So far we've seen three ways in which a value can be associated with a variable in Scheme:
Some variables, such as the names of built-in procedures, are
predefined. When Chez Scheme starts up, these variables
(cons and quotient, for example) are already
bound to the procedures they denote.
The programmer can introduce a new binding by means of a definition. A definition may introduce a new name for a previously computed value, or it may give a name to a newly constructed value.
When a programmer-defined procedure is called, the parameters of the procedure are bound to the values of the corresponding arguments in the procedure call. Unlike the other two kinds of bindings, parameter bindings are local -- they apply only within the body of the procedure. Scheme discards these bindings when it leaves the procedure and returns to the point at which it was called.
A let-expression in Scheme is an alternative way to create
local bindings. A let-expression contains a binding
list and a body. The body can be any expression, or sequence
of expressions, to be evaluated with the help of the local variable
bindings. The binding list is a pair of parentheses enclosing zero or more
binding specifications; a binding specification, in turn, is a
pair of parentheses enclosing a variable and an expression. Here's an
example of a binding list:
((next (car source)) (char-list '()))
This binding list contains two binding specifications -- one in which the
value of the expression (car source) is bound to the symbol
next, and the other in which the empty list is bound to the
symbol char-list. Notice that binding lists and binding
specifications are not procedure calls; their role in a
let-expression is structural.
When a let-expression is evaluated, the first thing that
happens is that the expressions in all of its binding specifications are
evaluated and collected. Then the symbols in the binding specifications
are bound to those values. Next, the expressions making up the body of the
let-expression are evaluated, in order; the value of the last
expression in the body becomes the value of the entire
let-expression. Finally, the local bindings of the variables
are cancelled. (Variables that were unbound before the
let-expression become unbound again; variables that had
different bindings before the let-expression resume those
earlier bindings.)
What are the values of the following let-expressions?
(let ((tone "fa") (call-me "al")) (string-append call-me tone "l" tone))
;; solving the quadratic equation x^2 - 5x + 4
;;
(let ((discriminant (- (* -5 -5) (* 4 1 4))))
(list (/ (+ (- -5) (sqrt discriminant)) (* 2 1))
(/ (- (- -5) (sqrt discriminant)) (* 2 1))))
(let ((sum (+ 8 3 4 2 7)))
(let ((mean (/ sum 5)))
(* mean mean)))
You may use Chez Scheme to help you answer these questions, but be sure you can explain how it arrived at its answers.
Using a let-expression often simplifies an expression that
contains two or more occurrences of the same subexpression. The programmer
can compute the value of the subexpression just once, bind a variable to
it, and then use that variable whenever the value is needed again.
Sometimes this speeds things up by avoiding such redundancies as the
recomputation of the discriminant in 1(b) above; in other cases, there is
little difference in speed, but the code may be a little clearer. For
instance, here is an alternative definition of the remove-all
procedure that was presented as Program 4.8 in the text (page 105):
(define remove-all
(lambda (item ls)
(if (null? ls)
'()
(let ((first-element (car ls))
(rest-of-result (remove-all item (cdr ls))))
(cond ((equal? first-element item) rest-of-result)
((pair? first-element)
(cons (remove-all item first-element) rest-of-result))
(else (cons first-element rest-of-result)))))))
One of the least attractive features of the text's version of this program
was the repetition of the recursive call (remove-all item (cdr
ls)) in three different places. Consolidating the repeated code and
giving a name to the value it returns makes it a little easier to
understand what the three cond-clauses are doing.
Rewrite the count-all-symbols procedure from the lab on deep recursion, using a
let-expression to consolidate repeated subexpressions in the
same manner.
As shown in 1c, above, it is possible to nest one
let-expression inside another. One might be tempted to try to
combine the binding lists for the nested let-expressions,
thus:
;; Combining the binding lists doesn't work!
;;
(let ((sum (+ 8 3 4 2 7))
(mean (/ sum 5)))
(* mean mean))
This wouldn't work (try it and see!), and it's important to understand why
not. The problem is that, within one binding list, all of the
expressions are evaluated before any of the variables are bound.
Specifically, Scheme will try to evaluate both (+ 8 3 4 2 7)
and (/ sum 5) before binding either of the variables
sum and mean; since (/ sum 5) can't
be computed until sum has a value, an error occurs. You have
to think of the local bindings coming into existence simultaneously rather
than one at a time.
Because one often needs sequential rather than simultaneous binding, Scheme
provides a variant of the let-expression that rearranges the
order of events: If one writes let* rather than
let, each binding specification in the binding list is
completely processed before the next one is taken up:
;; Using let* instead of let works!
;;
(let* ((sum (+ 8 3 4 2 7))
(mean (/ sum 5)))
(* mean mean))
The star in the symbol let* has nothing to do with
multiplication; just think of it as an oddly shaped letter.
Write a nested let-expression that binds a total of five
variables, a, b, c, d,
and e, with a bound to 9387 and each subsequent
variable bound to a value twice as large as the one before it --
b should be twice as large as a, c
twice as large as b, and so on. The body of the innermost
let-expression should compute the sum of the values of the
five variables.
Write a let*-expression equivalent to the
let-expression in the previous exercise.
One can use a let- or let*-expression to create a
local name for a procedure:
(define hypotenuse-of-right-triangle
(lambda (first-leg second-leg)
(let ((square (lambda (n)
(* n n))))
(sqrt (+ (square first-leg) (square second-leg))))))
Regardless of whether square is defined outside this
procedure, the local binding gives it the appropriate meaning in the body
of the let-expression.
Rewrite the longest-on-list procedure from the first lab on recursion so that it incorporates
the longer-string procedure by means of a local binding.
This document is available on the World Wide Web as
http://www.math.grin.edu/~stone/courses/scheme/local-bindings.html
created February 26, 1997
last revised October 2, 1997