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Alternative lambda Signatures

In the previous chapter we discussed the creation of procedures with the signature

(lambda (<var> ...) <exp1> <exp2> ...)

In this each <var> represents a single argument that is expected by and then available within the procedure. But this isn't the only form of specifying a procedure's signature in Scheme, there are two other options available, allowing for more flexibility.

The following form allows to pass an arbitrary number of actual arguments to a procedure:

(lambda <var> <exp1> <exp2> ...)

All arguments that follow the lambda expression are then wrapped into a list that is bound to the name <var> within the procedure body:

((lambda var-list
    (display (car var-list))
    (length var-list))
 'one 'two 'three 'four)

The four arguments are wrapped in the list '(one two three four) which is available as var-list in the procedure. This way we can handle arbitrary numbers of arguments within a function. The first expressions in the procedure body print the first element of the argument list while the last expression determines the value of the whole expression, which is then printed on the last line of output.

Please note that a) when you pass a single argument to such a procedure you still have to unpack it from the list, and b) there is no extra pair of parens around the variable declaration or the procedure body - it's basically lambda with an arbitrary number of expressions, whose first represents the name to which the argument list will be bound.

A third form is actually a hybrid of the two others, accepting both a fixed number of named arguments plus a list of unnamed remaining ones.

(lambda (<var-1> ... <var-n> . <var-last>) <exp1> <exp2> ...)

The “formals” are given as an improper list here, while the starting entries <var-1> through <var-n> represent individual actual arguments, while <var-last> after the dot collects all remaining arguments in a list:

((lambda (x y . z)
    (* (+ x y)
       (length z)))
    1 2 3 4 5 6)

Of course the procedure is pretty useless, but it shows how the signature works. We have two actual arguments, x and y, which are taken from the first two arguments passed to the list: x = 1 and y = 2. The remaining arguments are wrapped to the list '(3 4 5 6) and bound to the name of z. The body adds x and y (= 3) and multiplies that with the number of remaining arguments (4).

As said earlier it will rarely make sense to create a procedure using lambda for a single application as seen so far. I think each of these examples would have been realized simpler with “normal” expressions. Procedures are getting interesting when they are bound to a name and made reusable.

Last update: November 3, 2022