I am new to lisp and I had a question about this LISP syntax:
(defparameter *binary-operators*
'((+ 1 +) (- 1 -) (* 2 *)
(x 2 *) (/ 2 %) (^ 3 expt)))
From what I understand, defparameter allows the binary operators variable to be reassigned but I am confused as to how the (+ 1 +), (- 1 -) ... are evaluated. I know in LISP that (+ 4 6) would result in (4 + 6) = 10 but the same logic would result in (1 + +) which does not make sense. What does the above syntax represent?
In Common Lisp,
(defparameter name initial-value)
(see the manual) introduces a new special (global) variable name with a new value, given by evaluating initial-value.
So, in the example above, the special variable *binary-operators* is assigned a list of triples, each of them constitued by a symbol, a number, and another symbol. In other words, it assigns some data to a variable, and not, as you were thinking, redefines the syntax of the language.
Guessing from the values present in the list, this seems a variable that is assigned a list of arithmetic operators, each of them with the priority, and with the equivalent Common Lisp operator/function. Maybe this is a line of some program that maps arithmetic expressions in lisp s-expressions, or something like that.
Lisp: lists and symbols are used in data and in code
This is one of the applications where code is data. In Lisp symbols and lists are data. But they are also used to write programs: the symbols then are used for variable names, function names and much more. Lists are used to write expressions in the Lisp language - these are called forms.
In a Lisp program
(+ 1 2)
is a function call of the function named + with two values.
'(+ 1 2)
or
(quote (+ 1 2))
then is data -> the list of the symbol + and the numbers 1 and 2.
Example: infix to prefix conversion
The form you used defines a mapping from a symbol denoting a mathematical function to the weight and the actual Lisp function it represents for the conversion.
See Lispology: Infix to prefix
(defparameter *binary-operators*
; operator weight Lisp function
'((+ 1 +)
(- 1 -)
(* 2 *)
(x 2 *)
(/ 2 %)
(^ 3 expt)))
We can use it to convert infix mathematical expressions to prefix Lisp expressions (see the above linked article for the code):
CL-USER 52 > (infix-prefix '(2 * 3 ^ 4))
(* 2 (EXPT 3 4))
When we change that assoc list, then the conversion will be different. Let's change the weight of the ^ operator:
CL-USER 53 > (defparameter *binary-operators*
'((+ 1 +)
(- 1 -)
(* 2 *)
(x 2 *)
(/ 2 %)
(^ 1 expt))) ; weight changed to 1
*BINARY-OPERATORS*
Now we can convert the example from above and we get a different Lisp form:
CL-USER 54 > (infix-prefix '(2 * 3 ^ 4))
(EXPT (* 2 3) 4)
So, *binary-operators* is data, which drives the conversion from infix mathematical expressions to Lisp forms. Instead of hardwiring the rules into the code, here we are using an assoc list to keep the mappings. Thus allows us to add new operators by changing the assoc list, without changing the actual code.
Related
I have two different Clojure macros, but based on the operation (~# and ~), I need to quote the input or not.
(defmacro make2 [t]
`(list 1 ~#t))
(defmacro make3 [t]
`(list 1 ~t))
(make2 (1 2 3)) -> (1 1 2 3)
(make3 '(1 2 3)) -> (1 (1 2 3))
Why is this? I can guess that with macro, the arguments are not evaluated (that's the reason why make2 doesn't cause an error). However after getting the arguments, I'm not sure the logic to process them.
(macroexpand-1 '(make2 (1 2 3)))
;; ==> (clojure.core/list 1 1 2 3)
(macroexpand-1 '(make3 (1 2 3)))
;;==> (clojure.core/list 1 (1 2 3))
~# splices the list (1 2 3) into the expression (list 1 ...) and then evaluates the resulting expression, i.e. evaluates the function list with the arguments 1 1 2 3. Clojure evaluates each argument, but numbers evaluate to themselves, of course.
~ just inserts the argument (1 2 3) into (list 1 ...) as its second argument and then evaluates the entire expression, evaluating each argument to list as well. When it does, Clojure sees that there is an unquoted pair of parentheses in the second argument, and assumes that the first expression after that left parenthesis is a function (or macro). That is, Clojure assumes that the inner instance of 1 is a function, which it's not. That's why you get the exception
ClassCastException java.lang.Long cannot be cast to clojure.lang.IFn ...
which says that a Long integer cannot be transformed into a function.
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I need to write a program in Lisp to see the number of occurrences of a specific character in a list. For example the occurrences of 1 in the following list [1, 2, 3, 1,1]
A list in Lisp is a sequence of cons nodes: pairs of pointers - the first to the payload datum, and the second to the rest of the list. E.g. for [1,2,3,1,1],
.
/ \
1 .
/ \
2 .
/ \
3 ...... .
/ \
1 NIL
NIL is a special value signaling the empty list, such that the system knows not to try to explore it any further. In Scheme,
(define NIL '())
Recursive list processing paradigm is captured by the notion of fold, where each node . is "replaced" with a binary function f, and the special node NIL is replaced with some special "zero" value z, to create an application chain (f 1 (f 2 (f 3 (... (f 1 z) ...)))). In Scheme,
(define (myfold f z list)
(cond
((null? list) z) ; replace NIL with the initial ("zero") value
(else
(f ; combine
(car list) ; the payload datum, and the delayed,
(lambda () ; by creating a function to calculate it,
(myfold f z ; result of recursively folding
(cdr list))))))) ; the rest of list
That way, the combining function f must process two values: one is a node's payload datum, the other is the (delayed) result of recursively folding, with the same f and z, the rest of the list after that node.
(define (keep-equals v list)
(myfold
(lambda (a r) ; combine ...
(if (equal? v a)
(cons a ... ) ; the same thing goes over the dots, here
... )) ; and here
'() ; replace the NIL of the argument list with this
list))
Since the recursive folding results' calculation is delayed by creating a function to-be-called when the results are needed, we need to "force" that calculation to be performed, when we indeed need those results, by calling that function.
And if you want to count the number of occurrences instead of collecting them in a list, you just need to use a different combining function with a different initial ("zero") value.
In particular, we build a list by consing a value onto the rest of list (with NIL as the initial value, the empty list); whereas we count by incrementing a counter (with 0 as the initial value of that counter).
Calculating e.g. a list's length by folding, we essentially turn its elements each into 1: length [a,b,c,d,e] == 1 + (1 + (1 + (1 + (1 + 0)))). Here, the combining function will need to increment the counter conditionally, only when the payload data are such that we want to count them.
I like pretty well the answers already posted to this question. But it seems like they both involve a fair bit more than the necessary amount of work. On the other hand, given all the thought everyone's put into this, I'm almost embarrassed of how simple my answer is. Anyway, here's what I did:
(defun count-things-in (needle haystack)
"Count the number of NEEDLEs in HAYSTACK."
(reduce '+
(map 'list
#'(lambda (straw)
(if (equalp straw needle) 1 0))
haystack)))
(count-things-in 1 '(1 2 3 1 1))
;; => 3
It's pretty straightforward: you just map over HAYSTACK a function which returns 1 for an element which is EQUALP to NEEDLE or 0 for an element which isn't, and then reduce the resulting list by +. For the given example list, the map operation results in a list (1 0 0 1 1), which the reduce operation then treats as (1 + (0 + (0 + (1 + 1)))), which evaluates to 3.
Benefits of this approach include the use of an equality predicate loose enough to work with strings as well as numbers, and with numbers of different types but the same value -- that is, (equalp 1 1.0) => t; if you desire different behavior, use another equality predicate instead. Using the standard MAP and REDUCE functions, rather than implementing your own, also gives you the benefit of whatever optimizations your Lisp system may be able to apply.
Drawbacks include being not nearly as impressive as anyone else's implementation, and being probably not low-level enough to satisfy the requirements of the asker's homework problem -- not that that latter especially dismays me, given that this answer does satisfy the stated requirement.
I'm new to lisp myself but here is how I would do it. I haven't looked at the other answer yet from Will so I'll check that out after I post this. The member function has the utility of both telling you if it found something in a list, and also returning the rest of that list starting from where it found it:
CL-USER> (member '1 '(0 1 2 3))
(1 2 3)
You could then recursively call a function that uses member and increment a counter from returned values in a variable from a let:
(defun find1 (alist)
(let ((count 0))
(labels ((findit (list)
(let ((part (member '1 list)))
(if part
(progn (incf count)
(findit (rest part)))
0))
count))
(findit alist))))
Here is the result:
CL-USER> (find1 '(1 2 3 4 5))
1
CL-USER> (find1 '(1 1 2 3 4 5))
2
CL-USER> (find1 '(1 1 1 2 3 1 4 5 1 1))
6
You could get rid of that unattractive progn by using cond instead of if
UPDATE: Here is an updated and more elegant version of the above, based on the comments, that I think would qualify as tail recursive as well:
(defun find1 (alist &optional (accum 0))
(let ((part (member '1 alist)))
(if part
(find1 (rest part) (+ accum 1))
accum)))
Here it is in action:
CL-USER> (find1 '(1 2 3 4))
1
CL-USER> (find1 '(1 1 1 1))
4
CL-USER> (find1 '(1 1 0 1 1))
4
CL-USER> (find1 '(0 2 1 0 1 1 0 1 1))
5
I am trying define symbols a and b in following way
a + 1 1 b
2
I am trying to do this by using define-symbol-macro
(define-symbol-macro a '( )
(define-symbol-macro b ') )
but this way is not working.
What Lisp does with source code
Common Lisp is an incredibly flexible language, in part because its source code can be easily represented using the same data structures that are used in the language. The most common form of macro expansion transforms the these structures into other structures. These are the kind of macros that you can define with define-symbol-macro, define-compiler-macro, defmacro, and macrolet. Before any of those kind of macroexpansions can be performed, however, the system first needs to read the source from an input stream (typically a file, or an interactive prompt). That's the reader's responsibility. The reader also is capable of executing some special actions when it encounters certain characters, such ( and '. What you're trying to do probably needs to be happening down at the reader level, if you want to have, e.g., (read-from-string "a + 1 1 b") return the list (+ 1 1), which is what you want if you want (eval (read-from-string "a + 1 1 b")) to return 2. That said, you could also define a special custom language (like loop does) where a and b are treated specially.
Use set-macro-character, not define-symbol-macro
This isn't something that you would do using symbol-macros, but rather with macro characters. You can set macro characters using the aptly named set-macro-character. For instance, in the following, I set the macro character for % to be a function that reads a list, using read-delimited-list that should be terminated by ^. (Using the characters a and b here will prove very difficult, because you won't be able to write things like (set-macro-character ...) afterwards; it would be like writing (set-m(cro-ch(r(cter ...), which is not good.)
CL-USER> (set-macro-character #\% (lambda (stream ignore)
(declare (ignore ignore))
(read-delimited-list #\^ stream)))
T
CL-USER> % + 1 1 ^
2
The related set-syntax-from-char
There's a related function that almost does what you want here, set-syntax-from-char. You can use it to make one character behave like another. For instance, you can make % behave like (
CL-USER> (set-syntax-from-char #\% #\()
T
CL-USER> % + 1 1 )
2
However, since the macro character associated with ( isn't looking for a character that has the same syntax as ), but an actual ) character, you can't simply replace ) with ^ in the same way:
CL-USER> (set-syntax-from-char #\^ #\))
T
CL-USER> % + 1 1 ^
; Evaluation aborted on #<SB-INT:SIMPLE-READER-ERROR "unmatched close parenthesis" {1002C66031}>.
set-syntax-from-char is more useful when there's an existing character that, by itself does something that you want to imitate. For instance, if you wanted to make ! an additional quotation character:
CL-USER> (set-syntax-from-char #\! #\')
T
CL-USER> (list !a !(1 2 3))
(A (1 2 3))
or make % be a comment character, like it is in LaTeX:
CL-USER> (set-syntax-from-char #\% #\;)
T
CL-USER> (list 1 2 % 3 4
5 6)
(1 2 5 6)
But consider why you're doing this at all…
Now, even though you can do all of this, it seems like something that would be utterly surprising to anyone who ran into it. (Perhaps you're entering an obfuscated coding competition? ;)) For the reasons shown above, doing this with commonly used characters such as a and b will also make it very difficult to write any more source code. It's probably a better bet to define an entirely new readtable that does what you want, or even write a new parser. even though (Common) Lisp lets you redefine the language, there are still things that it probably makes sense to leave alone.
A symbol-macro is a symbol that stands for another form. Seems like you want to look at reader macros.
http://clhs.lisp.se/Body/f_set__1.htm
http://dorophone.blogspot.no/2008/03/common-lisp-reader-macros-simple.html
I would second Rainer's comment though, what are you trying to make?
Ok so I love your comment on the reason for this and now I know this is for 'Just because it's lisp' then I am totally on board!
Ok so you are right about lisp being great to use to make new languages because we only have to 'compile' to valid lisp code and it will run. So while we cant use the normal compiler to do the transformation of the symbols 'a and 'b to brackets we can write this ourselves.
Ok so lets get started!
(defun symbol-name-equal (a b)
(and (symbolp a) (symbolp b) (equal (symbol-name a) (symbol-name b))))
(defun find-matching-weird (start-pos open-symbol close-symbol code)
(unless (symbol-name-equal open-symbol (nth start-pos code))
(error "start-pos does not point to a weird open-symbol"))
(let ((nest-index 0))
(loop :for item :in (nthcdr start-pos code)
:for i :from start-pos :do
(cond ((symbol-name-equal item open-symbol) (incf nest-index 1))
((symbol-name-equal item close-symbol) (incf nest-index -1)))
(when (eql nest-index 0)
(return i))
:finally (return nil))))
(defun weird-forms (open-symbol close-symbol body)
(cond ((null body) nil)
((listp body)
(let ((open-pos (position open-symbol body :test #'symbol-name-equal)))
(if open-pos
(let ((close-pos (find-matching-weird open-pos open-symbol close-symbol body)))
(if close-pos
(weird-forms open-symbol close-symbol
`(,#(subseq body 0 open-pos)
(,#(subseq body (1+ open-pos) close-pos))
,#(subseq body (1+ close-pos))))
(error "unmatched weird brackets")))
(if (find close-symbol body :test #'symbol-name-equal)
(error "unmatched weird brackets")
(loop for item in body collect
(weird-forms open-symbol close-symbol item))))))
(t body)))
(defmacro with-weird-forms ((open-symbol close-symbol) &body body)
`(progn
,#(weird-forms open-symbol close-symbol body)))
So there are a few parts to this.
First we have (symbol-name-equal), this is a helper function because we are now using symbols and symbols belong to packages. symbol-name-equal gives us a way of checking if the symbols have the same name ignoring what package they reside in.
Second we have (find-matching-weird). This is a function that takes a list and and index to an opening weird bracket and returns the index to the closing weird bracket. This makes sure we get the correct bracket even with nesting
Next we have (weird-forms). This is the juicy bit and what it does is to recursively walk through the list passed as the 'body' argument and do the following:
If body is an empty list just return it
if body is a list then
find the positions of our open and close symbols.
if only one of them is found then we have unmatched brackets.
if we find both symbols then make a new list with the bit between the start and end positions inside a nested list.
we then call weird forms on this result in case there are more weird-symbol-forms inside.
there are no weird symbols then just loop over the items in the list and call weird-form on them to keep the search going.
OK so that function transforms a list. For example try:
(weird-forms 'a 'b '(1 2 3 a 4 5 b 6 7))
But we want this to be proper lisp code that executes so we need to use a simple macro.
(with-weird-forms) is a macro that takes calls the weird-forms function and puts the result into our source code to be compiled by lisp. So if we have this:
(with-weird-forms (a b)
(+ 1 2 3 a - a + 1 2 3 b 10 5 b 11 23))
Then it macroexpands into:
(PROGN (+ 1 2 3 (- (+ 1 2 3) 10 5) 11 23))
Which is totally valid lisp code, so it will run!
CL-USER> (with-weird-forms (a b)
(+ 1 2 3 a - a + 1 2 3 b 10 5 b 11 23))
31
Finally if you have settled on the 'a' and 'b' brackets you could write another little macro:
(defmacro ab-lang (&rest code)
`(with-weird-forms (a b) ,#code))
Now try this:
(ab-lang a let* a a d 1 b a e a * d 5 b b b a format t "this stupid test gives: ~a" e b b)
Cheers mate, this was great fun to write. Sorry for dismissing the problem earlier on.
This kind of coding is very important as ultimately this is a tiny compiler for our weird language where symbols can be punctuation. Compilers are awesome and no language makes it as effortless to write them as lisp does.
Peace!
I'm learning lisp and have a question about a simple list:
(setq stuff '(one two three (+ 2 2)))
stuff ; prints "one two three (+ 2 2)"
(setq stuff (list `one `two `three (+ 2 2)))
stuff ; prints "one two three 4"
The first setq creates a list "one two three (+ 2 2)". The second list creates "one two three 4". Why does the first list not evaluate the (+ 2 2), but the second one does? I read in the Emacs Lisp intro documentation that when the list is built that it evaluates from the inside out. Why doesn't the first list evaluate the addition before adding it to the list?
This is elisp in emacs 24.
' is not equivalent to list, it's shorthand for quote. You're really doing this:
(setq stuff (quote (one two three (+ 2 2))))
The argument to quote is the expression (one two three (+ 2 2)).
From http://www.gnu.org/software/emacs/manual/html_node/elisp/Quoting.html: "The special form quote returns its single argument, as written, without evaluating it".
Looks like you're coming to grips with the evaluation semantics of Lisp, so keep playing around!
You can think of quote as suppressing evaluation of its argument. This allows you to write expressions that you can manipulate or pass around. It is also used to write data structures that should not be evaluated as function calls.
Data structures:
'(1 2 3) ; => '(1 2 3)
(1 2 3) ; => Lisp error: (invalid-function 1)
;; The Lisp reader sees the number 1 in the function position and tries to call it, signalling an error.
Syntax transformations:
(setq x '(string-to-int "123"))
(setf (car x) 'string-to-list)
x ; => '(string-to-list "123")
Delayed evaluation:
(setq x '(message "Hello World")) ; => '(message "Hello World")
(eval x) ; => "Hello World"
There is a closely related special operator called syntax quote, written using the backtick. It allows you to evaluate individual forms in a quoted expression using the comma ( , ) operator. It is like quote with an escape hatch.
`(1 2 (+ 3 4)) ; => '(1 2 (+ 3 4))
`(1 2 ,(+ 3 4)) ; => '(1 2 7) ;; Note the comma!
Syntax quote also permits list splicing using the ,# syntax:
`(1 2 ,#(+ 3 4)) ; => '(1 2 + 3 4)
As you can see, it splices the subsequent expression into the containing one. You probably won't see it all that often until you start writing macros.
list on the other hand is a simple function. It evaluates its arguments, then returns a new data structure containing these items.
(list 1 2 (+ 3 4)) ; => '(1 2 7)
Why in lisp (Emacs Lisp and Scheme as I know) construction like (*) returns 1?
What I multiply here? How can I call this function * without arguments?
This is a mathematical convention: the product of an empty sequence of numbers is one, by definition; note that one is the identity element for multiplication (1×a = a×1 = a). This is convenient because you can call * with a variable number of arguments without worrying about the case where there are no arguments present.
Similarly, the sum of an empty sequence of numbers is zero, the identity element for addition. Try issuing (+) at your Lisp prompt.
It's a property inherited from mathematics. It's like addition, you can add together any number of numbers, with the special case that adding no numbers together give you the sum zero.
Likewise for multiplication, if you multiply an arbitrary number of numbers, you will get the product. To get this to work for no numbers, 1 is used as the base value (which has some fancy name in mathematics, which I have forgotten many years ago).
So, do you have any practical use for this in a programming language. Yes, as you can call a functions like + and * with arbitrary number of arguments, I would say yes. For example:
(apply '+ '(2 3 4)) => 9
(apply '+ '(2 3)) => 5
(apply '+ '(2)) => 2
(apply '+ '()) => 0
(apply '* '(2 3 4)) => 24
(apply '* '(2 3)) => 6
(apply '* '(2)) => 2
(apply '* '()) => 1