# Jensen's Device - Description

Description

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.

A classic example of Jensen's device is a procedure that computes the sum of a series, :

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) `k`.

For example, code to compute the first 100 terms of a real array `V` would be:

Sum(i, 1, 100, V).

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 `V`.

Jensen's device is general. A double summation can be done as:

Sum(i, l, m, Sum(j, l, n, A))

The `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 `Sum`.

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.

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