Higher Order Function Syntax in Common Lisp - lisp

I'm teaching myself Common Lisp using Norvig's Paradigms of AI Programming and came across something I didn't understand and he didn't explain.
(defun mappend (fn the-list)
(apply #'append (mapcar fn the-list)))
What is the difference between calling a higher order function as follows, higherOrderFunc #'funcName funcArg and what he does when calling mapcar without #'? Is #' necessary when calling a higher order function?

Common Lisp has different namespaces for functions and variables.
(defun mappend (fn the-list)
(apply #'append (mapcar fn the-list)))
Above MAPPEND gets defined with two local variables fn and the-list
APPLY gets passed the function value of APPEND.
MAPCAR gets passed the variable value of FN.
Similar see this:
CL-USER 129 > (flet ((add-something (number)
(+ number 17)))
(let ((add-something (lambda (number)
(+ number 42))))
(list
(mapcar #'add-something '(1 2 3))
(mapcar add-something '(1 2 3)))))
->
((18 19 20) (43 44 45))
LET creates local variables, FLET creates local functions.
The first mapcar uses the function namespace and the second uses the variable namespace.
Common Lisp uses a special function namespace because it was thought to be more efficient (slightly easier to implement a fast Lisp) and to allow functions and variables to have the same name.
In Common Lisp we can write:
(defun list-me (list)
(list list))
In Scheme, which does not have separate namespaces one would write something like this:
(define (list-me lst)
(list lst))

#' is syntactic sugar for function: #'foo is read as (function foo).
Function is a special operator that returns the function value bound to the name given. If you pass a function as a parameter, that parameter (in your case, fn) has its value bound to the function. To pass it on to another function, you can simply put the variable name into the call form. However, to get the function value of a name, you need to access it with function.

Using #' is not strictly required. If instead you simply pass 'foo the symbol-function will be invoked. Consider the following:
* (defvar foo #'(lambda (a) 'var))
* (setf (symbol-function 'foo) #'(lambda (a) 'fun))
* (mapcar 'foo '(a b))
(FUN FUN)
* (mapcar #'foo '(a b))
(FUN FUN)
* (mapcar foo '(a b))
(VAR VAR)
Practially #'foo or 'foo are equivalent:
X3J13 voted [...] to allow the 'function' to the only of type 'symbol'
or 'function'; [...] one must use the 'function' special form [...]
before a lambda-expression [...].
Specification of the function in flet has some interesting properties:
* (flet ((foo (a) 'FLET))
(mapcar foo '(a b))) ; Uses 'value' of foo
(VAR VAR)
* (flet ((foo (a) 'FLET))
(mapcar 'foo '(a b))) ; Uses 'function' of foo
(FUN FUN)
* (flet ((foo (a) 'FLET))
(mapcar #'foo '(a b))) ; Uses local binding 'flet' of foo
(FLET FLET)

Related

Is defun or setf preferred for creating function definitions in common lisp and why?

What is the fundamental difference in the functions defined using defun and setf as below and is one method preferred over another outside of style considerations?
Using defun:
* (defun myfirst (l)
(car l) )
MYFIRST
* (myfirst '(A B C))
A
Using setf:
* (setf (fdefinition 'myfirst) #'(lambda (l) (car l)))
#<FUNCTION (LAMBDA (L)) {10021B477B}>
* (myfirst '(A B C))
A
If, as according to Wikipedia:
named functions are created by storing a lambda expression in a symbol using the defun macro
Using setf to create a variable in a different way requires the use of funcall:
* (defvar myfirst)
MYFIRST
* (setf myfirst (lambda (l) (car l)))
#<Interpreted Function (LAMBDA (X) (+ X X)) {48035001}>
* (funcall myfirst '(A B C))
A
My understanding is that this type of variable is different than the previous in that this variable is not found in the same namespace as the defun bound symbol as described in Why multiple namespaces?.
First of all, one should never underestimate the importance of style.
We write code not just for computers to run, but, much more importantly, for people to read.
Making code readable and understandable for people is a very important aspect of software development.
Second, yes, there is a big difference between (setf fdefinition) and defun.
The "small" differences are that defun can also set the doc string of the function name (actually, depending on how your imeplementation works, it might do that with lambda also), and creates a named block (seen in the macroexpansions below) which you would otherwise have to create yourself if you want to.
The big difference is that the compiler "knows" about defun and will process it appropriately.
E.g., if your file is
(defun foo (x)
(+ (* x x) x 1))
(defun bar (x)
(+ (foo 1 2 x) x))
then the compiler will probably warn you that you call foo in bar with the wrong number of arguments:
WARNING: in BAR in lines 3..4 : FOO was called with 3 arguments, but it requires 1
argument.
[FOO was defined in lines 1..2 ]
If you replace the defun foo with (setf (fdefinition 'foo) (lambda ...)), the compiler is unlikely to handle it as carefully. Moreover, you will probably get a warning along the lines of
The following functions were used but not defined:
FOO
You might want to examine what defun does in your implementation by macroexpanding it:
(macroexpand-1 '(defun foo (x) "doc" (print x)))
CLISP expands it to
(LET NIL (SYSTEM::REMOVE-OLD-DEFINITIONS 'FOO)
(SYSTEM::EVAL-WHEN-COMPILE
(SYSTEM::C-DEFUN 'FOO (SYSTEM::LAMBDA-LIST-TO-SIGNATURE '(X))))
(SYSTEM::%PUTD 'FOO
(FUNCTION FOO
(LAMBDA (X) "doc" (DECLARE (SYSTEM::IN-DEFUN FOO)) (BLOCK FOO (PRINT X)))))
(EVAL-WHEN (EVAL)
(SYSTEM::%PUT 'FOO 'SYSTEM::DEFINITION
(CONS '(DEFUN FOO (X) "doc" (PRINT X)) (THE-ENVIRONMENT))))
'FOO)
SBCL does:
(PROGN
(EVAL-WHEN (:COMPILE-TOPLEVEL) (SB-C:%COMPILER-DEFUN 'FOO NIL T))
(SB-IMPL::%DEFUN 'FOO
(SB-INT:NAMED-LAMBDA FOO
(X)
"doc"
(BLOCK FOO (PRINT X)))
(SB-C:SOURCE-LOCATION)))
The point here is that defun has a lot "under the hood", and for a reason. setf fdefinition is, on the other hand, more of "what you see is what you get", i.e., no magic involved.
This does not mean that setf fdefinition has no place in a modern lisp codebase. You can use it, e.g., to implement a "poor man's trace" (UNTESTED):
(defun trace (symbol)
(setf (get symbol 'old-def) (fdefinition symbol)
(fdefinition symbol)
(lambda (&rest args)
(print (cons symbol args))
(apply (get symbol 'old-def) args))))
(defun untrace (symbol)
(setf (fdefinition symbol) (get symbol 'old-def))
(remprop symbol 'odd-def))

How is sharp quote (#') different from symbol-function?

To me these operators seem to do the same thing. Both take a symbol and return the function associated with it. Is there any difference?
elisp evaluation returns the following:
(defun foo (x) (+ 1 x))
foo
(foo 3)
4
#'foo
Which I don't understand either.
Furthermore is there a difference between common lisp and elisp? I'm learning from resources on either.
Common Lisp:
SYMBOL-FUNCTION can't retrieve functions from lexically bound functions. FUNCTION references the lexically bound function by default. #'foo is just a shorter notation for (FUNCTION foo).
CL-USER 1 > (defun foo () 'foo)
FOO
CL-USER 2 > (flet ((foo () 'bar))
(list (funcall (symbol-function 'foo))
(funcall #'foo)
(funcall (function foo))
(eq (function foo) (symbol-function 'foo))))
(FOO BAR BAR NIL)
CL-USER 3 > (eq (function foo) (symbol-function 'foo))
T
Rainer's answer discusses the things that you can do with function that you can't do with symbol-function, namely retrieve the value of lexically scoped functions, but there are a few other differences too.
The special operator FUNCTION
The special operator FUNCTION provides a way to find the functional value of a name in a lexical environment. Its argument is either a function name or a lambda expression. That function can take a lambda expression means that you can write: (function (lambda (x) (list x x))). The term function name includes more than just symbols. It also includes lists of the form (setf name), which means that you can do things like (function (setf car)).
The accessor SYMBOL-FUNCTION
The accessor symbol-function, on the other hand, lets you retrieve and set the functional value of a symbol. Since it requires a symbol, you can't do (symbol-function (lambda …)) or (function (setf name)). Symbol-function also can't see lexical environments; it only works with global definitions. E.g.,
(flet ((foo () 'result))
(symbol-function 'foo))
;=> NIL
Since symbol-function is an accessor, you can change the value of a function's symbol with it. E.g.:
CL-USER> (setf (symbol-function 'foo) (lambda () 42))
#<FUNCTION (LAMBDA ()) {1005D29AAB}>
CL-USER> (foo)
42
CL-USER> (setf (symbol-function 'foo) (lambda () 26))
#<FUNCTION (LAMBDA ()) {1005D75B9B}>
CL-USER> (foo)
26
The accessor FDEFINITION
There's also the accessor fdefinition which is kind of like symbol-function in that is can only access globally defined functions, but kind of like function in that it can access of symbols and (setf name) lists. However, it does not retrieve the value of lambda functions.

Still about quote in Lisp

I am a novice in Lisp, learning slowly at spare time... Months ago, I was puzzled by the error report from a Lisp REPL that the following expression does not work:
((if (> 2 1) + -) 1 2)
By looking around then I knew that Lisp is not Scheme...in Lisp, I need to do either:
(funcall (if (> 2 1) '+ '-) 2 1), or
(funcall (if (> 2 1) #'+ #'-) 2 1)
I also took a glimpse of introductary material about lisp-1 and lisp-2, although I was not able to absort the whole stuff there...in any case, I knew that quote prevents evaluation, as an exception to the evaluation rule.
Recently I am reading something about reduce...and then as an exercise, I wanted to write my own version of reduce. Although I managed to get it work (at least it seems working), I realized that I still cannot exactly explain why, in the body of defun, that some places funcall is needed, and at some places not.
The following is myreduce in elisp:
(defun myreduce (fn v lst)
(cond ((null lst) v)
((atom lst) (funcall fn v lst))
(t (funcall fn (car lst) (myreduce fn v (cdr lst))))))
(myreduce '+ 0 '(1 2 3 4))
My questions are about the 3rd and 4th lines:
The 3rd line: why I need funcall? why not just (fn v lst)? My "argument" is that in (fn v lst), fn is the first element in the list, so lisp may be able to use this position information to treat it as a function...but it's not. So certainly I missed something here.
The 4th line in the recursive call of myreduce: what kind of fn be passed to the recursive call to myreduce? '+ or +, or something else?
I guess there should be something very fundamental I am not aware of...I wanted to know, when I call myreduce as shown in the 6th/last line, what is exactly happening afterwards (at least on how the '+ is passed around), and is there a way to trace that in any REPL environment?
Thanks a lot,
/bruin
Common Lisp is a LISP-2 and has two namespaces. One for functions and one for variables. Arguments are bound in the variable namespace so fn does not exist in the function namespace.
(fn arg) ; call what fn is in the function namespace
(funcall fn ...) ; call a function referenced as a variable
'+ is a symbol and funcall and apply will look it up in the global function namespace when it sees it's a symbol instead of a function object. #'+ is an abbreviation for (function +) which resolves the function from the local function namespace. With lots of calls #'+ is faster than '+ since '+ needs a lookup. Both symbol and a function can be passed as fn to myreduce and whatever was passed is the same that gets passed in line 4.
(myreduce '+ 0 '(1 2 3 4)) ; here funcall might lookup what '+ is every time (CLISP does it while SBLC caches it)
(myreduce #'+ 0 '(1 2 3 4)); here funcall will be given a function object looked up in the first call in all consecutive calls
Now if you pass '+ it will be evaluated to + and bound to fn.
In myreduce we pass fn in the recursion and it will be evaluated to + too.
For #'+ it evaluates to the function and bound to fn.
In myreduce we pass fn in the recursion and it will be evaluated to the function object fn was bound to in the variable namespace.
Common Lisp has construct to add to the function namespace. Eg.
(flet ((double (x) (+ x x))) ; make double in the function namespace
(double 10)) ; ==> 20
But you could have written it and used it on the variable namespace:
(let ((double #'(lambda (x) (+ x x)))) ; make double in the variable namespace
(funcall double 10))
Common Lisp has two (actually more than two) namespaces: one for variables and one for functions. This means that one name can mean different things depending on the context: it can be a variable and it can be a function name.
(let ((foo 42)) ; a variable FOO
(flet ((foo (n) (+ n 107))) ; a function FOO
(foo foo))) ; calling function FOO with the value of the variable FOO
Some examples how variables are defined:
(defun foo (n) ...) ; n is a variable
(let ((n 3)) ...) ; n is a variable
(defparameter *n* 41) ; *n* is a variable
So whenever a variable is defined and used, the name is in the variable namespace.
Functions are defined:
(defun foo (n) ...) ; FOO is a function
(flet ((foo (n) ...)) ...) ; FOO is a function
So whenever a function is defined and used, the name is in the function namespace.
Since the function itself is an object, you can have function being a variable value. If you want to call such a value, then you need to use FUNCALL or APPLY.
(let ((plus (function plus)))
(funcall plus 10 11))
Now why are things like they are? ;-)
two namespaces allow us to use names as variables which are already functions.
Example: in a Lisp-1 I can't write:
(defun list-me (list) (list list))
In Common Lisp there is no conflict for above code.
a separate function namespace makes compiled code a bit simpler:
In a call (foo 42) the name FOO can only be undefined or it is a function. Another alternative does not exist. So at runtime we never have to check the function value of FOO for actually being a function object. If FOO has a function value, then it must be a function object. The reason for that: it is not possible in Common Lisp to define a function with something other than a function.
In Scheme you can write:
(let ((list 42))
(list 1 2 3 list))
Above needs to be checked at some point and will result in an error, since LIST is 42, which is not a function.
In Common Lisp above code defines only a variable LIST, but the function LIST is still available.

Tacit programming in Lisp

Is it possible to use/implement tacit programming (also known as point-free programming) in Lisp? And in case the answer is yes, has it been done?
This style of programming is possible in CL in principle, but, being a Lisp-2, one has to add several #'s and funcalls. Also, in contrast to Haskell for example, functions are not curried in CL, and there is no implicit partial application. In general, I think that such a style would not be very idiomatic CL.
For example, you could define partial application and composition like this:
(defun partial (function &rest args)
(lambda (&rest args2) (apply function (append args args2))))
(defun comp (&rest functions)
(flet ((step (f g) (lambda (x) (funcall f (funcall g x)))))
(reduce #'step functions :initial-value #'identity)))
(Those are just quick examples I whipped up – they are not really tested or well thought-through for different use-cases.)
With those, something like map ((*2) . (+1)) xs in Haskell becomes:
CL-USER> (mapcar (comp (partial #'* 2) #'1+) '(1 2 3))
(4 6 8)
The sum example:
CL-USER> (defparameter *sum* (partial #'reduce #'+))
*SUM*
CL-USER> (funcall *sum* '(1 2 3))
6
(In this example, you could also set the function cell of a symbol instead of storing the function in the value cell, in order to get around the funcall.)
In Emacs Lisp, by the way, partial application is built-in as apply-partially.
In Qi/Shen, functions are curried, and implicit partial application (when functions are called with one argument) is supported:
(41-) (define comp F G -> (/. X (F (G X))))
comp
(42-) ((comp (* 2) (+ 1)) 1)
4
(43-) (map (comp (* 2) (+ 1)) [1 2 3])
[4 6 8]
There is also syntactic threading sugar in Clojure that gives a similar feeling of "pipelining":
user=> (-> 0 inc (* 2))
2
You could use something like (this is does a little more than -> in
Clojure):
(defmacro -> (obj &rest forms)
"Similar to the -> macro from clojure, but with a tweak: if there is
a $ symbol somewhere in the form, the object is not added as the
first argument to the form, but instead replaces the $ symbol."
(if forms
(if (consp (car forms))
(let* ((first-form (first forms))
(other-forms (rest forms))
(pos (position '$ first-form)))
(if pos
`(-> ,(append (subseq first-form 0 pos)
(list obj)
(subseq first-form (1+ pos)))
,#other-forms)
`(-> ,(list* (first first-form) obj (rest first-form))
,#other-forms)))
`(-> ,(list (car forms) obj)
,#(cdr forms)))
obj))
(you must be careful to also export the symbol $ from the package in
which you place -> - let's call that package tacit - and put
tacit in the use clause of any package where you plan to use ->, so -> and $ are inherited)
Examples of usage:
(-> "TEST"
string-downcase
reverse)
(-> "TEST"
reverse
(elt $ 1))
This is more like F#'s |> (and the shell pipe) than Haskell's ., but they
are pretty much the same thing (I prefer |>, but this is a matter of personal taste).
To see what -> is doing, just macroexpand the last example three times (in SLIME, this is accomplished by putting the cursor on the first ( in the example and typing C-c RET three times).
YES, it's possible and #danlei already explained very well. I am going to add up some examples from the book ANSI Common Lisp by Paul Graham, chapter 6.6 on function builders:
you can define a function builder like this:
(defun compose (&rest fns)
(destructuring-bind (fn1 . rest) (reverse fns)
#'(lambda (&rest args)
(reduce #'(lambda (v f) (funcall f v))
rest
:initial-value (apply fn1 args)))))
(defun curry (fn &rest args)
#'(lambda (&rest args2)
(apply fn (append args args2))))
and use it like this
(mapcar (compose #'list #'round #'sqrt)
'(4 9 16 25))
returns
((2) (3) (4) (5))
The compose function call:
(compose #'a #'b #'c)
is equlvalent to
#'(lambda (&rest args) (a (b (apply #'c args))))
This means compose can take any number of arguments, yeah.
Make a function which add 3 to argument:
(curry #'+ 3)
See more in the book.
Yes, this is possible in general with the right functions. For example, here is an example in Racket implementing sum from the Wikipedia page:
#lang racket
(define sum (curry foldr + 0))
Since procedures are not curried by default, it helps to use curry or write your functions in an explicitly curried style. You could abstract over this with a new define macro that uses currying.

Higher order programming with Lisp: Passing a function to mapcar?

I'm just learning ANSI Common Lisp (using clisp on a Win32 machine) and I was wondering if mapcar could use a function passed in as a formal argument? Please see the following:
(defun foo (fn seq)
(mapcar #'fn seq))
This would, in my opinion, provide a greater level of flexibility than:
(defun mult (i)
(* i 2))
(defun foo ()
(mapcar #'mult '(1 2 3)))
This is absolutely possible! You're almost there. You just bumped into Common Lisp's dual namespaces, which can take a lot of getting used to. I hope I can say a thing or two to make Common Lisp's two namespaces a bit less confusing.
Your code is almost correct. You wrote:
(defun foo (fn seq)
(mapcar #'fn seq))
But, what is that trying to do? Well, #' is shorthand. I'll expand it out for you.
(defun foo (fn seq)
(mapcar (function fn) seq))
So, #'symbol is shorthand for (function symbol). In Common Lisp -- as you seem to know -- symbols can be bound to a function and to a variable; these are the two namespaces that Lispers talk so much about: the function namespace, and the variable namespace.
Now, what the function special form does is get the function bound to a symbol, or, if you like, the value that the symbol has in the function namespace.
Now, on the REPL, what you wrote would be obviously what you want.
(mapcar #'car sequence)
Would map the car function to a sequence of lists. And the car symbol has no variable binding, only a function binding, which is why you need to use (function ...) (or its shorthand, #') to get at the actual function.
Your foo function doesn't work because the function you pass it as an argument is being bound to a symbol as a variable. Try this:
(let ((fn #'sqrt))
(mapcar #'fn '(4 9 16 25)))
You might have expected a list of all those numbers' square roots, but it didn't work. That's because you used let to bind the square root function to fn as a variable. Now, try this code:
(let ((fn #'sqrt))
(mapcar fn '(4 9 16 25)))
Delightful! This binds the square root function to the fn symbol as a variable.
So, let's go revise your foo function:
(defun foo (fn seq)
(mapcar fn seq))
That will work, because fn is a variable. Let's test it, just to make sure:
;; This will not work
(foo sqrt '(4 9 16 25))
;; This will work
(foo #'sqrt '(4 9 16 25))
The first one didn't work, because the square root function is bound to sqrt in the function namespace. So, in the second one, we grabbed the function from the symbol, and passed it to foo, which bound it to the symbol fn as a variable.
Okay, so what if you want to bind a function to a symbol in the function namespace? Well, for starters, defun does that, permanently. If you want it to be temporary, like a let binding, use flet. Flet is, in my opinion, stupid, because it doesn't work exactly like let does. But, I'll give an example, just so you can see.
(flet ((fn (x) (sqrt x)))
(mapcar fn '(4 9 16 25)))
will not work, because flet didn't bind the function to the symbol in the variable namespace, but in the function namespace.
(flet ((fn (x) (sqrt x)))
(mapcar #'fn '(4 9 16 25)))
This will do what you expect, because flet bound that function to the symbol fn in the function namespace. And, just to drive the idea of the function namespace home:
(flet ((fn (x) (sqrt x)))
(fn 16))
Will return 4.
Sure, you can do this:
(defun foo (fn)
(mapcar fn '(1 2 3)))
Examples:
(foo #'(lambda (x) (* x 2)))
(foo #'1+)
(foo #'sqrt)
(foo #'(lambda (x) (1+ (* x 3))))