Could someone please explain what happens once the continuation is called for this.
((cdr (or (call/cc (lambda (cc) (cons 2 (lambda () (cc #f))))) (cons 3 5))))
((cdr (or (call/cc (lambda (cc) (cons 2 (lambda () (cc #f))))) (cons 3 (lambda() (+ 3 2))))))
The first statement gives error but the second one returns 5. My question is why is call/cc searching for a procedure like the second statement and not output 5 directly.
In ((cdr X)) you will get an error, if X doesn't evaluate to a pair where the cdr is a thunk.
In your first expression, the initial value of X is (cons 2 (lambda () (cc #f))). So everything is fine. However when you invoke the thunk, the expression (cc #f) will return #f to the or, and thus (or #f (cons 3 5)) will evaluate to a pair with a 5 in the cdr. We now have the situation ((cdr (cons 3 5))) which will attempt to apply 5.
In short: (cc #f) will return a value to the context in which (call/cc _) appears. Here returning #f to that context implies that the or-expression will return the pair (cons 3 5) and thus the ((cdr X)) will fail.
Related
Sorry this simple continuation example evaluates to 4, but I could not figure out why:
(call/cc
(lambda (k)
(* 5 (k 4))))
Chez Scheme 9.5.3
call/cc lets you get the advantages of continuation passing style without having to write it in continuation passing style. eg.
(define (cars lsts)
(define (cars lsts k)
(cond ((null? lsts) (k '()))
((null? (car lsts)) '())
(else (cars (cdr lsts)
(lambda (r)
(k (cons (caar lsts) r)))))))
(cars lsts values))
;; eg
(cars '()) ; ==> ()
(cars '((1) (2) (3))) ; ==> (1 2 3)
(cars '((1) (2) ())) ; ==> ()
Can be written like this:
(define (cars lsts)
(call/cc
(lambda (bail)
(define (cars lsts)
(cond ((null? lsts) '())
((null? (car lsts)) (bail '()))
(else (cons (caar lsts) (cars (cdr lsts))))))
(cars lsts))))
call/cc& looks like this in CPS:
(define (call/cc& proc k)
(define (exit& v ignored-k)
(k v))
(proc exit& k))
And your simple example can easily be rewritten to continuation passing style:
(call/cc& (lambda (k& real-k)
(k& 4 (lambda (res)
(*& 5 res real-k))))
display)
So looking at that the ignore-k gets ignored and 4 gets passed to the continuation of call/cc& which I have put display which then displays 4 in the repl.
I would explain you by writing a code with the same semantics by using CPS.
((lambda (k)
(k 4
(lambda (v)
(* 5 v))))
(lambda (result stack)
;; this continuation will drop the stack
result))
After you call the continuation K, you also call it using the remained stack, but the stack is dropped.
Had you took into account the remaining stack you would have had:
((lambda (k)
(k 4
(lambda (v)
(* 5 v))))
(lambda (result stack)
;; this continuation will consider the stacked computation
(stack result)))
and in this case the result would have been 20.
But in the semantics from your code, by calling the continuation, you dropped the stack, the not-finished computation.
The continuation will return with the value passed to it (k 4), so 4 is the return value.
I would like to write a function that gets and infix expression and changes it to prefix.
at first let's assume we only deal with + operator, so I want to change the expression 1+1+1 into: (+ (+ 1 1) 1)
I want to do it using foldl or foldl-like matter:
taking the second item in the list (which is always the operand) appending it with the first and the third (in that order) then I would like the expression we've just appended to become the first item in the list so I would do the same on the rest of the list recursively.
Iv'e tried the following:
(lambda (lst)
(fold-left (lambda (pmLst)
`(,((cadr pmLst) ,(car pmLst) (caddr pmLst)) ,(cddr pmLst)))
'()
lst))
but then I realized that the lambda given to the fold-left has to have 2 arguments but I would like to deal with the first 3 items of the list.
I hope I've made myself clear cause it got a bit tricky..
A fold wont do what you want. If you imagine the expression (5 + 3 + 2) then using a fold with proc as the procedure do this:
(proc 2 (proc '+ (proc 3 (proc '+ (proc 5 '())))))
A way would be to make a function that returns the odd and even elements in their own list so that '(+ 2 - 3) becomes (+ -) and (2 3) and then you could do it like this:
(define (infix->prefix expr)
(if (pair? expr)
(let-values ([(ops args) (split (cdr expr))])
(fold (lambda (op arg acc)
(list op acc (infix->prefix arg)))
(car expr)
ops
args))
expr))
However the size of both is much greater than just rolling your own recursion:
(define (infix->prefix expr)
(define (aux lst acc)
(if (pair? lst)
(aux (cddr lst)
(list (car lst)
acc
(infix->prefix (cadr lst))))
acc))
(if (pair? expr)
(aux (cdr expr) (infix->prefix (car expr)))
expr))
(infix->prefix '(1 + 2 - 3))
; ==> (- (+ 1 2) 3)
There is no operator precedence here. Everything is strictly left to right.
I wanted to write a code in Scheme that writes the square odd elements in list.For example (list 1 2 3 4 5) for this list it should write 225.For this purpose i write this code:
(define (square x)(* x x))
(define (product-of-square-of-odd-elements sequence)
(cond[(odd? (car sequence)) '() (product-of-square-of-odd-elements (cdr sequence))]
[else ((square (car sequence)) (product-of-square-of-odd-elements (cdr sequence)))]))
For run i write this (product-of-square-of-odd-elements (list 1 2 3 4 5))
and i get error like this:
car: contract violation
expected: pair?
given: '()
What should i do to make this code to run properly? Thank you for your answers.
First of all, you need to do proper formatting:
(define (square x) (* x x))
(define (product-of-square-of-odd-elements sequence)
(cond
[(odd? (car sequence))
'() (product-of-square-of-odd-elements (cdr sequence))]
[else
((square (car sequence)) (product-of-square-of-odd-elements (cdr sequence)))]))
Now there are multiple issues with your code:
You are trying to work recursively on a sequence, but you are missing a termination case: What happens when you pass '() - the empty sequence? This is the source of your error: You cannot access the first element of an empty sequence.
You need to build up your result somehow: Currently you're sending a '() into nirvana in the first branch of your cond and put a value into function call position in the second.
So let's start from scratch:
You process a sequence recursively, so you need to handle two cases:
(define (fn seq)
(if (null? seq)
;; termination case
;; recursive case
))
Let's take the recursive case first: You need to compute the square and multiply it with the rest of the squares (that you'll compute next).
(* (if (odd? (car seq)
(square (car seq))
1)
(fn (cdr seq)))
In the termination case you have no value to square. So you just use the unit value of multiplication: 1
This is not a good solution, as you can transform it into a tail recursive form and use higher order functions to abstract the recursion altogether. But I think that's enough for a start.
With transducers:
(define prod-square-odds
(let ((prod-square-odds
((compose (filtering odd?)
(mapping square)) *)))
(lambda (lst)
(foldl prod-square-odds 1 lst))))
(prod-square-odds '(1 2 3 4 5))
; ==> 225
It uses reusable transducers:
(define (mapping procedure)
(lambda (kons)
(lambda (e acc)
(kons (procedure e) acc))))
(define (filtering predicate?)
(lambda (kons)
(lambda (e acc)
(if (predicate? e)
(kons e acc)
acc))))
You can decompose the problem into, for example:
Skip the even elements
Square each element
take the product of the elements
With this, an implementation is naturally expressed using simpler functions (most of which exist in Scheme) as:
(define product-of-square-of-odd-elements (l)
(reduce * 1 (map square (skip-every-n 1 l))))
and then you implement a helper function or two, like skip-every-n.
You are given a list of strings.
Generate a procedure such that applying this procedure to such a list
would result in a list of the lengths of each of the strings in the
input.
Use map, filter, or fold-right.
(lengths (list "This" "is" "not" "fun")) => (4 2 3 3)
(define lengths (lambda (lst) your_code_here))
I got stuck in the following code and I do not understand how can I use filter.
(define lengths
(lambda (lst)
(if (null? lst)
nil
(fold-right list (string-length (car lst)) (cdr lst)))))
This seems like a work for map, you just have to pass the right procedure as a parameter:
(define (lengths lst)
(map string-length lst))
As you should know, map applies a procedure to each of the elements in the input list, returning a new list collecting the results. If we're interested in building a list with the lengths of strings, then we call string-length on each element. The procedure pretty much writes itself!
A word of advice: read the documentation of the procedures you're being asked to use, the code you're writing is overly complicated. This was clearly not a job for filter, although fold-right could have been used, too. Just remember: let the higher-order procedure take care of the iteration, you don't have to do it explicitly:
(define (lengths lst)
(fold-right (lambda (x a)
(cons (string-length x) a))
'()
lst))
This looks like homework so I'll only give you pointers:
map takes a procedure and applies to to every element of a list. Thus
(define (is-strings lst)
(map string? lst))
(is-strings '("hello" 5 sym "89")) ; (#t #f #f #t)
(define (add-two lst)
(map (lambda (x) (+ x 2)) lst))
(add-two '(3 4 5 6)) ; ==> (5 6 7 8)
filter takes procedure that acts as a predicate. If #f the element is omitted, else the element is in the resulting list.
(define (filter-strings lst)
(filter string? lst))
(filter-strings '(3 5 "hey" test "you")) ; ==> ("hey" "you")
fold-right takes an initial value and a procedure that takes an accumulated value and a element and supposed to generate a new value:
(fold-right + 0 '(3 4 5 6)) ; ==> 18, since its (+ 3 (+ 4 (+ 5 (+ 6 0))))
(fold-right cons '() '(a b c d)) ; ==> (a b c d) since its (cons a (cons b (cons c (cons d '()))))
(fold-right - 0 '(1 2 3)) ; ==> -2 since its (- 1 (- 2 (- 3 0)))
(fold-right (lambda (e1 acc) (if (<= acc e1) acc e1)) +Inf.0 '(7 6 2 3)) ; ==> 2
fold-right has a left handed brother that is iterative and faster, though for list processing it would reverse the order after processing..
(fold-left (lambda (acc e1) (cons e1 acc)) '() '(1 2 3 4)) ; ==> (4 3 2 1)
I have this curry function:
(define curry
(lambda (f) (lambda (a) (lambda (b) (f a b)))))
I think it's like (define curry (f a b)).
my assignment is to write a function consElem2All using curry，which should work like
(((consElem2All cons) 'b) '((1) (2 3) (4)))
>((b 1) (b 2 3) (b 4))
I have wrote this function in a regular way:
(define (consElem2All0 x lst)
(map (lambda (elem) (cons x elem)) lst))
but still don't know how to transform it with curry. Can anyone help me?
thanks in advance
bearzk
You should begin by reading about currying. If you don't understand what curry is about, it may be really hard to use it... In your case, http://www.engr.uconn.edu/~jeffm/Papers/curry.html may be a good start.
One very common and interesting use of currying is with functions like reduce or map (for themselves or their arguments).
Let's define two currying operators!
(define curry2 (lambda (f) (lambda (arg1) (lambda (arg2) (f arg1 arg2)))))
(define curry3 (lambda (f) (lambda (arg1) (lambda (arg2) (lambda (arg3) (f arg1 arg2 arg3))))))
Then a few curried mathematical functions:
(define mult (curry2 *))
(define double (mult 2))
(define add (curry2 +))
(define increment (add 1))
(define decrement (add -1))
And then come the curried reduce/map:
(define creduce (curry3 reduce))
(define cmap (curry2 map))
Using them
First reduce use cases:
(define sum ((creduce +) 0))
(sum '(1 2 3 4)) ; => 10
(define product (creduce * 1))
(product '(1 2 3 4)) ; => 24
And then map use cases:
(define doubles (cmap double))
(doubles '(1 2 3 4)) ; => (2 4 6 8)
(define bump (cmap increment))
(bump '(1 2 3 4)) ; => (2 3 4 5)
I hope that helps you grasp the usefulness of currying...
So your version of curry takes a function with two args, let's say:
(define (cons a b) ...)
and turns that into something you can call like this:
(define my-cons (curry cons))
((my-cons 'a) '(b c)) ; => (cons 'a '(b c)) => '(a b c)
You actually have a function that takes three args. If you had a curry3 that managed 3-ary functions, you could do something like:
(define (consElem2All0 the-conser x lst) ...)
(like you did, but allowing cons-like functions other than cons to be used!)
and then do this:
(define consElem2All (curry3 consElem2All0))
You don't have such a curry3 at hand. So you can either build one, or work around it by "manually" currying the extra variable yourself. Working around it looks something like:
(define (consElem2All0 the-conser)
(lambda (x lst) ...something using the-conser...))
(define (consElem2All the-conser)
(curry (consElem2All0 the-conser)))
Note that there's one other possible use of curry in the map expression itself, implied by you wrapping a lambda around cons to take the element to pass to cons. How could you curry x into cons so that you get a one-argument function that can be used directly to map?...
Perhaps better use a generalized version:
(define (my-curry f)
(lambda args
(cond ((= (length args) 1)
(lambda lst (apply f (cons (car args) lst))))
((>= (length args) 2)
(apply f (cons (car args) (cdr args)))))))
(define (consElem2All0 x lst)
(map ((curry cons) x) lst))