Printer-friendly versionIn using sum as in section 1.3.1, it seems terribly awkward to have to define trivial procedures such as
pi-term and pi-next just so we can use them as arguments to
our higher-order procedure. Rather than define pi-next and pi-term, it would be more convenient
to have a way to directly specify “the procedure that returns its
input incremented by 4” and “the procedure that returns the
reciprocal of its input times its input plus 2.” We can do this by
introducing the special form lambda, which creates procedures. Using lambda we can describe what we want as
(lambda (x) (+ x 4))and
(lambda (x) (/ 1.0 (* x (+ x 2))))Then our pi-sum procedure can be expressed without defining any auxiliary procedures as
(define (pi-sum a b)
(sum (lambda (x) (/ 1.0 (* x (+ x 2))))
a
(lambda (x) (+ x 4))
b))Again using lambda, we can write the integral procedure without having to define the auxiliary procedure add-dx:
(define (integral f a b dx)
(* (sum f
(+ a (/ dx 2.0))
(lambda (x) (+ x dx))
b)
dx))In general, lambda is used to create procedures in the same way as define, except that no name is specified for the procedure:
(lambda (<formal-parameters>) <body>)The resulting procedure is just as much a procedure as one that is
created using define. The only difference is that it has not
been associated with any name in the environment. In fact,
(define (plus4 x) (+ x 4))is equivalent to
(define plus4 (lambda (x) (+ x 4)))We can read a lambda expression as follows:
(lambda (x) (+ x 4))
↑ ↑ ↑ ↑ ↑
the procedure of an argument x that adds x and 4
Like any expression that has a procedure as its value, a lambda expression can be used as the operator in a combination such as
((lambda (x y z) (+ x y (square z))) 1 2 3)
12or, more generally, in any context where we would normally use a procedure name.[53]
Using let to create local variables
Another use of lambda is in creating local variables.
We often need local variables in our procedures other than those that have
been bound as formal parameters. For example, suppose we wish to
compute the function
which we could also express as
In writing a procedure to compute f, we would like to include as local variables not only x and y but also the names of intermediate quantities like a and b. One way to accomplish this is to use an auxiliary procedure to bind the local variables:
(define (f x y)
(define (f-helper a b)
(+ (* x (square a))
(* y b)
(* a b)))
(f-helper (+ 1 (* x y))
(- 1 y)))Of course, we could use a lambda expression to specify an anonymous procedure for binding our local variables. The body of
f then becomes a single call to that procedure:
(define (f x y)
((lambda (a b)
(+ (* x (square a))
(* y b)
(* a b)))
(+ 1 (* x y))
(- 1 y)))This construct is so useful that there is a special form called
let to make its use more convenient. Using let, the f procedure could be written as
(define (f x y)
((lambda (a b)
(+ (* x (square a))
(* y b)
(* a b)))
(+ 1 (* x y))
(- 1 y)))The general form of a let expression is
(let ((<var1> <exp1>) (<var2> <exp2>)⋮(<varn> <expn>)) <body>)
The first part of the let expression is a list of
name-expression pairs. When the let is evaluated, each name is associated with the value of the corresponding expression. The body
of the let is evaluated with
these names bound as local variables. The way this happens is that the let expression is interpreted as an alternate syntax for
((lambda (<var1> …<varn>) <body>) <exp1>⋮<expn>)
No new mechanism is required in the interpreter in order to
provide local variables. A let expression is simply syntactic sugar for the underlying lambda application.
We can see from this equivalence that the scope of a variable specified by a let expression is the body of the let. This implies that:
Letallows one to bind variables as locally as possible to where they are to be used. For example, if the value ofxis 5, the value of the expression(+ (let ((x 3)) (+ x (* x 10))) x)is 38. Here, the
xin the body of theletis 3, so the value of theletexpression is 33. On the other hand, thexthat is the second argument to the outermost+is still 5.The variables’ values are computed outside the
let. This matters when the expressions that provide the values for the local variables depend upon variables having the same names as the local variables themselves. For example, if the value of x is 2, the expression(let ((x 3) (y (+ x 2))) (* x y))will have the value 12 because, inside the body of the
let, x will be 3 and y will be 4 (which is the outer x plus 2).
Sometimes we can use internal definitions to get the same effect as
with let. For example, we could have defined the procedure f above as
(define (f x y)
(define a (+ 1 (* x y)))
(define b (- 1 y))
(+ (* x (square a))
(* y b)
(* a b)))We prefer, however, to use let in situations like this
and to use internal define only for internal procedures.[54]
lambda, such as make-procedure, were used. But the convention is firmly entrenched. The notation is adopted from the λ calculus, a mathematical formalism introduced by the mathematical logician Alonzo Church (1941). Church developed the λ calculus to provide a rigorous foundation for studying the notions of function and function application. The λ calculus has become a basic tool for mathematical investigations of the semantics of programming languages. [back]Exercises
Comments
error?
I believe the pic below the paragraph
“This construct is so useful that there is a special form called let to make its use more convenient. Using let, the f procedure could be written as”
is incorrect because it is identical to the one above.
typo
The code just after the paragraph
“This construct is so useful that there is a special form called let to make its use more convenient. Using let, the f procedure could be written as”
should be this:
(see http://mitpress.mit.edu/sicp/full-text/book/book-Z-H-12.html#%_sec_1.3.2)
Languge Interpreter Services
Nice Website containing full of Language knowledge ,
One of my friend has refered me for this Website
We provide Interpreter work and services in
all languages, for more info CALL US : +91 - 9873019933
Languge Interpreter Services in Noida
Languge Interpreter Services in NCR
Languge Interpreter Services in Delhi
www.apls.in/Interpretation
burberry trench coat
sell burberry quilted jacket UntKTCXB [URL=http://www.burberryoutlet-online2013.org/ - burberry outlet online[/URL - to take huge discount uIqEjQGd http://www.burberryoutlet-online2013.org/
Post new comment