In the following scheme code, accumulate does right-fold. When I tried to run using mit scheme. I ran into following error:
Transformer may not be used as an expression: #[classifier-item 13]
Classifier may not be used as an expression: #[classifier-item 12]
I google searched but didn't find useful information. Is it related a macro?
; This function is copied from SICP chapter 2
(define (accumulate op initial sequence)
(if (null? sequence)
initial
(op (car sequence)
(accumulate op initial (cdr sequence)))))
; works as expected
(accumulate
(lambda (x y) (or x y)) ; replace or with and also works
#f
'(#t #f #t #f #f)
))
; does not work
; error: Classifier may not be used as an expression: #[classifier-item 12]
(accumulate
or
#f
'(#t #f #t #f #f)
))
; does not work
; error: Transformer may not be used as an expression: #[classifier-item 13]
(accumulate
and
#f
'(#t #f #t #f #f)
))
Macros can be passed around in some languages, but not in Scheme and Common Lisp. The reason is that macros should be able to be expanded ahead of time. eg.
(define (cmp a b)
(cond ((< a b) -1)
((> a b) 1)
(else 0)))
Now a compiling Scheme will expand each node recursively replacing it with the expansion until it is no change:
(define (cmp a b)
(if (< a b)
(begin -1)
(cond ((> a b) 1)
(else 0))))
(define (cmp a b)
(if (< a b)
-1
(cond ((> a b) 1)
(else 0))))
(define (cmp a b)
(if (< a b)
-1
(if (> a b)
(begin 1)
(cond (else 0)))))
(define (cmp a b)
(if (< a b)
-1
(if (> a b)
1
(cond (else 0)))))
; end result
(define (cmp a b)
(if (< a b)
-1
(if (> a b)
1
0)))
From this point of cond doesn't need to exist in the underlying language at all since you'll never ever use it, but how would this have to be implemented to work:
(define (test syntax a b)
(syntax a b))
(test or #f #t)
For this to work the underlying language needs to know what or is even after expansion since syntax would need to be bound to or and then the transformation can happen. But when the code runs the macro expansion has already happened and in most implementations you would see something indicating that or is an unbound variable. It seems like MIT Scheme has added error checking for top level syntax syntax that will fire an error if you don't override it. Eg. if you add this you will not see any problems whatsoever:
(define (or a b) (if a a b))
(define (and a b) (if a b #f))
Now after those lines any reference to and and or are not the syntax, but these procedures. There are no reserved words in Scheme so if you do something crazy, like defining define you just cannot use it for the rest f that scope:
(define define display) ; defiens define as a top level variable
(define define) ; prints the representation of the function display
(define test 10) ; fail since test is an undefined variable so it cannot be displayed.
I created a interpreted lisp with macros that actually could be passed, but it isn't very useful and the chances of optimization is greatly reduced.
Yes it's related to the macros / special forms like and and or.
You can make it work simply by wrapping them as lambdas, (accumulate (lambda (a b) (or a b)) ...) -- the results will be correct but of course there won't be any short-circuiting then. The op is a function and functions receive their arguments already evaluated.
Either hide the arguments behind lambdas ((lambda () ...)) and evaluate them manually as needed, or define specific versions each for each macro op, like
(define (accumulate-or initial sequence)
(if (null? sequence)
initial
(or (car sequence)
(accumulate-or initial (cdr sequence)))))
Here sequence will still be evaluated in full before the call to accumulate-or, but at least the accumulate-or won't be working through it even after the result is already known.
If sequence contains some results of heavy computations which you want to avoid in case they aren't needed, look into using "lazy sequences" for that.
Related
I'm just starting to write in scheme in DrRacket. However, like we all probably know, those small changes in syntax always mess us up!
I believe my error is in the and conditional. If someone could take a look and tell me what's wrong that would be great!
; in-range?: int int list of numbers --> boolean
(define in-range?
(lambda (a b s)
(cond [(null? s) #t] ;List is empty
[(null? a) #f]
[(null? b) #f]
[((and >= (car s)) ((a) <= (car s)) (b)) (in-range? (a) (b) (cdr s))]
[else #f]
)))
Imagine this form:
(test a b)
You can see it is an application because of the parentheses when test is not a syntax operand. Then test is evaluated and the expected outcome is a procedure that can be called with the evaluated arguments a and b.
You have this as the only epression in a cond term:
((and >= (car s)) ((a) <= (car s)) (b)) (in-range? (a) (b) (cdr s))
This is an application. (and >= (car s)) ((a) <= (car s)) (b)) is not a syntax operand. Then it is evaluated and the expected outcome is a procedure that takes at least one argument, the evaluation of (in-range? (a) (b) (cdr s)).
Since the expression is and which is a syntax operand we know it will either be #f or #t and you should have gotten an error like Application: not a procedure
Parentheses around something in Scheme is like parentheses after something in algol languages like C# and JavaScript. Imagine this expression:
((a.car >=)(), (<= a() s.car)())(in-range(a(), b(), s.cdr))
Lots of syntax errors there in JavaScript too :-o
I am trying to write a scheme program that counts the number of if-statement a file containing code. I know how to read in the file but I don't know how to go about counting the number of if-statements.
This is very hard without actually implementing reducing the language to a more primitive form. As an example, imagine this:
(count-ifs '(let ((if +))
(if 1 2 3)))
; ==> 0
0 is the correct amount as if is a binding shadowing if and Scheme supports shadowing so the result of that expression is 6 and not 2. let can be rewritten such that you can check this instead:
(count-ifs '((lambda (if)
(if 1 2 3))
+))
; ==> 0
It might not look like an improvement, but here you can actually fix it:
(define (count-ifs expr)
(let helper ((expr expr) (count 0))
(if (or (not (list? expr))
(and (eq? (car expr) 'lambda)
(memq 'if (cadr expr))))
count
(foldl helper
(if (eq? (car expr) 'if)
(add1 count)
count)
expr))))
(count-ifs '((lambda (if)
(if 1 2 3))
(if #t + (if if if))))
; ==> 2
Challenge is to expand the macros. You actually need to make a macro expander to rewrite the code such that the only form making bindings would be lambda. This is the same amount of work as making 80% of a Scheme compiler since once you've dumbed it down the rest is easy.
A simple way to do it could be recursion structure like this:
(define (count-ifs exp)
(+ (if-expression? exp 1 0)))
(if (pair? exp)
(+ (count-ifs (car exp)) (count-ifs (cdr exp))))
0)))
But this might overcount.
A more correct way to do it would be to process the code by checking each type of expression you see - and when you enter a lambda you need to add the variables it binds to a shadowed symbols list.
I'm reading The Little Schemer. And thanks to my broken English, I was confused by this paragraph:
(cond ... ) also has the property of not considering all of its
arguments. Because of this property, however, neither (and ... ) nor
(or ... ) can be defined as functions in terms of (cond ... ), though
both (and ... ) and (or ... ) can be expressed as abbreviations of
(cond ... )-expressions:
(and a b) = (cond (a b) (else #f)
and
(or a b) = (cond (a #t) (else (b))
If I understand it correctly, it says (and ...) and (or ...) can be replaced by a (cond ...) expression, but cannot be defined as a function that contains (cond ...). Why is it so? Does it have anything to do with the variant arguments? Thanks.
p.s. I did some searching but only found that (cond ...) ignores the expressions when one of its conditions evaluate to #f.
Imagine you wrote if as a function/procedure rather than a user defined macro/syntax:
;; makes if in terms of cond
(define (my-if predicate consequent alternative)
(cond (predicate consequent)
(else alternative)))
;; example that works
(define (atom? x)
(my-if (not (pair? x))
#t
#f))
;; example that won't work
;; peano arithemtic
(define (add a b)
(my-if (zero? a)
b
(add (- a 1) (+ b 1))))
The problem with my-if is that as a procedure every argument gets evaluated before the procedure body gets executed. thus in atom? the parts (not (pair? x)), #t and #f were evaluated before the body of my-if gets executed.
For the last example means (add (- a 1) (+ b 1)) gets evaluated regardless of what a is, even when a is zero, so the procedure will never end.
You can make your own if with syntax:
(define-syntax my-if
(syntax-rules ()
((my-if predicate consequent alternative)
(cond (predicate consequent)
(else alternative)))))
Now, how you read this is the first part is a template where the predicate consequent and alternative represent unevaluated expressions. It's replaced with the other just reusing the expressions so that:
(my-if (check-something) (display 10) (display 20))
would be replaced with this:
(cond ((check-something) (display 10))
(else (display 20)))
With the procedure version of my-if both 10 and 20 would have been printed. This is how and and or is implemented as well.
You cannot define cond or and or or or if as functions because functions evaluate all their arguments. (You could define some of them as macros).
Read also the famous SICP and Lisp In Small Pieces (original in French).
What is the smartest way to create a switch statement in Scheme?
I want to check one value up against several others, if one results true the entire function should result true, otherwise false. I am not very good with the syntax in scheme.
In Scheme you have case:
(case (car '(c d))
((a e i o u) 'vowel)
((w y) 'semivowel)
(else 'consonant)) ; ==> consonant
As you see it compares against literal data. Thus you cannot compare the value with other variables. Then you need cond
An alternative to an explicit comparison agains each value, is to use member:
> (define (vowel? x) (member x '(a e i o u))
> (vowel? 'b)
#f
Base Case
Often if you want to return a boolean value a simple boolean expression will be enough. In the simple case several checks within an or will be enough:
(define (switch val)
(or (equal? val 'some-value)
(equal? val 'some-other-value)
(equal? val 'yet-another-value)))
Higher Order Function
Is we're doing this often it's a lot of work, so we can make a function called make-switch that takes a list of values and returns a function that serves as a switch statement for those values:
(define (make-switch list-of-vals)
(define (custom-switch val)
(define (inner vals)
(cond ((null? vals) #f)
((equal? val (first vals)) #t)
(else
(inner (rest vals)))))
(inner list-of-vals))
Then we can use make-switch like this:
> (define k (make-switch '(1 2 a "b")))
> (k 1)
#t
> (k 5)
#f
> (k "a")
#f
> (k "b")
#t
Faster Lookups
If we're mostly checking against a static set of values, then a hash-table is another alternative. This code in #lang racket shows the general approach, an R5RS Scheme could use SRFI-69:
#lang racket
(define (make-switch alist)
(define (list->hash alist)
(make-hash (map (lambda (x) (cons x x))
alist)))
(lambda (val)
(if (hash-ref (list->hash alist) val #f)
#t
#f)))
Note
There may be cases where you want to use eq? or some other test for equality, but I've left make-custom-make-switch as an exercise for further exploration.
I'm reading The Little Schemer. And thanks to my broken English, I was confused by this paragraph:
(cond ... ) also has the property of not considering all of its
arguments. Because of this property, however, neither (and ... ) nor
(or ... ) can be defined as functions in terms of (cond ... ), though
both (and ... ) and (or ... ) can be expressed as abbreviations of
(cond ... )-expressions:
(and a b) = (cond (a b) (else #f)
and
(or a b) = (cond (a #t) (else (b))
If I understand it correctly, it says (and ...) and (or ...) can be replaced by a (cond ...) expression, but cannot be defined as a function that contains (cond ...). Why is it so? Does it have anything to do with the variant arguments? Thanks.
p.s. I did some searching but only found that (cond ...) ignores the expressions when one of its conditions evaluate to #f.
Imagine you wrote if as a function/procedure rather than a user defined macro/syntax:
;; makes if in terms of cond
(define (my-if predicate consequent alternative)
(cond (predicate consequent)
(else alternative)))
;; example that works
(define (atom? x)
(my-if (not (pair? x))
#t
#f))
;; example that won't work
;; peano arithemtic
(define (add a b)
(my-if (zero? a)
b
(add (- a 1) (+ b 1))))
The problem with my-if is that as a procedure every argument gets evaluated before the procedure body gets executed. thus in atom? the parts (not (pair? x)), #t and #f were evaluated before the body of my-if gets executed.
For the last example means (add (- a 1) (+ b 1)) gets evaluated regardless of what a is, even when a is zero, so the procedure will never end.
You can make your own if with syntax:
(define-syntax my-if
(syntax-rules ()
((my-if predicate consequent alternative)
(cond (predicate consequent)
(else alternative)))))
Now, how you read this is the first part is a template where the predicate consequent and alternative represent unevaluated expressions. It's replaced with the other just reusing the expressions so that:
(my-if (check-something) (display 10) (display 20))
would be replaced with this:
(cond ((check-something) (display 10))
(else (display 20)))
With the procedure version of my-if both 10 and 20 would have been printed. This is how and and or is implemented as well.
You cannot define cond or and or or or if as functions because functions evaluate all their arguments. (You could define some of them as macros).
Read also the famous SICP and Lisp In Small Pieces (original in French).