well after building a whole function I got many problems and now I am breaking it down into small parts.
My func gets two vars one is a list and the other is a pair. When using (first var1) I get an error.
Here is the code:
#lang pl
(define (maxMin list maxiMini)
(if (null? maxiMini)
(first list)
2
)
)
Here is the error:
Type Checker: Polymorphic function `first' could not be applied to
arguments:
Domains: (Listof a)
(Pairof a (Listof b))
Arguments: Any
in: (first list)
While in this youtube tutorial at minute 1 and 10 seconds the professor uses the first function the same way as me and it does work there.
My guess is that Racket does not recognize myList as a list and sets it as "any" is this possible?
Since you have a Type Checker error, I assume you're using either #lang typed/racket, or some variant of it.
If you look closely at the error itself, it is telling you that first is a polymorphic function, meaning that it can be applied to arguments of different types. Furthermore, the error also states the different types the function first expects under "Domains:", ie. its argument should either be (Listof a) or (Pairof a (Listof b)).
The problem is, you've not actually defined a type for your function maxMin. And if a type annotation is omitted, the inferred type is often Any. As a result, your function does not type-check, because first does not expect the type Any and that's what it is getting.
Since you stated
My func gets two vars one is a list and the other is a pair
consider the following type annotation for your function:
(: max-min (-> (Listof Any) (U Null (Pairof Any Any)) Any))
(define (max-min lst maxi-mini)
(if (null? maxi-mini)
(first lst)
2))
which will type-check, and you can have:
(max-min '(1 2 3) '())
=> 1
Related
My goal is to be able to apply a macro to an argument list in the same way the apply primitive procedure applies a procedure to an argument list.
The list will already be evaluated at the time of application of the macro, there is no way around that and that’s fine; I am wondering if there is any way to programmatically “splice” the list into the macro application (in the same sense as with unquote-splicing). The difficulty resides in that one cannot pass the macro identifier as an argument.
One use case would be
(apply and list)
which would be equivalent to
(not (memq #f list))
to see if there is a #f in list.
Preferably this would be R7RS conformant.
One sort of hacky way would be (as suggested on reddit)
(eval (cons 'and list))
but this is not R7RS conformant, as eval must take an environment argument and it seems to me the standard doesn’t specify how to snatch the environment in effect at the call to eval.
Another half solution is the following, which only works if the list is given directly as a parenthesized sequence of values:
(syntax-rules ()
((_ identifier (val ...))
(identifier val ...)))
I'm posting this as a partial answer I found to my own question, and I'll accept it in a few days if nothing new pops up.
The following works, but only if the macro to apply is contained in a library.
(import (scheme base)
(scheme eval)
(scheme write))
(define (apply-macro mac args . libs)
(eval (cons mac args)
(apply environment libs)))
(define list '(#f #t #t #t))
(display (apply-macro 'and list '(scheme base))) ; => #f
(display (apply-macro 'and (cdr list) '(scheme base))) ; => #t
You can't do that; macros apply to syntax, transforming code fragments into other code fragments, not to values.
Even if you could do it, it would not be equivalent to applying and, since all the elements of list would be evaluated.
For instance, if you define the non-terminating procedure,
(define (forever) (forever))
then (and #f (forever)) is #f, but (apply and (list #f (forever))) would not terminate.
You cannot do this without eval. You would need to implement a procedure version of AND.
The reason it's impossible is because macro expansion is one phase and evaluation is a later phase. The list is piece of dynamic data existing only in the later phase, so a macro cannot use that.
What I'm trying to do seems simple enough, and whatever's wrong must be a really dumb mistake, since I couldn't find other people getting the same error. I just want to apply a lambda to a list - the lambda here isn't what I actually want to do, but it gives the same error.
(apply
(lambda (arg)
(+ 5 arg)
)
(list 2 3 4)
)
When I try to run this, it tells me that I'm passing the lambda an invalid number of arguments. Do you have any advice?
apply calls the function once, passing it the list you've given as the arguments. I think you instead want to use mapcar:
M-: (mapcar (lambda (arg) (+ 5 arg)) (list 2 3 4)) RET
will return the list (7 8 9).
Just to make the problem a bit clearer:
This form
(apply
(lambda (arg)
(+ 5 arg))
(list 2 3 4))
is basically similar to
(funcall
(lambda (arg)
(+ 5 arg))
2
3
4)
In above we try to call a function with one parameter arg with three arguments.
Now if you want to pass more than one argument and receive it as a single list you would need a function with a &rest parameter:
(lambda (&rest args) ...)
You say
I just want to apply a lambda
This is not what you want. You want to map the function over a list. Which means calling the function for each element of the list and returning a new list with the results. This operation is called in Lisp mapping. See the answer by Stefan for an example.
Applying a function to a list would be: call the function with the arguments taken from the list.
The Emacs lisp manual states about the function nconc that:
Since the last argument of nconc is not itself modified, it is reasonable to use a constant list, such as '(4 5), as in the above example. For the same reason, the last argument need not be a list
And indeed I can write
(setq x '(1 2 3))
=> (1 2 3)
(nconc x 0)
=> (1 2 3 . 0)
but that yields a totally broken list:
(length x)
=> eval: Wrong type argument: listp, 0
(butlast x)
=> butlast: Wrong type argument: listp, 0
How can I retrieve the original list? (reverse (cdr (reverse '(1 2 3 . 0)))) doesn't cut it either.
In which contexts is this a useful pattern? In the standard distribution some functions in minibuffer.el use it, in particular completion-all-completions and the like.
They're not "broken" lists; they're actually known as improper lists (as opposed to nil-terminated lists, which are proper lists). Many list functions, such as length and butlast that you just named, expect proper lists, and listp returns true only for proper lists.
Improper lists are used in association lists (where the associations are often not proper; though the alist itself must be proper).
If you want to make an improper list proper, you have two options:
Remove the "improper" element.
Treat the improper element as the last element of the proper list.
Here's a procedure I wrote called properise which will do the former:
(defun properise (x)
(let ((r nil))
(while (consp x)
(push (pop x) r))
(nreverse r)))
(If you want the latter behaviour, add (unless (null x) (push x r)) just before the nreverse line.)
Generally I would avoid creating data structures like that, where the last element is a cons cell with some object other than NIL in the cdr... It makes debugging harder, it's a hack, makes code more difficult to understand, ...
I'm still unsure why this is a good pattern, but here's an easy way of getting a proper list out of an improper one, without making a copy:
(defun nmake-proper-list (x)
(let ((y (last x)))
(setcdr y nil)
x))
I'm very new to scheme and am trying to figure out how to define a function that tests if the parameter to that function is a list, where being a proper list doesn't matter.
I've discerned that I need to check if the argument is either the empty list or a pair. I have the empty list case working fine, but I'm not sure how to check for the pair. I'm just coming off working with prolog, so my initial thought was to do something like this:
(define list?
(lambda (ls)
(if (or (eq? ls (quote()))
(cons(car(ls) cdr(ls))))
true false)))
My thinking was that if scheme could car and cdr the parameter, then it must be a pair, and it would return true. Otherwise it would just fail.
However, passing the argument '(1 2) yields this result:
(list? '(1 2))
. . application: not a procedure;
expected a procedure that can be applied to arguments
given: (1 2)
arguments...: [none]
I don't really understand what's going on here. Additionally, I feel like my thinking as to how to make this function is flawed, but I don't really know how to correct it.
EDIT: Is the issue that (if .....) is looking for a boolean from cons?
You have right idea! But the main reason why your code is not working is that on fourth line you have wrong brackets. This is right transcription of your code:
(define list?
(lambda (ls)
(if (or (eq? ls (quote()))
(cons (car ls) (cdr ls)))
#t #f)))
But in my opinion this solution is bad for these reasons:
If you supply improper list to this procedure it will end by an error when trying to do car or cdr.
For example: (1 2 3 . 4) will end by an error.
In Scheme you have to use literals #t and #f to denote true and false.
Cons always end by "true"
It will not check entire list.
I would write that procedure like this:
(define list?
(lambda (ls)
(if (null? ls)
#t
(and (pair? ls)
(list? (cdr ls))))))
Lets try this on an example: (3 . 4). It is just pair - not a list.
The ls is (3 . 4). Is it null? No, then continue to second if branch.
Is it pair? Yes - continue in and and recursively call list? with 4
The ls is 4. Is it null? No. Again, continue to second branch.
Is it pair? No! Procedure returns #f
That is, when you call a function with >1 arity with only one argument, it should, instead of displaying an error, curry that argument and return the resulting function with decreased arity. Is this possible to do using Lisp's macros?
It's possible, but not easy if you want a useful result.
If you want a language that always does simple currying, then the implementation is easy. You just convert every application of more than one input to a nested application, and the same for functions of more than one argument. With Racket's language facilities, this is a very simple exercise. (In other lisps you can get a similar effect by some macro around the code where you want to use it.)
(Incidentally, I have a language on top of Racket that does just this. It gets the full cuteness of auto-curried languages, but it's not intended to be practical.)
However, it's not too useful since it only works for functions of one argument. You could make it useful with some hacking, for example, treat the rest of the lisp system around your language as a foreign language and provide forms to use it. Another alternative is to provide your language with arity information about the surrounding lisp's functions. Either of these require much more work.
Another option is to just check every application. In other words, you turn every
(f x y z)
into code that checks the arity of f and will create a closure if there are not enough arguments. This is not too hard in itself, but it will lead to a significant overhead price. You could try to use a similar trick of some information about arities of functions that you'd use in the macro level to know where such closures should be created -- but that's difficult in essentially the same way.
But there is a much more serious problem, at the highlevel of what you want to do. The thing is that variable-arity functions just don't play well with automatic currying. For example, take an expression like:
(+ 1 2 3)
How would you decide if this should be called as is, or whether it should be translated to ((+ 1 2) 3)? It seems like there's an easy answer here, but what about this? (translate to your favorite lisp dialect)
(define foo (lambda xs (lambda ys (list xs ys))))
In this case you can split a (foo 1 2 3) in a number of ways. Yet another issue is what do you do with something like:
(list +)
Here you have + as an expression, but you could decide that this is the same as applying it on zero inputs which fits +s arity, but then how do you write an expression that evaluates to the addition function? (Sidenote: ML and Haskell "solves" this by not having nullary functions...)
Some of these issues can be resolved by deciding that each "real" application must have parens for it, so a + by itself will never be applied. But that loses much of the cuteness of having an auto-curried language, and you still have problems to solve...
In Scheme it's possible to curry a function using the curry procedure:
(define (add x y)
(+ x y))
(add 1 2) ; non-curried procedure call
(curry add) ; curried procedure, expects two arguments
((curry add) 1) ; curried procedure, expects one argument
(((curry add) 1) 2) ; curried procedure call
From Racket's documentation:
[curry] returns a procedure that is a curried version of proc. When the resulting procedure is first applied, unless it is given the maximum number of arguments that it can accept, the result is a procedure to accept additional arguments.
You could easily implement a macro which automatically uses curry when defining new procedures, something like this:
(define-syntax define-curried
(syntax-rules ()
((_ (f . a) body ...)
(define f (curry (lambda a (begin body ...)))))))
Now the following definition of add will be curried:
(define-curried (add a b)
(+ a b))
add
> #<procedure:curried>
(add 1)
> #<procedure:curried>
((add 1) 2)
> 3
(add 1 2)
> 3
The short answer is yes, though not easily.
you could implament this as a macro that wrapped every call in partial, though only in limited context. Clojure has some features that would make this rather difficult such as variable arity functions and dynamit calls. Clojure lacks a formal type system to concretely decide when the call can have no more arguments and should actually be called.
As noted by Alex W, the Common Lisp Cookbook does give an example of a "curry" function for Common Lisp. The specific example is further down on that page:
(declaim (ftype (function (function &rest t) function) curry)
(inline curry)) ;; optional
(defun curry (function &rest args)
(lambda (&rest more-args)
(apply function (append args more-args))))
Auto-currying shouldn't be that hard to implement, so I took a crack at it. Note that the following isn't extensively tested, and doesn't check that there aren't too many args (the function just completes when there are that number or more):
(defun auto-curry (function num-args)
(lambda (&rest args)
(if (>= (length args) num-args)
(apply function args)
(auto-curry (apply (curry #'curry function) args)
(- num-args (length args))))))
Seems to work, though:
* (auto-curry #'+ 3)
#<CLOSURE (LAMBDA (&REST ARGS)) {1002F78EB9}>
* (funcall (auto-curry #'+ 3) 1)
#<CLOSURE (LAMBDA (&REST ARGS)) {1002F7A689}>
* (funcall (funcall (funcall (auto-curry #'+ 3) 1) 2) 5)
8
* (funcall (funcall (auto-curry #'+ 3) 3 4) 7)
14
A primitive (doesn't handle full lambda lists properly, just simple parameter lists) version of some macro syntax sugar over the above:
(defmacro defun-auto-curry (fn-name (&rest args) &body body)
(let ((currying-args (gensym)))
`(defun ,fn-name (&rest ,currying-args)
(apply (auto-curry (lambda (,#args) ,#body)
,(length args))
,currying-args))))
Seems to work, though the need for funcall is still annoying:
* (defun-auto-curry auto-curry-+ (x y z)
(+ x y z))
AUTO-CURRY-+
* (funcall (auto-curry-+ 1) 2 3)
6
* (auto-curry-+ 1)
#<CLOSURE (LAMBDA (&REST ARGS)) {1002B0DE29}>
Sure, you just have to decide exact semantics for your language, and then implement your own loader which will translate your source files into the implementation language.
You could e.g. translate every user function call (f a b c ... z) into (...(((f a) b) c)... z), and every (define (f a b c ... z) ...) to (define f (lambda(a) (lambda(b) (lambda(c) (... (lambda(z) ...) ...))))) on top of a Scheme, to have an auto-currying Scheme (that would forbid varargs functions of course).
You will also need to define your own primitives, turning the varargs functions like e.g. (+) to binary, and turning their applications to using fold e.g. (+ 1 2 3 4) ==> (fold (+) (list 1 2 3 4) 0) or something - or perhaps just making such calls as (+ 1 2 3 4) illegal in your new language, expecting of its user to write fold forms by themselves.
That's what I meant by "deciding ... semantics for your language".
The loader can be as simple as wrapping the file contents into a call to a macro - which you would then have to implement, as per your question.
Lisp already has Functional Currying:
* (defun adder (n)
(lambda (x) (+ x n)))
ADDER
http://cl-cookbook.sourceforge.net/functions.html
Here's what I was reading about Lisp macros: https://web.archive.org/web/20060109115926/http://www.apl.jhu.edu/~hall/Lisp-Notes/Macros.html
It's possible to implement this in pure Lisp. It's possible to implement it using macros as well, however it seems as though macros would make it more confusing for very basic stuff.