style based on the lambda-calculus-theoretic models of higher-level constructs such as DO loops (see [Stoy 74] [Steele 76]) will be correctly compiled. As an example, consider this iterative factorial function:

  (DEFINE FACT
          (LAMBDA (N)
                  (LABELS ((FACT1
                            (LAMBDA (M A)
                                    (IF (= M 0) A
                                        (FACT1 (- M 1)
                                               (* M A))))))
                          (FACT1 N 1))))

Let us step through a complete compilation process for this function, based on the ideas we have seen. (This scenario is intended only to exemplify certain ideas, and does not reflect entirely accurately the targeting and preferencing techniques described in [Wulf 75] and [Johnsson 75].)

First, let us assign names to all the intermediate quantities (temporaries) which will arise:

  (DEFINE FACT
          (LAMBDA (N)
               T1=(LABELS ((FACT1
                             (LAMBDA (M A)
                                  T2=(IF T3=(= M 0) A
                                         T4=(FACT1 T5=(- M 1)
                                                   T6=(* M A))))))
                       T7=(FACT1 N 1))))

We have attached a name T1-T7 to all the function calls in the definition; these names refer to the quantities which will result from these function calls.

Now let us place the names in preference classes. Since N is used only once, as an argument to FACT1, which will call that argument M, N and M belong in the same class; T5 also belongs to this class for the same reason. T1, T2, T4, and T7 belong in the same class because they are all names, in effect, for the result of FACT1 or FACT. T6 and A belong in the same class, because T6 is an argument to FACT1; T2 and A belong in the same class, because A is one possible result of the IF. T3 is in a class by itself.

  {M, N, T5}
  {A, T1, T2, T4, T6, T7}
  {T3}

A fairly complicated analysis of the “lifetimes” of these quantities shows that M and T5 must coexist simultaneously (while calculating T6), and so cannot really be assigned the same memory location. Hence we must split T5 off into a class of its own after all.

Let us suppose that we prefer to target the result of a global function into register RESULT, and the single argument to a function into register ARG. (FACT1, which is not a global function, is not subject to these preferences.) Then we have:

  {M, N}                  target ARG (by virtue of N)
  {T5}
  {A, T1, T2, T4, T6, T7} target RESULT (by virtue of T1)
  {T3}

T3, on the other hand, will need no memory location (a property of the PDP-10 instruction set). Thus we might get this assignment of locations:

  {M, N}                  ARG
  {T5}                    R1
  {A, T1, T2, T4, T6, T7) RESULT

where R1 is an arbitrarily chosen register.

We now really have two functions to compile, FACT and FACT1. Up to now we have used the renaming properties of LAMBDA to assign registers; now we use the GOTO property of function calls to construct this code skeleton:

  FACT:   <set up arguments for FACT1>
          GOTO FACT1              ;call FACT1

  FACT1:  <if quantity named M is non-zero go to FACT1A>
          <return quantity named A in register RESULT>
          POPJ

  FACT1A: <do subtraction and multiplication>
          GOTO FACT1              ;FACT1 calling itself

Filling in the arithmetic operations and register assignments gives:

  ;;; On arrival here, quantity named N is in register ARG.
  FACT:   MOVEI RESULT,1          ;N already in ARG; set up 1
          GOTO FACT1              ;call FACT1

  ;;; On arrival here, quantity named M is in ARG,
  ;;;  and quantity named A is in RESULT.
  FACT1:  JUMPN ARG,FACT1A
          POPJ                    ;A is already in RESULT!

  FACT1A: MOVE R1,ARG             ;must do subtraction in R1
          SUBI R1,1
          IMUL RESULT,ARG         ;do multiplication
          MOVE ARG,R1             ;now put result of subtraction in ARG
          GOTO FACT1              ;FACT1 calling itself

This code, while not perfect, is not bad. The major deficiency, which is the use of R1, is easily cured if the compiler could know at some level that the subtraction and multiplication can be interchanged (for neither has side effects which would affect the other), producing:

  FACT1A: IMUL RESULT,ARG
          SUBI ARG,1
          GOTO FACT1

Similarly, the sequence:

          GOTO FACT1

FACT1:

could be optimized by removing the GOTO. These tricks, however, are known by any current reasonably sophisticated optimizing compiler.

What is more important is the philosophy taken in interpreting the meaning of the program during the compilation process. The structure of this compiled code is a loop, not a nested sequence of stack-pushing function calls. Like the SCHEME interpreter or the various PLASMA implementations, a compiler based on these ideas would correctly reflect the semantics of lambda-calculus-based models of high-level constructs.

1.5. Who Pops the Return Address?

Earlier we showed a translation of BAR into “machine language”, and noted that there was no code which explicitly popped a return address; the buck was always passed to another function (F, G, or H). This may seem surprising at first, but it is in fact a necessary consequence of our view of function calls as “GOTOs with a message”. We will show by induction that only primitive functions not expressible in our language (SCHEME) perform POPJ; indeed, only this nature of the primitives determines the fact that our language is functionally oriented!

What is the last thing performed by a function? Consider the definition of one:

  (DEFINE FUN (LAMBDA (X1 X2 ... XN) <body>))

Now <body> must be a form in our language. There are several cases:

1. Constant, variable, or closure. In this case we actually compiled a POPJ in the case of FACT above, but we could view constants, variables, and closures (in general, things which “evaluate trivially” in the sense described in [Steele 76]) as functions of zero arguments if we wished, and so GOTO a place which would get the value of the constant, variable, or closure into RESULT. This place would inherit the return address, and so our function need not pop it. Alternatively, we may view constants, etc. as primitives, the same way we regard integer addition as a primitive (note that CTA2 above {in section 2 below} required a POPJ, since we had “open-coded” the addition primitive).
2. (IF <pred> <exp1> <exp2>). In this case the last thing our function does is the last thing <exp1> or <exp2> does, and so we appeal to this analysis inductively.
3. (LABELS <defns> <exp>). In this case the last thing our function does is the last thing <exp> does. This may involve invoking a function defined in the LABELS, but we can consider them to be separate functions for our purposes here.
4. A function call. In this case the function called will inherit the return address.

Since these are all the cases, we must conclude that our function never pops its return address! But it must get popped at some point so that the final value may be returned.

Or must it? If we examine the four cases again and analyze the recursive argument, it becomes clear that the last thing a function that we define in SCHEME eventually does is invoke another function. The functions we define therefore cannot cause a return address to be popped. It is, rather, the primitive, built-in operators of the language which pop return addresses. These primitives cannot be directly expressed in the language itself (or, more accurately, there is some basis set of them which cannot be expressed). It is the constants (which we may temporarily regard as zero-argument functions), the arithmetic operators, and so forth which pop the return address. (One might note that in the compilation of CURRIED-TRIPLE-ADD above {in section 2 below}, a POPJ appeared only at the point the primitive “+” function was open-coded as ADD instructions.)

3.1. Actors ≡ Closures (mod Syntax)

In [Sussman 75] Sussman and Steele note that actors (other than those which embody side effects and synchronization) and closures of LAMBDA expressions are isomorphic in their behavior. Smith and Hewitt [Smith 75] describe an actor as a combination of a script (code to be executed) and a set of acquaintances (computational quantities available to the code). A LISP closure in like manner is a combination of a body of code and a set of variable bindings (or, using our idea of renaming, a set of computational quantities with (possibly implicitly) associated names). Hewitt [Hewitt 76] has challenged this isomorphism, saying that closures may contain unnecessary quantities, but I have already dealt with this issue above.

Let us therefore examine this isomorphism more closely. We have noted above that it is more accurate to think of the caller of a LAMBDA as performing a GOTO rather than the LAMBDA itself. It is the operation of invocation that is the transfer of control. This transfer of control is similar to the transfer of control from one actor to another.

In the actors model, when control is passed from one actor to another, more than a GOTO is performed. A computed quantity, the message, is passed to the invoked actor. This corresponds to the set of arguments passed to a LAMBDA expression. Now if we wish to regard the actor/LAMBDA expression as a black box, then we need not be concerned with the renaming operation; all we care about is that an answer eventually comes out. We do not care that the LAMBDA expression will “spread” the set of arguments out and assign names to various quantities. In fact, there are times when the caller may not wish to think of the argument set as a set of distinct values; this attitude is reflected in the APPLY primitive of LISP, and in the FEXPR calling convention. The actors model points out that, at the interface of caller and callee, we may usefully think of the argument set as a single entity.

In the actors model, one important element of the standard message is the continuation. This is equivalent to the notion of return address in a LISP system (more accurately, the continuation is equivalent to the return address plus all the quantities which will be needed by the code at that address). We do not normally think of the return address as an argument to a LAMBDA expression, because standard LISP notation suppresses that fact.

On the one hand, though, Steele and Sussman [Steele 76] point out that it is possible to write LISP code in such a manner that return addresses are passed explicitly. (This style corresponds to the use in PLASMA of ==> and <== to the exclusion of =>, <=, and functional notation.) When code is written in this “continuation-passing style”, no implicit return addresses are ever created on the control stack. all that is necessary to write code entirely in this style is that continuation-passing primitives be available.

The reason LISP is so function-oriented is that all the primitives (CAR, CONS, +, etc.) are functions, expecting return addresses on the stack. The stack is simply a conventional place to pass some (or all) of the arguments. If, for example, we consider the LSUBR argument-passing convention described earlier, it is easy to think of the return address as being the “zeroth” argument, for it is passed on the stack just below arguments 1 through n.

On the other hand, the PLASMA language, while based on actor semantics, has a number of abbreviations which allow the user to ignore the continuation portion of a message in the same way he would in LISP. When the user writes in PLASMA what would be a function invocation in LISP, the PLASMA interpreter automatically supplies an “underlying continuation” which is passed in a standard component of the message packet. This is analogous to the way the LISP system automatically supplies a return address in a standard place (the control stack). (Hewitt [Hewitt 76] has expressed doubt as to whether these underlying continuations can themselves be represented explicitly as LAMBDA expressions. My impression is that he sees a potential infinite regression of underlying continuations. If the underlying continuations are written in pure continuation-passing style as defined in [Steele 76], however, this problem does not arise.)

Let us define a convenient set of continuation-passing primitives. Following the convention used in [Steele 76], we will let the last argument(s) to such a primitive be the continuation(s), where a continuation is simply a “function” of values delivered by the primitive.

  (++ a b c)    delivers the sum of a and b to the continuation c.
  (-- a b c)    delivers the difference of a and b to the continuation c.
  (** a b c)    delivers the product of a and b to the continuation c.
  (^^ a b c)    delivers a raised to the power b to the continuation c.
  (%= a b c)    delivers T to continuation c if a and b are arithmetically
                equal, and otherwise NIL.
  (== a b c d)  invokes continuation c if a and b are arithmetically
                equal, and otherwise continuation d (c and d receive
                no values from ==).

Note that predicates may usefully be defined in at least two ways. The predicate %= is analogous to a functional predicate in LISP, in that it delivers a truth value to its continuation, while == actually implements a conditional control primitive.

Thus far in our comparison of closures and actors we have focused on aspects of control. Now let us consider the manipulation of environments. When an actor is invoked, it receives a message. It is convenient to assign names to parts of this message for future reference within the script. This is done by pattern matching in PLASMA, and by “spreading” in LISP. This assignment of names is a matter purely internal to the workings of the actor/LAMBDA expression; the outside world should not be affected by which names are used. (This corresponds indirectly to the notion of referential transparency.

In discussing control we noted that on invoking a function the LISP and PLASMA interpreters create an implicit underlying continuation, a return address. This is a hidden creation of a control operation. Are there any hidden environment operations?

The hidden control operation occurs just before invocation of a function. We might expect, by symmetry, a hidden environment operation to occur on return from the function. This is in fact the case. The underlying continuation, itself an actor, will assign one or more hidden names to the contents of the message it receives. If the actor originally invoked was a function, then the message is the returned value of the function. Consider this example, taken from [Steele 76]:

  (- (^ B 2) (* 4 A C))

When the function “^” is invoked, the message to it contains three items: the value of B, the value of 2, and the implicit continuation. When it returns, the implicit continuation saves the returned value in some internal named place, then invokes the function “*”. The message to “*” contains four items: the values of 4, A, and C, and a second implicit continuation. This continuation contains the internal place where the value from “^” was saved! When “*” returns, the continuation then calls “-”, giving it the saved result from “^”, the result freshly obtained from “*”, and whatever continuation was given for the evaluation of the entire expression; “-” will deliver its result to that (inherited) continuation.

This is all made more clear by writing the example out in pure continuation-passing style, using our continuation-passing primitives:

  (^^ B 2
      (LAMBDA (X)
              (** 4 A C
                  (LAMBDA (Y)
                          (-- X Y <the-inherited-continuation>)))))

Here X and Y are the explicit names for intermediate quantities which were hidden before by the function-calling syntax. We use LAMBDA to express the continuations passed to “^^” and “**”. These LAMBDA expressions are not functions; they never return values, but rather merely invoke more continuation-passing primitives. However, the interpretation of a LAMBDA expression is as before: when invoked, the arguments are assigned the additional names specified in the LAMBDA variables list, and then the body of the LAMBDA expression is executed.

In the context of a compiler, the intermediate quantities passed to the continuations are usually known as “temporaries”, or are kept in places called temporaries. Usually the temporaries are mentioned in the context of the problem of allocating them. The present analysis indicates that they are just like names assigned by the user; they are different only in that the user is relieved by the syntax of a functional language of having to mention their names explicitly. This is made even more clear by considering two extremes. In assembly language, there are no implicitly named quantities; every time one is used, its name (be it a register name, a memory location, or whatever) must be mentioned. On the other hand, in a data flow language (e.g. some of the AMBIT series) it is possible to draw arrows and never mention names at all.

By considering temporaries as just another kind of name (or alternatively, user names to be just another kind of temporary), the example of allocation of temporaries given earlier may be understood on a firmer theoretical level. Furthermore, greater understanding of this uniformity may lead to advances in language design. Let us consider two examples.

First, we may notice that the underlying continuations in LISP and PLASMA take only one argument: the returned value. Why are there not implicit continuations of more than one argument? The answer is that this characteristic is imposed by the syntax and set of primitives provided in functional languages. Suppose we were to augment LISP as follows (this is not a serious proposal for a language extension, but only an example):

1. Wherever n consecutive arguments might be written in a function call, one may instead write {f x1 ... xm}n, where n is a positive integer. The “function” f must return n values, which are used as n arguments in the function call.
2. The primitive (values x1 ... xn) returns its n arguments as its n values. Thus writing “{values x1 ... xn}” is the same as writing “x1 ... xn” as arguments in a function call.

Then we might write code such as:

  (DEFINE FOO
          (LAMBDA (A)
                  (VALUES (^ A 2) (^ A 3))))
  (LIST {FOO 5}2 (+ {FOO 4}2) {FOO 3}2)

Evaluating the second form produces (25 125 80 9 27). When FOO is invoked, it is provided an implicit continuation which expects two arguments, i.e. two returned values from FOO. We need VALUES as a primitive in order to be able to return several values. (We could imagine syntactic sugar for this, such as (LAMBDA (A) (^ A 2) (^ A 3)), but it is no more than sugar.) When (^ A 2) and (^ A 3) have been evaluated, FOO does a GOTO to VALUES, whereupon VALUES inherits the two-argument continuation given to FOO. Thus the LAMBDA expression for FOO never needs to know how many arguments its continuation takes; that is a matter for the primitives to decide.

All this suggests our second example, namely a way to return multiple values from a function without all the extra syntax and primitives. All that is necessary is to use explicit continuation-passing. Thus the above example might be written:

  (DEFINE FOO
          (LAMBDA (A CONT)
                  (CONT (^ A 2) (^ A 3))))
  (FOO 5 ( LAMBDA (X1 X2)
              (FOO 4 (LAMBDA (Y1 Y2)
                         ((LAMBDA (X3)
                              (FOO 7 (LAMBDA (X4 X5)
                                         (LIST X1 X2 X3 X4 X5))))
                          (+ Y1 Y2))))))

Here we have used a mixture of functional and continuation-passing styles, employing only enough of the latter to express the multiple values returned by FOO. The implicit continuations for the evaluation of the arguments to LIST and “*” (and their implicit temporaries X1, X2, X3, X4, X5, Y1, and Y2) have been made explicit. While one might see how to implement multiple-value-return in an interpreter on the basis of the first example (by augmenting the interpreter to handle the new “primitives”), the second makes it clear how to compile it without introducing new primitives at the low level. (Appendix A presents a program which converts ordinary SCHEME programs to pure continuation-passing style; Appendix B presents a modification to this program which handles the multiple-value-return construct.) Furthermore, by using the same mechanism to compile both function calls and multiple value returns, the multiple values will get returned in registers in the same way arguments might be passed, without the need for any additional machinery. {Note PLASMA Registers}

3.2. The Procedural View of Data Types

Up to now we have concentrated on LAMBDA and function calling as environment and control primitives. Based on the actor approach, we will see that a certain amount of useful data manipulation can be expressed in terms of LAMBDA expressions. If compiled well enough, such data manipulation would be no more costly than code generated by special-case compiler routines. Thus, yet one more programming construct could be handled by this general compilation mechanism, making the compiler yet more uniform.

The procedural approach to data type behavior has been developing for many years. Typical of languages of the early 1970’s with such ideas are ECL [Wegbreit 74] and MUDDLE [Galley 75]. Each allows certain characteristics of a data type to be expressed as an arbitrary procedure. Specifically, ECL allows the behavior of the creation, assignment, coercion, subscripting, and printing operations to be procedurally specified; MUDDLE allows procedural specification of the methods for evaluation and application of objects. The pieces of data are still thought of as objects, however, and there are mechanisms for defeating the procedural specifications by “lowering” a data type to a more primitive type (such mechanisms are necessary for use by the behavior specification procedures themselves). One problem with (feature of??) the lowering mechanism is that any procedure, not just one controlling the behavior of a data type, can use the lowering primitive and so defeat the data type functions.

The next step in this direction is the idea that the notion of a data type is meaningful only in terms of the operations that can be performed on it; that is, all that one can do with an object is give it to one of a defined set of procedures which know how to operate on that data type. This notion is exemplified in the CLU language. [Liskov 74] [Liskov 76] Associated with a data type is a cluster of procedures; only those procedures can manipulate the data type. Unfortunately, a “lowering” (“rep”) mechanism is still needed within the cluster so that cluster procedures can get at the “underlying representation” of a data object. The definition of this mechanism causes certain problems. CLU at least solves the problem of indiscriminate use of the mechanism, by restricting its use to the cluster procedures.

Carrying this notion still further, Hewitt has proposed the notion of “actors”. [Hewitt 73] Rather than dichotomizing the world into data objects and procedures, he suggests that only procedures are meaningful; each “data object” actually embodies all the operations on itself as a procedure. The only operation one can perform on an object is to invoke its procedure. There is no problem of “lowering” the data type to an underlying representation, because an object of the data type does not exist as such to be lowered. In this way the integrity of a data type is much more easily preserved. (While some people object to having to use this model of data types in writing their programs, there is no reason it cannot be hidden with syntactic sugar. {Note PLASMA Sugar} There is much to be said for it as a formal model of data type behavior, but as a practical programming tool it is not always conceptually convenient)

Let us consider abstractly (though not rigorously) the motivation for the notion of data types. Typically we have an object X and want to perform some operation F on it. Suppose that F is a non-primitive operator; then it must decide what set of primitive actions to perform. Let such decisions made by F partition its domain into classes, such that all objects in a class cause the same set of primitive actions to occur when given to F. One may then define the data type of X with respect to F to be the class into which F’s decisions place X. By extension, one may let F range over some set of operations with similar domains, and let the union of their decisions determine the classes. Loosely speaking, then, a data type is a class of objects which may be operated on in a uniform manner. The notion of data types provides a simple conceptual way to classify an object for the purposes of deciding how to operate on it.

Now let us approach the problem from another direction. Consider a prototypical function call (F X). (We may consider a function call of more than one argument to be equivalent to (F (LIST X1 ... Xn)) for our purposes here.) When executed, this function call is to be elaborated into some series of more primitive operations. It may help to think of execution as a mapping from the product space of the sets of operators and operands to the space sequences of more primitive operations. Such a mapping can be expressed as a matrix. For example:

                             -- Operation --
           TYPE         PRINT      ATOM      FIRST    CAR      ...
Operand
  0        RET(FIXNUM)  TYO("0")   RET(T)    ERROR    ERROR    ...

  43       RET(FIXNUM)  TYO("4")   RET(T)    ERROR    ERROR    ...
                        TYO("3")

  (A B)    RET(LIST)    TYO("(")   RET(NIL)  RET(A)   RET(A)   ...
                        TYO("A")
                        TYO(" ")
                        TYO("B")
                        TYO(")")

  [1]      RET(VECTOR)  TYO("[")   RET(NIL)  RET(1)   RET(1)   ...
                        TYO("1")
                        TYO("]")

           ...          ...        ...       ...      ...      ...

        Legend: TYO outputs a character; RET returns a value.

Now it would be completely impractical to specify this matrix explicitly in its entirety. It is convenient to lump all FIXNUM objects, for example, into one class, and provide a matrix entry under PRINT which is less efficient for any one application but which works for all such objects. That is, rather than having a separate entry for each FIXNUM under PRINT which knows exactly what characters to output, we have some algorithm which generates digits arithmetically. (Similarly, for lists and vectors we have an algorithm which knows how to print subcomponents in a general manner.) We say that 0 and 43, or [1 2] and [4 5 6], have the same type because almost all operations which apply to both can use the same set of primitive actions, appropriately chosen. Operators may similarly [be] lumped together; for example, in many LISP implementations CAR will get the first element of any composite data object, lumping in such operators as FIRST of a vector or an array.

It is hard to think of natural examples of operator lumping since it seldom occurs in practice. Historically, the tendency has been to break up the matrix by columns. All the entries for TYPE are lumped together, all those for PRINT, and so on. When one invents a new operator, one merely writes a routine encoding the new column of entries; such a routine typically begins with a dispatch on the data type of its argument. When one invents a new data type, however, it is necessary to change every routine a little bit to incorporate the new row entry.

The procedural approach to data types includes, in effect, a suggestion that the matrix be sliced up by rows instead of columns. The result of this is to group all the operations for a single data type together. This of course yields the inverse problem: adding a new data type is easy, but adding a new generic operator is difficult because many data type routines must be changed. {Note Slice Both Ways}

The important point, however, is that the data type of an object provides a way of selecting a row of the operations matrix. Whether this selection is represented as a procedure, a symbol, or a set of bits does not concern us. When combined with a column selector (choice of operator), it determines what set of actions to undertake. {Note Turing Machines}

Hewitt has pointed out that non-primitive actors can be made to implement data structures such as queues and list cells. It is shown in [Sussman 75] that the PLASMA expression (from [Smith 75]):

may be written in terms of LAMBDA expressions:

  (DEFINE CONS
          (LAMBDA (A B)
                  (LAMBDA (M)
                          (IF (EQ M 'FIRST?) A
                              (IF (EQ M 'REST?) B
                                  (IF (EQ M 'LIST?) 'YES
                                      (ERROR ...)))))))

(For some reason, Hewitt seems to prefer FIRST? and REST? to CAR and CDR.)

There are two points to note here. One is that what we normally think of as a data structure (a list cell) has been implemented by means of a closure; the result of CONS is a closure of the piece of code (LAMBDA (M) ...) and the environment containing A and B. The other is that the body of the code is essentially a decision procedure for selecting a column of our operations matrix. This suggests a pretty symmetry: we may either first determine an operator and then submit an object-specifier to the row-selection procedure for that operator, or first determine an operand and submit an operator-specifier to the column-selection procedure for that operand.

This kind of definition has been well known to lambda-calculus theoreticians for years; examples of it occur in Church’s monograph. [Church 41] It has generally not been used as a practical definition technique in optimizing compilers, however. Hewitt has promoted this idea in PLASMA, but he has only described an interpreter implementation with no clues as to how to compile it. Moreover, no one seems to have stated the inverse implication, namely, that the way to approach the problem of compiling closures is to think of them as data structures, with all structures produced by closing a given LAMBDA expression being thought of as having the same data type. Up to now closures have generally been thought of as expensive beasts to implement in a programming language; however, thinking of them in terms of data types should make them appear much less frightening. Consider this definition of CAR:

  (DEFINE CAR
          (LAMBDA (CELL)
                  (CELL 'FIRST?)))

Now consider this code fragment:

  ((LAMBDA (FOO)
           ...
           (CAR FOO)
           ...)
   (CONS 'ZIP 'ZAP))

It may appear that this must compile into extremely poor code if we use the procedural definition of a list cell given above. However, at the point where the result of the CONS is given to CAR, the compiler can be made to output a HLRZ instruction and no more, just as if the MacLISP NCOMPLR optimizing compiler [Moon 74] had seen (CAR FOO) or the ECL compiler [Wegbreit 74] seen “FOO.LEFT”. All that is required is some knowledge that FOO was created by CONS (that is, we must know FOO’s “data type”), plus standard optimization techniques such as procedure integration, constants folding, and dead code elimination. The idea is to recognize that FOO names a closure of two data items with the code of the inner LAMBDA expression in CONS; this could be done either by declaration or by flow analysis. Integrating this LAMBDA expression as well as the definition of CAR into our code fragment yields:

  ((LAMBDA (FOO)
           ...
           ((LAMBDA (CELL) (CELL 'FIRST?))
            (LAMBDA (M)                           ;in FOO
                    (IF (EQ M 'FIRST?) A
                        (IF (EQ M 'REST?) B
                            (IF (EQ M 'LIST?) 'YES
                                (ERROR ...))))))
           ...)
   (CONS 'ZIP 'ZAP))

The comment “in FOO” means that any free variables in the expression are meant to refer to quantities in the closure FOO. Notice that we do not take advantage of the explicit appearance of 'ZIP and 'ZAP as arguments to CONS, though we might do so in practice; our purpose here is to illustrate the more general case where we know that FOO names some result of CONS but we don’t know which one.

Integrating (LAMBDA (M) ...) into (LAMBDA (CELL) ...) and then substituting through the argument FIRST? yields:

  ((LAMBDA (FOO)
           ...
           (IF (EQ 'FIRST? 'FIRST?) A ...)      ;in FOO
               ...)
           ...)
   (CONS 'ZIP 'ZAP))

Standard constants folding and dead code elimination leads to:

  ((LAMBDA (FOO)
           ...
           A              ;in FOO
           ...)
   (CONS 'ZIP 'ZAP))

Now the compiler presumably knows the format of the closures produced by CONS; all it needs to do is generate the instruction(s) to fetch the quantity named A out of the closure FOO. If, for example, closures are represented as vectors (as assumed above in the CURRIED-TRIPLE-ADD example) it would in fact take only one instruction on a PDP-10, just as it would for MacLISP.

All this may sound rather complicated, but these are all well-known optimization techniques (see [Allen 72], for example), which happen not to have been applied before in this context. The one tricky point is keeping track of environments correctly (as with the “in FOO” comment above). All kinds of heterogeneous data structures may be created in this way in terms of LAMBDA expressions; no separate primitive creation or selection operators are necessary. A certain amount of data type analysis will be necessary to carry this out. In this context, data type analysis would consist of determining of what LAMBDA expression a given data object is the closure. This may be determined by global data flow analysis (for example, the recent Allen and Cocke algorithm [Allen 76] might be applicable here), or by user-supplied declarations.

If data structures are specified in these terms, it is left up to the compiler to determine a good representation for these structures. If done properly, there is no reason why the creation of a list cell using CONS as above should not actually perform precisely the same storage allocation as might occur in ECL at the low level. In any case, the compiler should know something about designing and packing data structures. (Some work has been done on this already in the ECL system [Wegbreit 74], for example.)

One might object that this technique cannot quite produce the efficiency of MacLISP in performing CONS, since a standard MacLISP list cell contains only two pointers, while the LAMBDA version would produce a cell containing the two pointers plus a pointer to the code for the LAMBDA expression. In a sense this is true; it is necessary to have a pointer to the code. However, we need not actually have a pointer to the code in the closure; all that is necessary is that we be able to locate the code given the object. Standard LISP systems typically encode this information in other ways, calling it the data type. Remembering the operations matrix described earlier, we may think of the code as the data type of the closure; all either does is provide a row selector for the matrix. Current systems such as ECL and MUDDLE which allow definition of arbitrary numbers of data types have indeed found it necessary to store a full pointer, more or less, to describe the data type of an object. In special cases, however, ECL can compress a data type to only a few bits. There is no reason why a sufficiently clever compiler could not use equally clever encodings of the data type, including the technique of encoding the data type in the address of the closure much as the “Bibop” version of MacLISP does. [Moon 74]

In any case, we can see that the use of closures to define data types need not be expensive. Once again, LAMBDA seems to provide a uniform and general method which is, as always, subject to clever optimizations in special cases.

4.1. Basic Issues

The compiler will need to perform a large amount of global data flow and data type analysis; much of this can be based on the approach used by Wulf in the BLISS-11 compiler [Wulf 75], augmented by some general flow-graph analysis scheme. (The BLISS-11 flow analysis is not sufficiently general in that it only analyzes single functions, and within a function the only control constructs are conditionals, loops, and block exits.)

For the allocation of registers and temporaries I propose to use a modification of BLISS-11’s preferencing and targeting scheme. This will be tempered by the attitude towards LAMBDA-binding described earlier, namely that it is merely a renaming operation. Thus, no variable is considered to have a specific location or “home”; assignment to a variable should cause no motion of data, but merely reorganize the compiler’s idea of where the quantity involved is located at that point in the code. (At any point in the code a quantity may have several names, and may also have several homes, by which I mean physical copies in the runtime machine environment. For example, a quantity may happen to reside in two different registers at some point; there is no a priori reason for either one to be considered THE original copy of that quantity to be preserved for the future.) Data structures are another matter; assignment to a component must actually modify the component. This is the purpose of introducing the ASET primitive, since simple SETQ’s as used in LISP PROG statements can be simulated by using LAMBDA expressions (see [Steele 76]). (On the other hand, the modification to the component need not happen immediately, as long as it happens soon enough that some other process, if any cannot detect that the assignment did not happen immediately.) The essential set of primitives will include the following:

  LAMBDA, LABELS, IF
  ASET (perhaps restricted to a quoted first argument, i.e. ASETQ)
  EQ

These by themselves constitute an extremely rich domain for optimization! As shown above and in [Steele 76], they effectively encompass data structure creation, access, and modification; a host of control structures, including non-local exits; and a variety of parameter-passing disciplines, including call-by-name, call-by-need, and fluid variables. In fact, one of the great assets of this approach is that such constructs can be written as macros and used in both an interpreter and compiler; because the base language is essentially a lexically scoped LISP, the lambda-calculus-theoretic models of such constructs may be used almost directly to write such macros. Indeed, a library of such macros already exists for the SCHEME interpreter.

If time permits, extensions may be made to handle integers (strictly speaking, integers mod 2³⁶!) and these operations on them:

  +              addition
  -              subtraction
  *              multiplication
  //             division
  \              remainder
  MAX, MIN       maximum and mininum
  BOOLE          bit-wise boolean operations
  LSH            logical shifting relationals
  <, >, =        relationals

The compiler will need to contain the following kinds of knowledge in great detail:

• Knowledge about the behavior of LAMBDA expressions and closures, in particular how environments nest and interact, and how procedure integration works. For example, in the situation:

  (LABELS ((FOO (LAMBDA () ... (BAR)))
           (BAR (LAMBDA () ...)))
          ...)

  the compiler should be able to realize that FOO and BAR run in the same environment (since each adds no variables to the outer environment), and so the call to BAR in FOO can compile as if it were a GOTO, with no adjustment in environment necessary. If that is the only call on BAR, then no GOTO is needed; the code for BAR may simply follow (or be integrated into) FOO.

• Knowledge about how to construct data structures in the run-time environment. In MacLISP, this will imply using the built-in CONS and other low-level storage allocation primitives.

• Knowledge about how primitives can be compiled into machine code, or if they are run-time routines, with what conventions they are invoked.

• Knowledge about optimization of machine code, for example that a certain combination of PUSH and JRST can be combined into PUSHJ.

Each kind of knowledge should be represented as modularly as possible. It should not be necessary to change fifteen routines in the compiler just to install a new arithmetic primitive.

Although I propose to construct only the lower-level portion of the compiler, plus the necessary macros to provide standard LISP features such as COND and PROG, one could easily imagine constructing an ALGOL compiler, for example, by providing a parser plus the necessary macros as a front end. Indeed, by using CGOL [Pratt 76] for our parser we could create an ALGOL-like language quite easily, which could include such non-LISP features as multiple-value-return and call-by-name.

This possibility indicates that a carefully chosen small dialect of LISP would be a good UNCOL (UNiversal Computer-Oriented Language), that is, a good intermediate compilation language. The reason for trying to develop a good UNCOL is to solve the “m*n” problem compiler-builders face. If one has m programming languages and n machines, then it takes m*n compilers to compile each language for each machine; but it would require only m+n compilers if one had m language-to-UNCOL compilers and n UNCOL-to-machine compilers. Up to now the UNCOL idea has failed; the usual problem is that proposed UNCOLs are not sufficiently general. I suspect that this is because they tend to be too low-level, too much like machine language. I believe that LAMBDA expressions, combining the most primitive control operator (GOTO) with the most primitive environment operator (renaming) put LISP at a low enough level to make a good UNCOL, yet at a high enough level to be completely machine independent. It should be noted that a compiler which uses LAMBDA expressions internally does not have to be for a LISP-like language. The features of LISP as an UNCOL which interest me are the environment and control primitives, because they can be used easily to simulate the environment and control structures of most high-level languages.

4.2. Some Side Issues

In this section we discuss briefly some issues which are not directly relevant to LAMBDA expressions, but which will impinge on the design of a compiler. These are:

1. Order of argument evaluation (as opposed to order of evaluation, which is to be applicative order).
2. Analysis of side effects and their interactions.
3. Declarations versus compile-time analysis.
4. Block compilation (in the InterLISP sense); i.e., inter-function optimization.
5. Debugging; in particular, the ability to walk around environment structures and examine their contents.
6. Bootstrapping.

Because these are side issues, we will merely consider an easy way out for each, realizing that the compiler should be designed so as to allow for more complex ways of handling them later.

(1) The two standard choices for order of argument evaluation are “left to right” and “doesn’t matter”. Most LISP systems use the former convention; most languages with infix syntax, notably BLISS [Wulf 75], use the latter. If the latter is chosen, there is the matter of whether the compiler will enforce it by warning the user if he tries to depend on some ordering; if the former is chosen, there is the matter of determining whether the compiler can perform optimizations which depend on permuting the order. In either of these cases an analysis of side-effect interactions among arguments is necessary, and once we have decided to perform such an analysis, the choice of convention is not too important.

(2) Analysis of side effects is desirable not only between arguments in a single function call, but at all levels. For example, if a copy of a variable is in a register, then it need not be re-fetched unless an assignment has occurred. Similarly, if CONS as above were extended to have an RPLACA message, we would like to know whether sending a given cell an RPLACA message will require re-transmission of a CAR message. The easy approach is to assume that an unknown function changes everything, and not to attempt optimization across calls to unknown functions. Other increasingly clever approaches include:

• Declaration of whether a function can produce side effects or not.
• Declaration of what kinds of arguments to a function produce side effects.
• Declaration of classes of side effects. CAR operations to become invalid, but not simple variable fetches or GETs
• Declarations of classes of side effects as a function of certain objects and/or arguments. Thus (PUTPROP x y z) invalidates all previous GET operations; (PUTPROP x y 'ZAP) invalidates (GET x 'ZAP) and (GET x y), but not (GET x 'ZIP). Neither one invalidates (CAR FOO), probably. Similarly (RPLACA FOO) does not invalidate (CAR FIE) if it can be determined that FOO and FIE are distinct objects.

Naturally, anything described above as being declared could sometimes also be determined by a clever compile-time analysis.

(3) As for the issue of declarations versus analysis itself, probably both should be available. One might envision first implementing a declaration scheme which can be used to make the thing go, and then adding analysis routines afterwards. The analysis routines should merely create declarations in the same way the user can; this would allow uniformity of processing and extensibility of design.

(4) Block compilation might be necessary for production of very efficient code, though this will of course depend on the style of programming. It many data structures are defined in the actor-like style described above, much procedure integration will be necessary to produce good code. On the other hand, the code should still work if each procedure is compiled separately (which would be desirable for debugging purposes). A middle-of-the-road approach would be to block-compile a set of functions, and compile separate entry points to certain function for interpreted and compiled calls.

(5) While debugging, it may be desirable to be able to examine the environment structures created by compiled code. This probably will have to be a kind of deus ex machina rather than an integral part of the system, but in any case there must be enough information to determine where things are. Environments created by compiled code will not contain the names of the variables, since they are not logically necessary. Instead, the compiler can, for each LAMBDA expression, create a description, suitable for interpretation by a debugging program, of the format of closures created for that LAMBDA expression. This will be enough information to debug with. The compiler could also theoretically output information as to what data is in which registers when, though this would be a mountain of output. This would tie in well with a program-understanding program; one could provide information as to what compiled code correponds to what interpreted code, and how.

(6) One problem with constructing a compiler is deciding what language to code the compiler itself in. As a rule of thumb, one ought to take a very dim view of any supposedly general-purpose language which is not adequate to write its own compiler in. Thus the proposed compiler will be constructed in some superset of the basic LISP described above, one which can easily be transformed by macros into the basic LISP. One advantage of this carefully chosen minimal dialect is that an interpreter for it can be written and debugged in only a day or two. This interpreter can then be used as a development system for writing the machine-dependent portion of the compiler. Thus if necessary the proposed compiler could be bootstrapped onto a new machine easily without requiring the aid of a previously existing implementation.