In "The Scheme Programming Language 4th Edition" section 3.3 Continuations the following example is given:
(define product
(lambda (ls)
(call/cc
(lambda (break)
(let f ([ls ls])
(cond
[(null? ls) 1]
[(= (car ls) 0) (break 0)]
[else (* (car ls) (f (cdr ls)))]))))))
I can confirm it works in chezscheme as written:
> (product '(1 2 3 4 5))
120
What is 'f' in the above let? Why is the given ls being assigned to itself? It doesn't seem to match what I understand about (let ...) as described in 4.4 local binding:
syntax: (let ((var expr) ...) body1 body2 ...)
If 'f' is being defined here I would expect it inside parenthesis/square brackets:
(let ([f some-value]) ...)
This is 'named let', and it's a syntactic convenience.
(let f ([x y] ...)
...
(f ...)
...)
is more-or-less equivalent to
(letrec ([f (λ (x ...)
...
(f ...)
...)])
(f y ...))
or, in suitable contexts, to a local define followed by a call:
(define (outer ...)
(let inner ([x y] ...)
...
(inner ...)
...))
is more-or-less equivalent to
(define (outer ...)
(define (inner x ...)
...
(inner ...)
...)
(inner y ...))
The nice thing about named let is that it puts the definition and the initial call of the local function in the same place.
Cavemen like me who use CL sometimes use macros like binding, below, to implement this (note this is not production code: all its error messages are obscure jokes):
(defmacro binding (name/bindings &body bindings/decls/forms)
;; let / named let
(typecase name/bindings
(list
`(let ,name/bindings ,#bindings/decls/forms))
(symbol
(unless (not (null bindings/decls/forms))
(error "a syntax"))
(destructuring-bind (bindings . decls/forms) bindings/decls/forms
(unless (listp bindings)
(error "another syntax"))
(unless (listp decls/forms)
(error "yet another syntax"))
(multiple-value-bind (args inits)
(loop for binding in bindings
do (unless (and (listp binding)
(= (length binding) 2)
(symbolp (first binding)))
(error "a more subtle syntax"))
collect (first binding) into args
collect (second binding) into inits
finally (return (values args inits)))
`(labels ((,name/bindings ,args
,#decls/forms))
(,name/bindings ,#inits)))))
(t
(error "yet a different syntax"))))
f is bound to a procedure that has the body of let as a body and ls as a parameter.
http://www.r6rs.org/final/html/r6rs/r6rs-Z-H-14.html#node_sec_11.16
Think of this procedure:
(define (sum lst)
(define (helper lst acc)
(if (null? lst)
acc
(helper (cdr lst)
(+ (car lst) acc))))
(helper lst 0))
(sum '(1 2 3)) ; ==> 6
We can use named let instead of defining a local procedure and then use it like this:
(define (sum lst-arg)
(let helper ((lst lst-arg) (acc 0))
(if (null? lst)
acc
(helper (cdr lst)
(+ (car lst) acc)))))
Those are the exact same code with the exception of some duplicate naming situations. lst-arg can have the same name lst and it is never the same as lst inside the let.
Named let is easy to grasp. call/ccusually takes some maturing. I didn't get call/cc before I started creating my own implementations.
Related
I've read here that named let can be rewritten with letrec.
And so I proceeded to rewrite the following function with letrec:
(define (duplicate pos lst)
(let dup ([i 0] [lst lst])
(cond
[(= i pos) (cons (car lst) lst)]
[else (cons (car lst) (dup (+ i 1) (cdr lst)))])))
My attempt at this:
(define (duplicate pos lst)
(letrec ((dup (lambda ([i 0] [lst lst])
(cond
[(= i pos) (cons (car lst) lst)]
[else (cons (car lst) (dup (+ i 1) (cdr lst)))]))))))
Sadly, when I call it with (duplicate 1 (list "apple" "cheese burger!" "banana")) I get from Racket letrec: bad syntax (missing body). How might I rewrite duplicate with letrec?
As you can see in the documentation for letrec, it has these arguments:
(letrec ([id val-expr] ...) body ...+)
So, you have to add at least one body form after definitions.
I also replaced cond with if (you have only two branches of code), (+ ... 1) with add1 and improved indentation:
#lang racket
(define (duplicate pos lst)
(letrec ((dup (lambda ([i 0] [lst lst])
(if (= i pos)
(cons (car lst)
lst)
(cons (car lst)
(dup (add1 i) (cdr lst)))))))
(dup)))
Test:
> (duplicate 1 (list "apple" "cheese burger!" "banana"))
'("apple" "cheese burger!" "cheese burger!" "banana")
The named let is (more or less) a locally defined regular procedure that is called "behind the scenes".
The body of a named let is not the body of the equivalent "unnamed" let, but the body of that procedure;
(let f ([x init])
body)
can be rewritten as
(letrec ([f (lambda ([x init]) body)])
(f))
or, without using default arguments (which some would find clearer),
(letrec ([f (lambda (x) body)])
(f init))
Here is my code about postfix in scheme:
(define (stackupdate e s)
(if (number? e)
(cons e s)
(cons (eval '(e (car s) (cadr s))) (cddr s))))
(define (postfixhelper lst s)
(if (null? lst)
(car s)
(postfixhelper (cdr lst) (stackupdate (car lst) s))))
(define (postfix list)
(postfixhelper list '()))
(postfix '(1 2 +))
But when I tried to run it, the compiler said it takes wrong. I tried to check it, but still can't find why it is wrong. Does anyone can help me? Thanks so much!
And this is what the compiler said:
e: unbound identifier;
also, no #%app syntax transformer is bound in: e
eval never has any information about variables that some how are defined in the same scope as it is used. Thus e and s does not exist. Usually eval is the wrong solution, but if you are to use eval try doing it as as little as you can:
;; Use eval to get the global procedure
;; from the host scheme
(define (symbol->proc sym)
(eval sym))
Now instead of (eval '(e (car s) (cadr s))) you do ((symbol->proc e) (car s) (cadr s)). Now you should try (postfix '(1 2 pair?))
I've made many interpreters and none of them used eval. Here is what I would have done most of the time:
;; Usually you know what operators are supported
;; so you can map their symbol with a procedure
(define (symbol->proc sym)
(case sym
[(+) +]
[(hyp) (lambda (k1 k2) (sqrt (+ (* k1 k1) (* k2 k2))))]
[else (error "No such operation" sym)]))
This fixes the (postfix '(1 2 pair?)) problem. A thing that I see in your code is that you always assume two arguments. But how would you do a double? eg something that just doubles the one argument. In this case symbol->proc could return more information:
(define (symbol->op sym)
(case sym
[(+) (cons + 2)]
[(double) (cons (lambda (v) (* v v)) 1)]
[else (error "No such operation" sym)]))
(define op-proc car)
(define op-arity cdr)
And in your code you could do this if it's not a number:
(let* ([op (symbol->op e)]
[proc (op-proc op)]
[arity (op-arity op)])
(cons (apply proc (take s arity)
(drop s arity)))
take and drop are not R5RS, but they are simple to create.
Does anyone can help me to deal with the problem?
I tried for many times, but it still has the error information.
This is my code(scheme)
Thanks!!!
(define (postfix l s)
(cond(
((null? l)(car s))
(else (postfix (cdr l) update-s((car s)))))))
(define (update-s x s)
(cond(((number? x) (cons x s))
(else (cons (eval '(x (car s) (cadr s))) (scheme-report-environment 5) (cdr(cdr s)))))))
And this is the error inform:
else: not allowed as an expression in: (else (postfix (cdr l) update-s ((car s) s)))
Next time, don't forget to add a description of your problem (what should this code do?), expected inputs and outputs, and a version of Scheme you use.
You should also use better names for variables (no l, s, x) and describe their meaning and expected type in your question.
If I understand correctly, you were trying to create a calculator which uses reverse Polish/ postfix notation, where:
l is a list of numbers or symbols
s is a stack with results, represented as a list of numbers
x can be a number or symbol representing some function
From (scheme-report-environment 5) I guess you use r5rs Scheme.
Now some of your errors:
you should define update-s before function postfix
your cond has some additional parentheses
if cond has only two branches, you should use if instead
this part (postfix (cdr l) update-s((car s))) should be (postfix (cdr l) (update-s (car l) s)
(cdr(cdr s)) should be (cddr s)
as for eval, I understand why it's here, you were trying to get a function from the symbol, but you should be always careful, as it can also evaluate code provided by user. Consider this example: (postfix '(1 2 (begin (write "foo") +)) '()). Maybe it could be better to don't expect this input: '(1 2 +), but this: (list 1 2 +) and get rid of eval.
The whole code:
(define (update-s object stack)
(if (number? object)
(cons object stack)
(cons ((eval object (scheme-report-environment 5))
(car stack) (cadr stack))
(cddr stack))))
(define (postfix lst stack)
(if (null? lst)
(car stack)
(postfix (cdr lst)
(update-s (car lst) stack))))
Example:
> (postfix '(1 2 +) '())
3
Solution without eval with different input:
(define (update-s object stack)
(if (number? object)
(cons object stack)
(cons (object (car stack) (cadr stack))
(cddr stack))))
(define (postfix lst stack)
(if (null? lst)
(car stack)
(postfix (cdr lst)
(update-s (car lst) stack))))
Example:
> (postfix (list 1 2 +) '())
3
I am trying to write by myself the cons function in scheme. I have written this code:
(define (car. z)
(z (lambda (p q) p)))
and I am trying to run :
(car. '(1 2 3))
I expect to get the number 1, but it does not work properly.
When you implement language data structures you need to supply constructors and accessors that conform to the contract:
(car (cons 1 2)) ; ==> 1
(cdr (cons 1 2)) ; ==> 2
(pair? (cons 1 2)) ; ==> 2
Here is an example:
(define (cons a d)
(vector a d))
(define (car p)
(vector-ref p 0))
(define (cdr p)
(vector-ref p 1))
Now if you make an implementation you would implement read to be conformant to this way of doing pairs so that '(1 2 3) would create the correct data structure the simple rules above is still the same.
From looking at car I imagine cons looks like this:
(define (cons a d)
(lambda (p) (p a d)))
It works with closures. Now A stack machine implementation of Scheme would analyze the code for free variables living passed their scope and thus create them as boxes. Closures containing a, and d aren't much different than vectors.
I urge you to implement a minimalistic Scheme interpreter. First in Scheme since you can use the host language, then a different than a lisp language. You can even do it in an esoteric language, but it is very time consuming.
Sylwester's answer is great. Here's another possible implementation of null, null?, cons, car, cdr -
(define null 'null)
(define (null? xs)
(eq? null xs))
(define (cons a b)
(define (dispatch message)
(match message
('car a)
('cdr b)
(_ (error 'cons "unsupported message" message))
dispatch)
(define (car xs)
(if (null? xs)
(error 'car "cannot call car on an empty pair")
(xs 'car)))
(define (cdr xs)
(if (null? xs)
(error 'cdr "cannot call cdr on an empty pair")
(xs 'cdr)))
It works like this -
(define xs (cons 'a (cons 'b (cons 'c null))))
(printf "~a -> ~a -> ~a\n"
(car xs)
(car (cdr xs))
(car (cdr (cdr xs))))
;; a -> b -> c
It raises errors in these scenarios -
(cdr null)
; car: cannot call car on an empty pair
(cdr null)
; cdr: cannot call cdr on an empty pair
((cons 'a 'b) 'foo)
;; cons: unsupported dispatch: foo
define/match adds a little sugar, if you like sweet things -
(define (cons a b)
(define/match (dispatch msg)
(('car) a)
(('cdr) b)
(('pair?) #t)
((_) (error 'cons "unsupported dispatch: ~a" msg)))
dispatch)
((cons 1 2) 'car) ;; 1
((cons 1 2) 'cdr) ;; 2
((cons 1 2) 'pair?) ;; #t
((cons 1 2) 'foo) ;; cons: unsupported dispatch: foo
I have the following scheme function:
(define get-ivars
(λ (ivars num)
(cond ((null? ivars) '())
(else
(append (list (car ivars) `(nth args ,num)) (list (get-ivars (cdr ivars) (+ num 1))))))))
That returns the following in a specific instance:
(x (nth args 1) (y (nth args 2) ()))
The problem is, I need it to return:
((x (nth args1)) (y (nth args 2)) ())
-the two closing parenthesis at the end should be after the (nth statements.
How would I go about getting this to work properly?
get-ivars caller:
(define gen-classes
(λ (classes)
(cond ((null? classes) '())
(else
(let* ((class (car classes)))
(eval
`(define ,(cadr class)
(λ (args)
(let (
,(get-ivars (cdr (cadddr class)) 1)
)
(eval
(let* ,(cdar (cddddr class))
(λ (method . args)
,(get-methods (cdadr (cddddr class)))
))))))))))))
That second (list ...) in your else clause is what's screwing you up. It's nesting each successive call deeper and deeper. The recursion will naturally create the list; you don't need to wrap it again.
Try:
(define get-ivars
(λ (ivars num)
(if (null? ivars) '()
(cons (list (car ivars) `(nth args ,num))
(get-ivars (cdr ivars) (+ num 1))))))
Regarding the get-ivars caller code, the parentheses surrounding the unquoted call to get-ivars are what's giving you the trouble you mention in the comments. With them, this code:
`(define ClassName
(lambda (args)
(let (,(get-ivars '(iVar1 iVar2 iVar3) 1))
;; your method-getting code
)))
Gives you this:
(define ClassName
(lambda (args)
(let (((iVar1 (nth args 1))
(iVar2 (nth args 2))
(iVar3 (nth args 3))))
;; method-getting code
)))
Which, as you can see, gives you an extra set of parentheses around the assignments in the let.
So you want to do this:
`(define ClassName
(lambda (args)
(let ,(get-ivars '(iVar1 iVar2 iVar3) 1)
;; your method-getting code
)))
get-ivars is returning a list of lists, which is exactly what you want for the assignments in the let, so you don't need to wrap or (as I had it earlier) splice it. Just use the unquote on its own, and the result is:
(define ClassName
(lambda (args)
(let ((iVar1 (nth args 1))
(iVar2 (nth args 2))
(iVar3 (nth args 3)))
;; method-getting code
)))
Which should do the trick.
Incidentally, I found it helpful to leave off the eval when I was playing around with this; one can then visually inspect the result to make sure its syntax is okay.
I haven't tried this, but I think this would work:
(define (get-ivars ivars num)
(if (null? ivars)
'()
(list (list (car ivars) `(nth args ,num))
(get-ivars (cdr ivars) (1+ num)))))