Jensen's Device is a computer programming technique that exploits call by name. It was devised by Danish computer scientist Jørn Jensen, who worked with Peter Naur at Regnecentralen. They worked on the GIER Algol compiler, one of the earliest correct implementations of ALGOL 60. ALGOL 60 used call by name.
Jensen's device exploits call by name and side-effects. Call by name is an argument passing convention that delays the evaluation of an argument until it is actually used in the procedure (a consequence of the copy rule for procedures). Algol introduced call by name.
real procedure Sum(k, l, u, ak) value l, u; integer k, l, u; real ak; comment k and ak are passed by name; begin real s; s := 0; for k := l step 1 until u do s := s + ak; Sum := s end;
In the procedure, the index variable
k and summation term
ak are passed by name. Call by name enables the procedure to change the value of the index variable during execution of the
for loop. Call by name also causes the
ak argument to be reevaluated during each iteration of the loop. Typically,
ak will depend upon the changing (side-effected)
For example, code to compute the first 100 terms of a real array
V would be:
Sum(i, 1, 100, V[i]).
During the execution of
Sum, the actual argument
i will increment during each step of the
for loop, and each of the procedure's evaluations of
ak will use the current value of
i to access the successive array elements
Jensen's device is general. A double summation can be done as:
Sum(i, l, m, Sum(j, l, n, A[i,j]))
Sum function can be employed for arbitrary functions merely by employing the appropriate expressions. If a sum of integers were desired the expression would be just
Sum(i,1,100,i);, if a sum of squares of integers, then
Sum(i,1,100,i*i);, and so on. A slight variation would be suitable for initiating a numerical integration of an expression by a method very similar to that of
The evaluation of
ak is implemented with a thunk, which is essentially a subroutine with an environment. The thunk is a closure with no arguments. Each time a procedure needs the value of its formal argument, it simply calls the thunk. The thunk evaluates the actual argument in the scope of the calling code (not the scope of the procedure).
In the absence of this pass-by-name facility, it would be necessary to define functions embodying those expressions to be passed according to the protocols of the computer language, or to create a compendium function along with some arrangement to select the desired expression for each usage.
Another example is GPS(General Problem Solver), described in D. E. Knuth and J. N. Merner's ALGOL 60 confidential.
real procedure GPS(I, N, Z, V); real I, N, Z, V; begin for I := 1 step 1 until N do Z := V; GPS := 1 end;
Following is a single statement which finds m-th prime using GPS.
I := GPS(I, if I=0 then -1.0 else I, P, if I=1 then 1.0 else if GPS(A, I, Z, if A=1 then 1.0 else if entier(A)×(entier(I)÷entier(A))=entier(I) ∧ A<I then 0.0 else Z) = Z then (if P<m then P+1 else I×GPS(A, 1.0, I, -1.0)) else P)
(note: In the original paper, the expression of near of last, is
GPS(A, 1.0. I, 0.0). It would be due to corner case of specification of semantics of ALGOL 60's for statement)
Jensen's device relies on call by name, but call by name is subtle and has some problems. Consequently, call by name is not available in most languages. Knuth comments that ALGOL 60 cannot express an
increment(n) procedure that increases its argument by one; the call
increment(A[i]) does not do the expected action if
i is a functional that changes with each access. Knuth says, "The use of 'macro' definition facilities to extend language, instead of relying solely on procedures for this purpose, results in a more satisfactory running program."
Others point out that a call by name procedure that swaps its argument can have subtle problems. An obvious swapping procedure is:
procedure swap(a, b) integer a, b; begin integer temp; temp := a; a := b; b := temp; end;
The procedure does the right thing for many arguments, but the invocation of
swap(i,A[i]) is problematic. Using the Copy Rule leads to the assignments:
temp := i; i := A[i]; A[i] := temp;
The problem is the second assignment changes
i, so the
A[i] in the third assignment probably will not be the same array element as at the start. If on the other hand the procedure were to be coded the other way around (with b being saved to temp instead of a) then the desired action would result, unless it were invoked as
- Call stack – stack frame, static link, and display (closure including environment link)
- Funarg problem – closures can be complicated
- Man or boy test – environment test
- Peter Naur's 2005 Turing Award citation mentions his work with Jensen on GIER Algol
- MacLennan, Bruce J. (1987), Principles of Programming Languages: Design, Evaluation, and Implementation (Second ed.), Holt, Rinehart & Winston, ISBN 0-03-005163-0, pp 141–142
- Dijkstra, E. W. (November 1961), "Defense of ALGOL 60 (Letter to the Editor)", Communications of the ACM 4 (11): 502–503, doi:10.1145/366813.366844
- Knuth, D. E. (October 1967), "The Remaining Troublespots in ALGOL 60", Communications of the ACM 10 (10): 611–617, doi:10.1145/363717.363743
realargument for the term, so type conversion is assumed.
- Donald E. Knuth and Jack N. Merner. 1961. ALGOL 60 confidential. Commun. ACM 4, 6 (June 1961), 268-272. DOI=10.1145/366573.366599 http://doi.acm.org/10.1145/366573.366599
- Knuth 1967, p. 613. For example,
- MacLennan 1987