Typed lambda functions in Common Lisp - function

I don't know of any practical uses for this, it just came to my mind whether there is any thing comparable to defmethod to defun for lambda? Something like this
(defmacro tlambda (args &body body)
(let* ((gf-name (subseq (write-to-string (gensym)) 2))
(gf-sym (read-from-string gf-name)))
`(progn (defmethod ,gf-sym ,args ,#body)
(prog1 (symbol-function ',gf-sym) (unintern ',gf-sym)))))
(tlambda ((x fixnum))) ;#<STANDARD-GENERIC-FUNCTION #:G759 (1)>
(funcall (tlambda ((x fixnum)) (* x 2)) 4) ;8
(funcall (tlambda ((x list)) (second x)) '(a s d f)) ;S
(funcall (tlambda ((x string)) (string-upcase x)) "lambda") ;"LAMBDA"

I do not think that this makes sense in the shape you show. What should happen if the type doesn't match? If you just want to check types, use check-type.
Defmethod and defun are not really comparable, by the way. Defun registers a function, while defmethod adds a method to an existing (though maybe implicitly created) generic function. The types that you use in a method definition are used to dispatch (runtime polymorphism) to the right method upon invocation of the generic function. The mechanisms for this dispatch are a bit expensive when constructed, so you probably shouldn't try to do that on the fly (something like a generic-lambda) or transiently (something like a method-let).
Instead, use (e/c)typecase and similar for ad hoc dispatch, and check-type for checking types. There are also libraries for pattern-based polymorphism (e. g. optima, trivia), which you could use for more elaborate cases.

I agree with Svante that you probably don't want this. But if you did want it the way you are doing it is very confused: I simply don't understand what you are doing with gf-sym and gf-name but it represents some quite serious confusion about symbols I think (and is almost certainly unsafe). Instead you could do something like this:
(defmacro tlambda (&body cases)
(let* ((gf-name (gensym)))
`(progn
,#(mapcar (lambda (case)
`(defmethod ,gf-name ,#case))
cases)
(symbol-function ',gf-name))))
And now
> (let ((l (tlambda
((x y) (cons x y))
((x (y integer))
(declare (ignore x)) y))))
(values (funcall l 'a 'b)
(funcall l 'a 1)))
(a . b)
1
I'm not sure whether the objects created by tlambda can be garbage-collected: it may be they can.

Related

Feeding functions as parameters in Scheme

I am new to Scheme programming and working on an assignment. I have multiple functions with func3 sitting at the top and func1 feeding to func2 which then feeds into func3. For example I have something like this
(define func1
(lambda (a b)
(+ a b)))
(define func2
(lambda (x y)
(+ x y))) ;;; y is a function of above function1
I have created func3 as below
(define func3
(lambda (a b x)
func2 (x (func1 (a b)))))
Is there something that I doing grossly wrong or is it something simple? Let me know if any clarifications are needed. Thanks in advance for any help.
The way you're calling the procedures isn't right, this is how it should look like:
(define func3
(lambda (a b x)
(func2 x (func1 a b))))
As you can see, some of the parentheses in your code were misplaced. The key is to understand how to call a procedure, for example this was wrong:
func2(x ...) ; missing `(` at the left
This is also incorrect:
(func1 (a b)) ; don't surround parameters with `()`
The correct way is to surround each procedure call with () but not its parameters, unless they're procedure calls themselves. Like this:
(func1 a b)
(func2 x (func1 a b))

How to recreate apply in scheme

how would i create the function apply in scheme?
A my-apply function that does the same thing as it.
(define (my-apply fn lst)
(if (null? lst)
I'm not sure where to go from here or how to start.
I think apply is "more fundamental" than eval, so the following is cheating:
(define (my-apply func args)
(eval `(,func ,#args)))
I don't think you can do it without eval.
I created a lisp interpreter a while back and it has eval and macros, but it didn't have apply. I wondered if there was a way I could make my interpreter support apply so made an effort to try this. Here is my first attempt:
(define (my-apply proc args)
(eval (cons proc args)))
This clearly doesn't work since the function and the list of arguments gets evaluated twice. eg. (my-apply cons '(a b)) will give you (cons a b) and not (cons 'a 'b). I then thought that this might be a job for a macro but threw the idea away since the list of arguments are not known at macro expansion time. Procedure it needs to be so I though I could quote the list before I pass it to eval.
(define (my-apply proc args)
(define (q v)
(list 'quote v))
(eval (cons proc (map q args))))
This actually works, but this does a lot more work than a native apply would do to undo the job eval does.
If you are not allowed to use eval you are truely out of luck. It cannot be done. The same goes for implementing eval without using apply since then you have no way of doing primitives.
(define (my-two-arg-apply f a)
(let ((l (length a)))
(cond ((= l 0) (f))
((= l 1) (f (car a)))
((= l 2) (f (car a) (cadr a))
...
((= l 5) (f (car a) (cadr a) ... (caddddr a)))
...
((= l 7) (f (car a) (cadr a) ... (caddddr a)
(list-ref a 5) (list-ref a 6)))
... ;; lots more cases
(else (error "argument passing limit exceeded")))))
A macro could be used to generate the large quantity of code needed.
error was introduced in R6RS. Amazingly, Scheme programs had no reasonable way to report errors before that.
Don't even think about making a pop macro and using the pattern (f (pop a) (pop a) ... (pop a)); Scheme doesn't have a defined evaluation order for function arguments unlike some other Lisp dialects like ANSI CL.

"Smart" comparison of functions in Racket

I've got a bit exotic situation. I need to compare functions, but rather by their "origin" than by "instances". Here what I actually mean:
(define-values (a b c d) (values #f #f #f #f))
(define (f x)
(let ([g (λ (y) (printf "Please tell ~a this is ~a\n" x y))]
[h (curry printf "Don't tell ~a this is ~a\n" x)])
(if a
(set! b g)
(set! a g))
(if c
(set! d h)
(set! c h))))
(f "me")
(f " me")
(a "possible")
(d "impossible")
(equal? a b) ; <==== Is it possible to compare these guys
(equal? c d) ; <==== to get #t in both cases?
In both cases we get two different "instances" of functions (even with different values captured), but both declared in the same location of the source code. Of course, getting the actual text of the body of those functions will solve the problem, but other answers here on SO tell that this is impossible in Racket. Are there some tricks that can help me?
Edit:
This is not the question on theoretical equivalence of functions. This is completely technical question, much rather on Racket's functions representation in a compiled code. So it can be reformulated, for example, in a following way: can I get the line number of some routine from 'user' code? I suppose this should be feasible because Racket debugger somehow obtains it.
It can be done even without support from racket internals if you control the code that makes the functions. If you keep a counter (or some identifier) that will denote the particular lambda it can wrap different closures in a struct that can have the same identity from macro expansion. Here is a demonstration:
#lang racket
;; makes a procedure object that can have other data connected to it
(struct proc (id obj)
#:property prop:procedure
(struct-field-index obj)
#:methods gen:custom-write
[(define (write-proc x port mode)
(display (format "#<procedure-id-~a>" (proc-id x)) port))])
;; compares the ids of two proc objects if they are proc objects
(define (proc-equal? a b)
(and (proc? a)
(proc? b)
(= (proc-id a) (proc-id b))))
;; extends equal?, candidate to provide
(define (equal*? a b)
(or (proc-equal? a b)
(equal? a b)))
;; the state we keep
(begin-for-syntax
(define unique-proc-id-per-code 0))
;; a macro that changes (lambda* ...) to
;; (proc expansion-id (lambda ...))
(define-syntax (lambda* stx)
(let ((proc-id unique-proc-id-per-code))
(set! unique-proc-id-per-code (add1 unique-proc-id-per-code))
#`(proc #,(datum->syntax stx proc-id) (lambda #,#(datum->syntax stx (cdr (syntax-e stx)))))))
;; test with making a counter
(define counter-from
(lambda* (from)
(lambda* ()
(begin0
from
(set! from (add1 from))))))
;; evaluatin the outer shows it has id 0
counter-from ; ==> #<procedure-id-0>
;; make two counters that both use the inner lambda
(define from10 (counter-from 10))
(define from20 (counter-from 20))
;; both have the same expansion id
from10 ; ==> #<procedure-id-1>
from20 ; ==> #<procedure-id-1>
;; they are not equal?
(equal? from10 from20) ; ==> #f (different object instances of proc)
;; but they are procedure-equal?
(proc-equal? from10 from20) ; ==> #t (same id, thus came from same macroexpansion)
Disclaimer: I'm more a schemer than a racketeer so this could perhaps have been done more elegantly and I have no idea what performance penalties this will give.

"Adding" two functions together in Scheme

I am going through a practice exam for my programming languages course. One of the problems states:
Define a function named function+ that “adds” two functions together and returns this composition. For example:
((function+ cube double) 3)
should evaluate to 216, assuming reasonable implementations of the functions cube and double.
I am not sure how to approach this problem. I believe you are supposed to use the functionality of lambdas, but I am not entirely sure.
If you need a procedure which allows you two compose to unary procedures (procedure with only 1 parameter), you'll smack yourself in the head after seeing how simple the implementation is
(define (function+ f g)
(λ (x) (f (g x))))
(define (cube x)
(* x x x))
(define (double x)
(+ x x))
((function+ cube double) 3)
;=> 216
Basically if you need to do that you just do (x (y args ...)) so if you need to have a procedure that takes two arguments proc1 and proc2 returns a lambda that takes any number of arguments. You just use apply to give proc1 arguments as a list and pass the result to proc2. It would look something like this:
(define (compose-two proc2 proc1)
(lambda args
...))
The general compose is slightly more complicated as it takes any number of arguments:
#!r6rs
(import (rnrs))
(define my-compose
(let* ((apply-1
(lambda (proc value)
(proc value)))
(gen
(lambda (procs)
(let ((initial (car procs))
(additional (cdr procs)))
(lambda args
(fold-left apply-1
(apply initial args)
additional))))))
(lambda procs
(cond ((null? procs) values)
((null? (cdr procs)) (car procs))
(else (gen (reverse procs)))))))
(define (add1 x) (+ x 1))
((my-compose) 1) ;==> 1
((my-compose +) 1 2 3) ; ==> 6
((my-compose sqrt add1 +) 9 15) ; ==> 5

Standard function for replacing subsequences

Quite often I need to replace subsequence of certain elements with another sequence of the same type, but, probably with different length. Implementation of such function is no challenge, this is what I use now:
(defun substitute* (new old where &key key (test #'eql))
(funcall (alambda (rest)
(aif (search old rest :key key :test test)
(concatenate (etypecase rest
(string 'string)
(vector 'vector)
(list 'list))
(subseq rest 0 it)
new
(self (subseq rest (+ it (length old)))))
rest))
where))
Works like this:
CL-USER> (substitute* '(x y) '(z) '(1 z 5 8 y z))
(1 X Y 5 8 Y X Y)
CL-USER> (substitute* "green button" "red button"
"here are red indicator, red button and red wire")
"here are red indicator, green button and red wire"
CL-USER> (substitute* #(4) #(2 2) #(2 2 2 2 2))
#(4 4 2)
You see, it's very handy and useful, so I've feeling that I'm reinventing wheel and it must be in the standard library, I just don't know its name (sometimes names are not obvious, you may search for filter while what you need is set-difference).
As a result of compromise between clarity and efficiency:
(defun substitute* (new old where &key key (test #'eql))
(let ((type (etypecase where
(string 'string)
(vector 'vector)
(list 'list)))
(new (coerce new 'list))
(old (coerce old 'list))
(where (coerce where 'list)))
(coerce (funcall (alambda (rest)
(aif (search old rest :key key :test test)
(append (remove-if (constantly t) rest :start it)
new
(self (nthcdr (+ it (length old)) rest)))
rest))
where)
type)))
I don't think that there's any standard function for this. It's more complicated than the standard replace family of functions. Those can operate destructively because you know in advance that you can replace element by element. Even in that case, it's still somewhat difficult to do this efficiently, because the access time for lists and vectors is very different, so general-purpose functions like subseq can be problematic. As Rainer Joswig pointed out in a comment:
It's kind of unfortunate that for many algorithms over sequences there
is no single efficient implementation. I see often that there are two
versions, one for lists and one for vectors, which then get hidden
behind a dispatching function. For a hack a simple common version is
fine, but for a library function, often there are different
implementations - like shown here.
(In fact, in doing a bit of research on whether some library contains a function for this, one of the first Google results I got was a question on Code Review, Generic sequence splitter in Common Lisp, in which Rainer and I both had some comment similar to those here.)
A version for lists
However, your implementation is rather inefficient because it makes multiple copies of the the remainders of sequences. E.g., when you replace (z) in (1 z 2 z 3 z), with (x y), you'll first make (3 x y), then copy it in making (2 x y 3 z y), and then you'll copy that in making (1 x y 2 x y 3 x y). You might be better off in doing one pass over the sequence, determining the indices of the subsequences to replace, or collecting the bits that need to don't need to be replaced, etc. You'll probably want separate implementations for lists and for other sequences. E.g., with a list, you might do:
(defun splice-replace-list (old new list)
(do ((new (coerce new 'list))
(old-len (length old))
(parts '()))
((endp list)
(reduce 'append (nreverse parts) :from-end t))
(let ((pos (search old list)))
(push (subseq list 0 pos) parts)
(cond
((null pos)
(setf list nil))
(t
(push new parts)
(setf list (nthcdr (+ old-len pos) list)))))))
There are some optimizations you could make here, if you wanted. For instance, you could implement a search-list that, rather than returning the position of the first instance of the sought sequence, could return a copy of the head up until that point and the tail beginning with the sequence as multiple values, or even the copied head, and the tail after the sequence, since that's what you're really interested in, in this case. Additionally, you could do something a bit more efficient than (reduce 'append (nreverse parts) :from-end t) by not reversing parts, but using a reversed append. E.g.,
(flet ((xappend (l2 l1)
(append l1 l2)))
(reduce #'xappend '((5 6) (x y) (3 4) (x y))))
;=> (x y 3 4 x y 5 6)
I wrote this in a somewhat imperative style, but there's no reason that you can't use a functional style if you want. Be warned that not all Lisp implementation support tail call optimization, so it might be better to use do, but you certainly don't have to. Here's a more functional version:
(defun splice-replace-list (old new list)
(let ((new-list (coerce new 'list))
(old-len (length old)))
(labels ((keep-going (list parts)
(if (endp list)
(reduce 'append (nreverse parts) :from-end t)
(let* ((pos (search old list))
(parts (list* (subseq list 0 pos) parts)))
(if (null pos)
(keep-going '() parts)
(keep-going (nthcdr (+ old-len pos) list)
(list* new-list parts)))))))
(keep-going list '()))))
A version for vectors
For non lists, this is more difficult, because you don't have the specific sequence type that you're supposed to be using for the result. This is why functions like concatenate require a result-type argument. You can use array-element-type to get an element type for the input sequence, and then use make-array to get a sequence big enough to hold the result. That's trickier code, and will be more complicated. E.g., here's a first attempt. It's more complicated, but you'll get a result that's pretty close to the original vector type:
(defun splice-replace-vector (old new vector &aux (new-len (length new)))
(flet ((assemble-result (length parts)
(let ((result (make-array length :element-type (array-element-type vector)))
(start 0))
(dolist (part parts result)
(cond
((consp part)
(destructuring-bind (begin . end) part
(replace result vector :start1 start :start2 begin :end2 end)
(incf start (- end begin))))
(t
(replace result new :start1 start)
(incf start new-len)))))))
(do ((old-len (length old))
(total-len 0)
(start 0)
(indices '()))
((null start) (assemble-result total-len (nreverse indices)))
(let ((pos (search old vector :start2 start)))
(cond
((null pos)
(let ((vlength (length vector)))
(push (cons start vlength) indices)
(incf total-len (- vlength start))
(setf start nil)))
(t
(push (cons start pos) indices)
(push t indices)
(incf total-len (- pos start))
(incf total-len new-len)
(setf start (+ pos old-len))))))))
CL-USER> (splice-replace-vector '(#\z) '(#\x #\y) "12z")
"12xy"
CL-USER> (splice-replace-vector '(z) '(x y) #(x y))
#(X Y)
CL-USER> (splice-replace-vector '(z) '(x y) #(1 z 2 z 3 4 z))
#(1 X Y 2 X Y 3 4 X Y)
CL-USER> (splice-replace-vector '(#\z) #(#\x #\y) "1z2z34z")
"1xy2xy34xy"
If you only want to make one pass through the input vector, then you could use an adjustable array as the output, and append to it. An adjustable array will have a bit more overhead than a fixed size array, but it does make the code a bit simpler.
(defun splice-replace-vector (old new vector)
(do ((vlength (length vector))
(vnew (coerce new 'vector))
(nlength (length new))
(result (make-array 0
:element-type (array-element-type vector)
:adjustable t
:fill-pointer 0))
(start 0))
((eql start vlength) result)
(let ((pos (search old vector :start2 start)))
(cond
;; add the remaining elements in vector to result
((null pos)
(do () ((eql start vlength))
(vector-push-extend (aref vector start) result)
(incf start)))
;; add the elements between start and pos to the result,
;; add a copy of new to result, and increment start
;; accordingly
(t
;; the copying here could be improved with adjust-array,
;; and replace, instead of repeated calls to vector-push-extend
(do () ((eql start pos))
(vector-push-extend (aref vector start) result)
(incf start))
(loop for x across vnew
do (vector-push-extend x result))
(incf start (1- nlength)))))))
A “generic” version
Using these two functions, you could define a general splice-replace that checks the type of the original input sequence and calls the appropriate function:
(defun splice-replace (old new sequence)
(etypecase sequence
(list (splice-replace-list old new sequence))
(vector (splice-replace-vector old new sequence))))
CL-USER> (splice-replace #(z) '(x y) #(1 z 2 z 3 4 z))
#(1 X Y 2 X Y 3 4 X Y)
CL-USER> (splice-replace '(z) #(x y) '(1 z 2 z 3 4 z))
(1 X Y 2 X Y 3 4 X Y)