How to decide the parantheses in scheme - functional-programming

I am a little bit confused about putting the parantheses in scheme. The following example:
=>(define foo1 (lambda (n) (+ n 1)))
=>(foo1 ((lambda () 5)))
=>value:6
Gives the result 6. But i am surprised why this did not give an error. Here is how i thnik it should be computer: First the (lambda () 5) expression is computed and it returns 5. Now we an remove its parantheses:
=>(foo (5))
And now this should be invalid since we do not use parantheses for the parameters while calling a function. But it gives no error. Can somebody tell me what i am doing wrong?
Thanks

Alright! Finally figured out what's going on here.
This statement actually evaluates to 5:
((lambda () 5))
Try it in your REPL.
The inner part (lambda () 5) creates a procedure. The outer paranthesis pair '(', ')' invoke the function. Obviously that makes it return 5!

Scheme makes no fundamental distinction between code and data. Why do I mention this? It's because Lambda's return is always either a function or an error, that is it returns code rather than simple data. Any other function that returns a function is going to behave in the same way.

Related

Racket Code: Higher-Order Functions

I'm trying to implement higher level functions in my Racket code, specifically with regards to this function:
(define (indivisible e L)
(map (remove 0 ((map ((lambda (x y) (modulo x y))) L e)))))
Essentially, I'm trying to remove all the elements that are divisible by e from the list. However, it keeps giving me an error that says that "the expected number of arguments did not match the given number (0 vs 2)". Why is this so?
Several places you have two sets of parentheses. Unless the parentheses are a part of a special form or macro, eg. let, it represent an application. Ie.
((lambda (x y) (modulo x y)))
Here the form (lambda ...) is evaluated and become a function. The second set of parentheses calls this function with no arguments. Since you have two arguments, x and y and not supplying any in your application it signals an error.
Another place where you do the same is around (map ....). Since I know map always evaluates to a list or null it looks kind of strange that you call it as a function ((map ...)).
If you are more familiar with algol languages like python, what you are doing is like someFunc(arg1 args2)() where you clearly see someFunc needs to return a function wince it's immediately called afterwards. The same in Scheme looks like ((some-func arg1 arg2)).
remove removes the first argument from the second argument list. It does not return a function so the outer map won't work.
To solve this I think you are looking for filter. You only need to make a predicate that is #f for the elements you don't want and you're done.

not sure about the definition of a macro in a sample of OnLisp

Here are some sample codes from text of OnLisp.
My question is that why it bothers to use a lambda function,
`(funcall (alrec ,rec #'(lambda () ,base)) ,#lsts))
as second argument to alrec in the definition of on-cdrs?
What is the difference if I just define it without using lambda?
`(funcall (alrec ,rec ,base) ,#lsts))
(defun lrec (rec &optional base)
(labels ((self (lst)
(if (null lst)
(if (functionp base)
(funcall base)
base)
(funcall rec (car lst)
#'(lambda ()
(self (cdr lst)))))))
#'self))
(defmacro alrec (rec &optional base)
"cltl2 version"
(let ((gfn (gensym)))
`(lrec #'(lambda (it ,gfn)
(symbol-macrolet ((rec (funcall ,gfn)))
,rec))
,base)))
(defmacro on-cdrs (rec base &rest lsts)
`(funcall (alrec ,rec #'(lambda () ,base)) ,#lsts))
You don't say how this is intended to be called and this code is a bit of a tangle so at a quick glance I couldn't say how it's supposed to work. However, I can answer your question.
First, let me say that
(if (functionp base) (funcall base) base)
is terrible programming style. This effectively puts a whole in your semantic space, creating a completely different handling of functions as objects than other things as objects. In Common Lisp, a function is supposed to be an object you can choose to pass around. If you want to call it, you should do so, but you shouldn't just say to someone "if I give you a function you should call it and otherwise you should not." (Why this matters will be seen as you read on.)
Second, as Barmar notes, if you write ,base you are basically saying "take the code and insert it for evaluation here". If you write
#'(lambda () ,base)
you are saying put the code inside a function so that its execution is delayed. Now, you're passing it to a function that when it receives the function is going to call it. And, moreover, calling it will evaluate it in the lexical environment of the caller, and there is no intervening change in dynamic state. So you'd think this would be the same thing as just evaluating it at the call site (other than just a little more overhead). However, there is a case where it's different.
If the thing you put in the base argument position is a variable (let's say X) or a number (let's say 3), then you'll either be doing (lrec ... X) or (lrec 3) or else you'll be doing
(lrec ... #'(lambda () X))
or
(lref ... #'(lambda () 3))
So far so good. If it gets to the caller, it's going to say "Oh, you just meant the value of X (or of 3)." But there's more...
If you say instead an expression that yields a function in the base argument position of your call to on-cdrs or your call to alrec, you're going to get different results depending on whether you wrote ,base or #'(lambda () ,base). For example, you might have put
#'f
or
#'(lambda () x)
or, even worse,
#'(lambda (x) x)
in the base argument position. In that case, if you had used ,base, then that expression would be immediately evaluated before passing the argument to lrec, and then lrec would receive a function. And then it would be called a second time (which is probably not what the macro user expects unless the documentation is very clear about this inelegance and the user of the macro has cared enough to read the documentation in detail). In the first case, it will return 3, in the second case, the value of x, and in the third case an error situation will occur because it will be called with the wrong number of arguments.
If instead you implemented it with
#'(lambda () ,base)
then lrec will receive as an argument the result of evaluating one of
#'(lambda () #'f)
or
#'(lambda () #'(lambda () 3))
or
#'(lambda () #'(lambda (x) x))
depending on what you gave it as an argument from our examples above. But in any case what lrec gets is a function of one argument that, when evaluated, will return the result of evaluating its body, that is, will return a function.
The important takeaways are these:
The comma is dropping in a piece of evaluable code, and wrapping the comma'd experession with a lambda (or wrapping any expression with a lambda) delays evaluation.
The conditional in the lrec definition should either expect that the value is already evaluated or not, and should not take a conditional effect because it can't know whether you already evaluated something based purely on type unless it basically makes a mess of functions as first-class data.
I hope that helps you see the difference. It's subtle, but it's real.
So using
#'(lambda () ,base)
protects the macro from double-evaluation of a base that might yield a function, but on the other hand the bad style is something that shouldn't (in my view) happen. My recommendation is to remove the conditional function call to base and make it either always or never call the base as a function. If you make it never call the function, the caller should definitely use ,base. If you make it always call the function, the caller should definitely include the lambda wrapper. That would make the number of evaluations deterministic.
Also, as a purely practical matter, I think it's more in the style of Common Lisp just to use ,base and not bother with the closure unless the expression is going to do something more than travel across a function call boundary to be immediately called. It's a waste of time and effort and perhaps extra consing to have the function where it's really not serving any interesting purpose. This is especially true if the only purpose of the lrec function is to support this facility. If lrec has an independent reason to have the contract that it does, that's another matter and maybe you'd write your macro to accommodate.
It's more common in a functional language like Scheme, which has a different aesthetic, to have a regular function as an alternative to any macro, and to have that function take such a zero-argument function as an argument just in case some user doesn't like working with macros. But mostly Common Lisp programmers don't bother, and your question was about Common Lisp, so I've biased the majority of my writing here to that dialect.

Common Lisp Binary Tree

I am trying to write a program in Common Lisp using GNU ClISP to compile it. I would like to enter a list such as (A(B (C) ()) (D (E) (F (G) ()))) and depending on the first word print out the pre-, in-, or post-order traversal. Example:
(pre '(A(B (C)... etc))
I am having trouble putting my logic into Clisp notation. I currently have the following code:
(defun leftchild (L)(cadr L))
(defun rightchild (L)(caddr L))
(defun data (L)(car L))
(defun pre (L)(if (null L) '()((data L)(pre(leftchild L))(pre(rightchild L)))))
... similar in and post functions
I get compiling errors saying that I should use a lambda in my pre function. I think this is due to the double (( infront of data because it is expecting a command, but I am not sure what I should put there. I don't think cond would work, because that would hinder the recursive loop. Also, will data L print as it is now? The compiler did not recognize (print (data L)).
I have been working on this code for over a week now, trying to troubleshoot it myself, but I am at a loss. I would greatly appreciate it if someone could explain what I am doing incorrectly.
Another question that I have is how can I make the program prompt a line to the user to enter the (pre '(A... etc)) so that when I run the compiled file the program will run instead of giving a funcall error?
Thank you for your time.
Short answer: If you want to use if, note that you'll need a progn in order to have more than one form in the consequent and alternative cases.
Long answer – also explains how to traverse accumulating the visited nodes in a list:
I guess this is homework, so I won't give you a full solution, but your question shows that you have basically the right idea, so I'll show you an easy, idiomatic way to do this.
First, you're right: The car of an unquoted form should be a function, so basically anything like (foo ...), where foo is not a function (or macro, special form ...), and the whole thing is to be evaluated, will be an error. Note that this does not hold inside special forms and macros (like cond, for example). These can change the evaluation rules, and not everything that looks like (foo bar) has to be a form that is to be evaluated by the normal evaluation rules. The easiest example would be quote, which simply returns its argument unevaluated, so (quote (foo bar)) will not be an error.
Now, about your problem:
An easy solution would be to have an accumulator and a recursive helper function that traverses the tree, and pushes the values in the accumulator. Something like this:
(defun pre (node)
(let ((result (list)))
(labels ((rec (node)
(cond (...
...
...))))
(rec node)
(nreverse result))))
The labels just introduces a local helper function, which will do the actual recursion, and the outer let gives you an accumulator to collect the node values. This solution will return the result as a list. If you just want to print each nodes value, you don't need the accumulator or the helper function. Just print instead of pushing, and make the helper your toplevel function.
Remember, that you'll need a base case where the recursion stops. You should check for that in the cond. Then, you'll need the recursive steps for each subtree and you'll need to push the node's value to the results. The order in which you do these steps decides whether you're doing pre-, in-, or post-order traversal. Your code shows that you already understand this principle, so you'll just have to make it work in Lisp-code. You can use push to push values to result, and consp to check whether a node is a non-empty list. Since there's nothing to do for empty lists, you'll basically only need one test in the cond, but you can also explicitly check whether the node is null, as you did in your code.

Got some problems with CLISP's nested list and lambda expression

Nested lists in Common Lisp really confused me. Here is the problem:
By using recursion, let (nested-list 'b '(a (b c) d)) return t
if the first argument appears in the second argument (which could be
a nested list), and nil otherwise.
I tried find, but it only works if the first argument is '(b c).
I turned my eyes on lambda expressions. I want to flatten the second
argument first, and then use eq to compare the arguments.
(defun nested-list (x y)
(cond
((null y) ())
(t (append (lambda (flatten) (first y))
Then I got stuck. Even though I read a lot of stuff about lambda
expessions, it still confused me. I do not know how to recall it when
I need, I knew the funcall function, but you know I just cannot get
it. I just learnt Common Lisp for 5 days, so I hope you can give me a
hint. Thanks a lot!
First of all unless you mistyped if instead of iff the problem is quite trivial, just return t and you're done :-)
Seriously speaking instead when you need to solve a problem using recursion the idea often is simply:
if we're in a trivial case just return the answer
otherwise the answer is the same answer we'd get by solving a problem that it's just a little bit simpler that this, and we call ourself to solve this simplified version.
In the specific consider:
If the second argument is an empty list the answer is NIL
If the first argument is equal to the first element of the second argument then just return T instead
Otherwise if the first element of the second list is a list (therefore also possibly a nested list) and the element is contained in this multilist then return true (to check this case the function is calling itself)
Otherwise just check the same problem, but first dropping the first element of the second argument, because it has been checked (this also calls recursively the same function)
So basically 1 and 2 are the trivial cases; 3 and 4 are the cases in which you solve a simpler version of the problem.

lazy-seq for recursive function

Sorry for the vague title, I guess I just don't understand my problem well enough to ask it yet but here goes. I want to write a recursive function which takes a sequence of functions to evaluate and then calls itself with their results & so on. The recursion stops at some function which returns a number.
However, I would like the function being evaluated at any point in the recursion, f, to be wrapped in a function, s, which returns an initial value (say 0, or the result of another function i) the first time it is evaluated, followed by the result of evaluating f (so that the next time it is evaluated it returns the previously evaluated result, and computes the next value). The aim is to decouple the recursion so that it can proceed without causing this.
I think I'm asking for a lazy-seq. It's a pipe that's filling-up with evaluations of a function at one end, and historical results are coming out of the other.
Your description reminds me some of reductions? Reductions will perform a reduce and return all the intermediate results.
user> (reductions + (range 10))
(0 1 3 6 10 15 21 28 36 45)
Here (range 10) creates a seq of 0 to 9. Reductions applies + repeatedly, passing the previous result of + and the next item in the sequence. All of the intermediate results are returned. You might find it instructive to look at the source of reductions.
If you need to build a test (check for value) into this, that's easy to do with an if in your function (although it won't stop traversing the seq). If you want early exit on a condition being true, then you'll need to write your own loop/recur which amalloy has already done well.
I hate to say it, but I suspect this might also be a case for the State Monad but IANAMG (I Am Not A Monad Guy).
I don't understand your entire goal: a lot of the terms you use are vague. Like, what do you mean you want to evaluate a sequence of functions and then recur on their results? These functions must be no-arg functions (thunks), then, I suppose? But having a thunk which first returns x, and then returns y the next time you call it, is pretty vile and stateful. Perhaps trampoline will solve part of your problem?
You also linked to something you want to avoid, but seem to have pasted the wrong link - it's just a link back to this page. If what you want to avoid is stack overflow, then trampoline is likely to be an okay way to go about it, although it should be possible with just loop/recur. This notion of thunks returning x unless they return y is madness, if avoiding stack overflow is your primary goal. Do not do that.
I've gone ahead and taken a guess at the most plausible end goal you might have, and here's my implementation:
(defn call-until-number [& fs]
(let [numeric (fn [x] (when (number? x) x))]
(loop [fs fs]
(let [result (map #(%) fs)]
(or (some numeric result)
(recur result))))))
(call-until-number (fn [] (fn [] 1))) ; yields 1
(call-until-number (fn [] (fn [] 1)) ; yields 2
(fn [] 2))
(call-until-number (fn f [] f)) ; never returns, no overflow

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