Rest argument , zero or one argument procedures in racket - rest

I have this procedure:
(define count-calls
(let ((count 0))
(lambda char
(cond ((null? char)
(begin(set! count (+ 1 count))
count))
((eq? char 'how-many-calls) count)
((eq? char 'reset) (set! count 0))))))
It does add 1 when (count-calls) is called but when I call (count-calls 'how-many-calls) it doesn't work as intended. I found that if you define (lambda (char) instead of (lambda char the (eq? ...) part is found but for (lambda char) it doesn't seem to recognize char.

If you dont have parentheses around the lambda parameters then you get all the arguments in a list. So your code is comparing 'how-many-calls to a list.
Welcome to DrRacket, version 5.3.3.5 [3m].
Language: racket [custom]; memory limit: 8192 MB.
> ((lambda args (displayln args)) "a")
(a)
> ((lambda args (displayln args)) "a" "b")
(a b)
> ((lambda (args) (displayln args)) "a")
a
> ((lambda (args) (displayln args)) "a" "b")
#<procedure>: arity mismatch;
the expected number of arguments does not match the given number
expected: 1
given: 2
arguments...:
"a"
"b"

You have a couple of coding errors, this should fix them:
(define count-calls
(let ((count 0))
(lambda char
(cond ((null? char)
(set! count (+ 1 count))
count)
((eq? (car char) 'how-many-calls)
count)
((eq? (car char) 'reset)
(set! count 0))))))
In particular, notice that:
If a lambda's parameters are not surrounded by parenthesis (as is the case with char), then the procedure expects a list of arguments with variable size, possibly empty
With that in mind, it's clear why you need to do (car char) for extracting a parameter, if it was provided
It's not necessary to use a begin after a condition in cond, it's implicit
Use the procedure like this:
(count-calls)
=> 1
(count-calls 'how-many-calls)
=> 1
(count-calls 'reset)
=>
(count-calls 'how-many-calls)
=> 0

Extending stchang's answer, here's one way to solve this:
(define count-calls
(let ((count 0))
(case-lambda
(() (set! count (+ 1 count)) count)
((char) (cond
((eq? char 'how-many-calls) count)
((eq? char 'reset ) (set! count 0) 'reset)
(else 'wot?))))))

Related

How to modify list inside a function

(defun list-parser (list count)
...);;this function reads items by count from list and do some process to them.
;;i.e.convert items read from code to char, or to other things and then return it.
;;Also, the items in list should be consumed, globally.
(defmethod foo ((obj objtype-2) data-list)
(setf (slot-1 obj) (read-list data-list 1))
obj)
(defmethod foo ((obj objtype-1) data-list)
(setf (slot-1 obj) (read-list data-list 1)
(print data-list)
(slot-2 obj) (read-list data-list 2)
(print data-list)
(slot-3 obj) (foo (make-instance 'objtype-2) data-list)
(print data-list)
(slot-4 obj) (read-list data-list 3))
obj)
How to let it work like this:(read-list just works like read-byte in some way:
1.return a value read(and parsed here)
2.change the stream position(here the list)).
(let ((obj)
(data))
(setf data '(1 2 3 4 5 6 7 8)
obj (foo (make-instance 'objtype-1) data))
(print data))
>>(2 3 4 5 6 7 8)
>>(4 5 6 7 8)
>>(5 6 7 8)
>>(8)
Or rather, how do you deal with this kind of task? Do you convert list to other type?
I am not quite sure what you are after, but here is a function which creates a 'list reader' object (just a function). A list reader will let you read chunks of a list, treating it a bit like a stream.
(defun make-list-reader (l)
;; Make a list reader which, when called, returns three values: a
;; chunk of list, the length of tha chunk (which may be less than
;; how much was asked for) and the remaining length. The chunk is
;; allowed to share with L
(let ((lt l)
(len (length l)))
(lambda (&optional (n 1))
(cond
((zerop len)
(values nil 0 0))
((< len n)
(values lt len 0))
(t
(let ((it (subseq lt 0 n)))
(setf lt (nthcdr n lt)
len (- len n))
(values it n len)))))))
(defun read-from-list-reader (r &optional (n 1))
;; Read from a list reader (see above for values)
(funcall r n))
And now:
(defvar *l* (make-list-reader '(1 2 3)))
*l*
> (read-from-list-reader *l* 1)
(1)
1
2
> (read-from-list-reader *l* 2)
(2 3)
2
0
> (read-from-list-reader *l* 10)
nil
0
0
What you can't really do is write a function (not actually a function of course since it modifies its argument) which works like this while modifying its argument list. So you can write a function which will do this:
> (let ((l (list 1 2)))
(values (read-from-list l)
l))
(1)
(2)
which works by modifying the car and cdr of the first cons of l as you'd expect. But this can't work when there is no more to read: l is a cons and nil isn't a cons, so you can't ever make l nil with a function.
But in any case such a function is just a mass of traps for the unwary and generally horrid: for instance your example would involve modifying a literal, which isn't legal.

Simplify symbolic expressions

I am new in Lisp and i need some help.
I need to simplify next expressions:
from (+ (+ A B) C) to (+ A B C)
and from (- (- A B) C) to (- A B C).
If you could help me with one of them I'll understand how i need to do this to the next one.
Thanks a lot.
Assuming you have an input that matches this pattern, (+ e1 ... en), you want to recursively simplify all e1 to en, which gives you s1, ..., sn, and then extract all the si that start with a + to move their arguments one level up, to the simplified expression you are building.
An expression e matches the above pattern if (and (consp e) (eq '+ (car e))).
Then, all the ei are just given by the list that is (cdr e).
Consider the (+) case, how could you simplify it?
To apply a function f to a list of values, call (mapcar #'f list).
To split a list into two lists, based on a predicate p, you might use a loop:
(let ((sat nil) (unsat nil))
(dolist (x list (values sat unsat))
(if (funcall predicate x)
(push x sat)
(push x unsat))))
There is a purely functional way to write this, can you figure it out?
Here is a trivial simplifier written in Racket, with an implementation of a rather mindless simplifier for +. Note that this is not intended as anything serious: it's just what I typed in when I was thinking about this question.
This uses Racket's pattern matching, probably in a naïve way, to do some of the work.
(define/match (simplify expression)
;; simplifier driver
(((cons op args))
;; An operator with some arguments
;; Note that this assumes that the arguments to operators are always
;; expressions to simplify, so the recursive level can be here
(simplify-op op (map simplify args)))
((expr)
;; anything else
expr))
(define op-table (make-hash))
(define-syntax-rule (define-op-simplifier (op args) form ...)
;; Define a simplifier for op with arguments args
(hash-set! op-table 'op (λ (args) form ...)))
(define (simplify-op op args)
;; Note the slightly arcane fallback: you need to wrap it in a thunk
;; so hash-ref does not try to call it.
((hash-ref op-table op (thunk (λ (args) (cons op args)))) args))
(define-op-simplifier (+ exprs)
;; Simplify (+ ...) by flattening + in its arguments
(let loop ([ftail exprs]
[results '()])
(if (null? ftail)
`(+ ,#(reverse results))
(loop (rest ftail)
(match (first ftail)
[(cons '+ addends)
(append (reverse addends) results)]
[expr (cons expr results)])))))
It is possible to be more aggressive than this. For instance we can coalesce runs of literal numbers, so we can simplify (+ 1 2 3 a 4) to
(+ 6 a 4) (note it is not safe in general to further simplify this to (+ 10 a) unless all arithmetic is exact). Here is a function which does this coalescing for for + and *:
(define (coalesce-literal-numbers f elts)
;; coalesce runs of literal numbers for an operator f.
;; This relies on the fact that (f) returns a good identity for f
;; (so in particular it returns an exact number). Thisis true for Racket
;; and CL and I think any Lisp worth its salt.
;;
;; Note that it's important here that (eqv? 1 1.0) is false.
;;;
(define id (f))
(let loop ([tail elts]
[accum id]
[results '()])
(cond [(null? tail)
(if (not (eqv? accum id))
(reverse (cons accum results))
(reverse results))]
[(number? (first tail))
(loop (rest tail)
(f accum (first tail))
results)]
[(eqv? accum id)
(loop (rest tail)
accum
(cons (first tail) results))]
[else
(loop (rest tail)
id
(list* (first tail) accum results))])))
And here is a modified simplifier for + which uses this. As well as coalescing it notices that (+ x) can be simplified to x.
(define-op-simplifier (+ exprs)
;; Simplify (+ ...) by flattening + in its arguments
(let loop ([ftail exprs]
[results '()])
(if (null? ftail)
(let ([coalesced (coalesce-literal-numbers + (reverse results))])
(match coalesced
[(list something)
something]
[exprs
`(+ ,#exprs)]))
(loop (rest ftail)
(match (first ftail)
[(cons '+ addends)
(append (reverse addends) results)]
[expr (cons expr results)])))))
Here is an example of using this enhanced simplifier:
> (simplify 'a)
'a
> (simplify 1)
1
> (simplify '(+ 1 a))
'(+ 1 a)
> (simplify '(+ a (+ b c)))
'(+ a b c)
> (simplify '(+ 1 (+ 3 c) 4))
'(+ 4 c 4)
> (simplify '(+ 1 2 3))
6
For yet more value you can notice that the simplifier for * is really the same, and change things to this:
(define (simplify-arith-op op fn exprs)
(let loop ([ftail exprs]
[results '()])
(if (null? ftail)
(let ([coalesced (coalesce-literal-numbers fn (reverse results))])
(match coalesced
[(list something)
something]
['()
(fn)]
[exprs
`(,op ,#exprs)]))
(loop (rest ftail)
(match (first ftail)
[(cons the-op addends)
#:when (eqv? the-op op)
(append (reverse addends) results)]
[expr (cons expr results)])))))
(define-op-simplifier (+ exprs)
(simplify-arith-op '+ + exprs))
(define-op-simplifier (* exprs)
(simplify-arith-op '* * exprs))
And now
(simplify '(+ a (* 1 2 (+ 4 5)) (* 3 4) 6 (* b)))
'(+ a 36 b)
Which is reasonably neat.
You can go further than this, For instance when coalescing numbers for an operator you can simply elide sequences of the identity for that operator: (* 1 1 a 1 1 b) can be simplified to (* a b), not (* 1 a 1 b). It may seem silly to do that: who would ever write such an expression, but they can quite easily occur when simplifying complicated expressions.
There is a gist of an elaborated version of this code. It may still be buggy.

How to double a list using tail recursive?

(define (lst-double-helper lst acc)
(if (empty? list)
acc
(lst-double-helper (rest lst) (cons (* (first lst) 2) acc))))
(define (lst-double lst)
(lst-double-helper lst '()))
I feel I'm doing it in the right way. But this gives me an error
(lst-double '(1,2,3))
*: contract violation
expected: number?
given: ',2
argument position: 1st
other arguments...:
Why do it expect the second argument to be a number?
A couple of comments:
List elements are separated by spaces, not commas. That's the error being reported.
The base case of the recursion must refer to the parameter lst, not to list.
Your tail-recursive solution reverses the list, an extra reverse is needed at the end to restore the original order
With the above changes in place, it works as expected:
(define (lst-double-helper lst acc)
(if (empty? lst) ; parameter is called `lst`
acc
(lst-double-helper (rest lst) (cons (* (first lst) 2) acc))))
(define (lst-double lst)
(reverse ; required to restore original order
(lst-double-helper lst '())))
(lst-double '(1 2 3)) ; use spaces to separate elements
=> '(2 4 6)
Be aware that a tail-recursive solution that traverses an input list and conses its elements to build an output list, will necessarily reverse the order of the elements in the input list. This is ok, and it's normal to do a reverse at the end. Possible alternatives to avoid reversing the elements at the end would be to reverse the input list at the beginning or to write a non-tail-recusive solution.
One such way is by using continuation-passing style. Here we add a parameter named return which effectively encodes a return-like behavior with a lambda. double now takes two arguments: the list to double, xs, and the continuation of the result, return –
(define (double xs return)
(if (empty? xs)
(return empty)
(double (cdr xs)
(lambda (result)
(return (cons (* 2 (car xs))
result))))))
As an example, the result of double applied to a list of '(1 2 3) is sent to print
(double '(1 2 3) print)
;; '(2 4 6)
;; => #<void>
double evaluates to whatever the final continuation evaluates to; in this case, print evaluates to #<void>. We can use the identity function to effectively get the value out –
(double '(1 2 3) identity)
;; => '(2 4 6)
Racket allows you to easily specify default arguments, so we can modify double to use identity as the default continuation
(define (double xs (return identity))
;; ...
)
This style results in convenient programs that work in two call styles at simultaneously: continuation-passing style –
(double '(10 11 12) print)
;; '(20 22 24)
;; => #<void>
(double '(10 11 12) length)
;; => 3
(double '(10 11 12) car)
;; => 20
(double '(10 11 12) cdr)
;; => '(22 24)
... or in direct style, using the default identity continuation
(print (double '(10 11 12)))
;; '(20 22 24)
(length (double '(10 11 12)))
;; => 3
(car (double '(10 11 12)))
;; => 20
(cdr (double '(10 11 12)))
;; => '(22 24)
use map.
(map (lambda (a) (* a 2)) '(1 2 3))
For nested lists:
(define (atom? x)
(and (not (null? x))
(not (pair? x))))
(define (lst-double-helper lst acc)
(cond ((empty? lst) acc)
((atom? (car lst)) (lst-double-helper (rest lst) (cons (* (first lst) 2) acc)))
(else (lst-double-helper (rest lst) (cons (lst-double (first lst))
acc) ))))
(define (lst-double lst)
(reverse ; required to restore original order
(lst-double-helper lst '())))
but actually to make this function tail-recursive is a little bit meaningless,
because as #simmone mentioned, map would do it
(define (list-doubler lst)
(map (lambda (x) (* 2 x)) lst))
(list-doubler '(1 2 3))
;; '(2 4 6)

Trying to rewrite an ugly macro

I'm new to lisp, and have been trying to learn Common Lisp by diving in and writing some code. I've read plenty of documentation on the subject, but it's taking a while to really sink in.
I have written a couple of macros (? and ??) for performing unit tests, but I'm having some difficulty. The code is at the end of the post, to avoid cluttering the actual question.
Here is an example of usage:
(??
(? "Arithmetic tests"
(? "Addition"
(= (+ 1 2) 3)
(= (+ 1 2 3) 6)
(= (+ -1 -3) -4))))
And an example of output:
[Arithmetic tests]
[Addition]
(PASS) '(= (+ 1 2) 3)'
(PASS) '(= (+ 1 2 3) 6)'
(PASS) '(= (+ -1 -3) -4)'
Results: 3 tests passed, 0 tests failed
Now, the existing code works. Unfortunately, the (? ...) macro is ugly, verbose, resistant to change - and I'm pretty sure also badly structured. For example, do I really have to use a list to store pieces of output code and then emit the contents at the end?
I'd like to modify the macro to permit description strings (or symbols) to optionally follow each test, whereupon it would replace the test literal in the output, thus:
(??
(? "Arithmetic tests"
(? "Addition"
(= (+ 1 2) 3) "Adding 1 and 2 results in 3"
(= (+ 1 2 3) 6)
(= (+ -1 -3) -4))))
Output:
[Arithmetic tests]
[Addition]
(PASS) Adding 1 and 2 results in 3
(PASS) '(= (+ 1 2 3) 6)'
(PASS) '(= (+ -1 -3) -4)'
But unfortunately I can't find a sensible place in the macro to insert this change. Depending on where I put it, I get errors like you're not inside a backquote expression, label is not defined or body-forms is not defined. I know what these errors mean, but I can't find a way to avoid them.
Also, I'll be wanting to handle exceptions in the test, and treat that as a failure. Currently, there is no exception handling code - the test result is merely tested against nil. Again, it is not clear how I should add this functionality.
I'm thinking that maybe this macro is over-complex, due to my inexperience in writing macros; and perhaps if I simplify it, modification will be easier. I don't really want to separate it out into several smaller macros without good reason; but maybe there's a terser way to write it?
Can anyone help me out here, please?
A complete code listing follows:
(defmacro with-gensyms ((&rest names) &body body)
`(let ,(loop for n in names collect `(,n (gensym)))
,#body))
(defmacro while (condition &body body)
`(loop while ,condition do (progn ,#body)))
(defun flatten (L)
"Converts a list to single level."
(if (null L)
nil
(if (atom (first L))
(cons (first L) (flatten (rest L)))
(append (flatten (first L)) (flatten (rest L))))))
(defun starts-with-p (str1 str2)
"Determine whether `str1` starts with `str2`"
(let ((p (search str2 str1)))
(and p (= 0 p))))
(defmacro pop-first-char (string)
`(with-gensyms (c)
(if (> (length ,string) 0)
(progn
(setf c (schar ,string 0))
(if (> (length ,string) 1)
(setf ,string (subseq ,string 1))
(setf ,string ""))))
c))
(defmacro pop-chars (string count)
`(with-gensyms (result)
(setf result ())
(dotimes (index ,count)
(push (pop-first-char ,string) result))
result))
(defun format-ansi-codes (text)
(let ((result ()))
(while (> (length text) 0)
(cond
((starts-with-p text "\\e")
(push (code-char #o33) result)
(pop-chars text 2)
)
((starts-with-p text "\\r")
(push (code-char 13) result)
(pop-chars text 2)
)
(t (push (pop-first-char text) result))
))
(setf result (nreverse result))
(coerce result 'string)))
(defun kv-lookup (values key)
"Like getf, but works with 'keys as well as :keys, in both the list and the supplied key"
(setf key (if (typep key 'cons) (nth 1 key) key))
(while values
(let ((k (pop values)) (v (pop values)))
(setf k (if (typep k 'cons) (nth 1 k) k))
(if (eql (symbol-name key) (symbol-name k))
(return v)))))
(defun make-ansi-escape (ansi-name)
(let ((ansi-codes '( :normal "\\e[00m" :white "\\e[1;37m" :light-grey "\\e[0;37m" :dark-grey "\\e[1;30m"
:red "\\e[0;31m" :light-red "\\e[1;31m" :green "\\e[0;32m" :blue "\\e[1;34m" :dark-blue "\\e[1;34m"
:cyan "\\e[1;36m" :magenta "\\e[1;35m" :yellow "\\e[0;33m"
:bg-dark-grey "\\e[100m"
:bold "\\e[1m" :underline "\\e[4m"
:start-of-line "\\r" :clear-line "\\e[2K" :move-up "\\e[1A")))
(format-ansi-codes (kv-lookup ansi-codes ansi-name))
))
(defun format-ansi-escaped-arg (out-stream arg)
(cond
((typep arg 'symbol) (format out-stream "~a" (make-ansi-escape arg)))
((typep arg 'string) (format out-stream arg))
(t (format out-stream "~a" arg))
))
(defun format-ansi-escaped (out-stream &rest args)
(while args
(let ((arg (pop args)))
(if (typep arg 'list)
(let ((first-arg (eval (first arg))))
(format out-stream first-arg (second arg))
)
(format-ansi-escaped-arg out-stream arg)
))
))
(defmacro while-pop ((var sequence &optional result-form) &rest forms)
(with-gensyms (seq)
`(let (,var)
(progn
(do () ((not ,sequence))
(setf ,var (pop ,sequence))
(progn ,#forms))
,result-form))))
(defun report-start (form)
(format t "( ) '~a'~%" form))
(defun report-result (result form)
(format-ansi-escaped t "(" (if result :green :red) `("~:[FAIL~;PASS~]" ,result) :normal `(") '~a'~%" ,form))
result)
(defmacro ? (name &body body-forms)
"Run any number of test forms, optionally nested within further (?) calls, and print the results of each test"
(with-gensyms (result indent indent-string)
(if (not body-forms)
:empty
(progn
(setf result () indent 0 indent-string " ")
(cond
((typep (first body-forms) 'integer)
(setf indent (pop body-forms))))
`(progn
(format t "~v#{~A~:*~}" ,indent ,indent-string)
(format-ansi-escaped t "[" :white ,name :normal "]~%")
(with-gensyms (test-results)
(setf test-results ())
,(while-pop (body-form body-forms `(progn ,#(nreverse result)))
(cond
( (EQL (first body-form) '?)
(push `(progn
(setf test-results (append test-results (? ',(nth 1 body-form) ,(1+ indent) ,#(nthcdr 2 body-form))))
(format t "~%")
test-results
) result)
)
(t
(push `(progn
(format t "~v#{~A~:*~}" ,(1+ indent) ,indent-string)
(report-start ',body-form)
(with-gensyms (result label)
(setf result ,body-form)
(format-ansi-escaped t :move-up :start-of-line :clear-line)
(format t "~v#{~A~:*~}" ,(1+ indent) ,indent-string)
(push (report-result result ',body-form) test-results)
test-results
)) result))))))))))
(defun ?? (&rest results)
"Run any number of tests, and print a summary afterward"
(setf results (flatten results))
(format-ansi-escaped t "~&" :white "Results: " :green `("~a test~:p passed" ,(count t results)) :normal ", "
(if (find NIL results) :red :normal) `("~a test~:p failed" ,(count NIL results))
:yellow `("~[~:;, ~:*~a test~:p not run~]" ,(count :skip results))
:brown `("~[~:;, ~:*~a empty test group~:p skipped~]" ,(count :empty results))
:normal "~%"))
For my part, the ? macro is rather technical and it's hard to follow the logic behind the formatting functions. So instead of tracking errors I'd like to suggest my own attempt, perhaps it'll be of use.
I think that actually your ?? doesn't want to evaluate anything, but rather to treat its body as individual tests or sections. If the body includes a list starting with ?, this list represents a section; other elements are test forms optionally followed by descriptions. So in my implementation ?? will be a macro, and ? will be just a symbol.
I start with wishful thinking. I suppose I can create individual tests using a function make-test-item and test sections using a function make-test-section (their implementation is unimportant for now), that I can display them using an auxiliary function display-test and compute results using the function results, which returns two values: the total number of tests and the number of passed ones. Then I'd like the code
(??
(? "Arithmetic tests"
(? "Addition"
(= (+ 1 2) 3) "Adding 1 and 2 results in 3"
(= (+ 1 2 3) 6)
(= (+ -1 -3) 4))
(? "Subtraction"
(= (- 1 2) 1)))
(= (sin 0) 0) "Sine of 0 equals 0")
to expand into something like
(let ((tests (list (make-test-section :header "Arithmetic tests"
:items (list (make-test-section :header "Addition"
:items (list (make-test-item :form '(= (+ 1 2) 3)
:description "Adding 1 and 2 results in 3"
:passp (= (+ 1 2) 3))
(make-test-item :form '(= (+ 1 2 3) 6)
:passp (= (+ 1 2 3) 6))
(make-test-item :form '(= (+ -1 -3) 4)
:passp (= (+ -1 -3) 4))))
(make-test-section :header "Subtraction"
:items (list (make-test-item :form '(= (- 1 2) 1)
:passp (= (- 1 2) 1))))))
(make-test-item :form '(= (sin 0) 0)
:passp (= (sin 0) 0)
:description "Sine of 0 equals 0"))))
(loop for test in tests
with total = 0
with passed = 0
do (display-test test 0 t)
do (multiple-value-bind (ttl p) (results test)
(incf total ttl)
(incf passed p))
finally (display-result total passed t)))
Here a list of tests is created; then we traverse it printing each test (0 denotes the zero level of indentation and t is as in format) and keeping track of the results, finally displaying the total results. I don't think explicit eval is needed here.
It may not be the most exquisite piece of code ever, but it seems manageable. I supply missing definitions below, they are rather trivial (and can be improved) and have nothing to do with macros.
Now we pass on to the macros. Consider both pieces of code as data, then we want a list processing function which would turn the first one into the second. A few auxiliary functions would come in handy.
The major task is to parse the body of ?? and generate the list of test to go inside the let.
(defun test-item-form (form description)
`(make-test-item :form ',form :description ,description :passp ,form))
(defun test-section-form (header items)
`(make-test-section :header ,header :items (list ,#items)))
(defun parse-test (forms)
(let (new-forms)
(loop
(when (null forms)
(return (nreverse new-forms)))
(let ((f (pop forms)))
(cond ((and (listp f) (eq (first f) '?))
(push (test-section-form (second f) (parse-test (nthcdr 2 f))) new-forms))
((stringp (first forms))
(push (test-item-form f (pop forms)) new-forms))
(t (push (test-item-form f nil) new-forms)))))))
Here parse-test essentially absorbs the syntax of ??. Each iteration consumes one or two forms and collects corresponding make-... forms. The functions can be easily tested in REPL (and, of course, I did test them while writing).
Now the macro becomes quite simple:
(defmacro ?? (&body body)
`(let ((tests (list ,#(parse-test body))))
(loop for test in tests
with total = 0
with passed = 0
do (display-test test 0 t)
do (multiple-value-bind (ttl p) (results test)
(incf total ttl)
(incf passed p))
finally (display-result total passed t))))
It captures a few symbols, both in the variable name space and in the function one (the expansion may contain make-test-item and make-test-section). A clean solution with gensyms would be cumbersome, so I'd suggest just moving all the definitions in a separate package and exporting only ?? and ?.
For completeness, here is an implementation of the test API. Actually, it's what I started coding with and proceeded until I made sure the big let-form works; then I passed on to the macro part. This implementation is fairly sloppy; in particular, it doesn't support terminal colours and display-test can't even output a section into a string.
(defstruct test-item form description passp)
(defstruct test-section header items)
(defun results (test)
(etypecase test
(test-item (if (test-item-passp test)
(values 1 1)
(values 1 0)))
(test-section (let ((items-count 0)
(passed-count 0))
(dolist (i (test-section-items test) (values items-count passed-count))
(multiple-value-bind (i p) (results i)
(incf items-count i)
(incf passed-count p)))))))
(defparameter *test-indent* 2)
(defun display-test-item (i level stream)
(format stream "~V,0T~:[(FAIL)~;(PASS)~] ~:['~S'~;~:*~A~]~%"
(* level *test-indent*)
(test-item-passp i)
(test-item-description i)
(test-item-form i)))
(defun display-test-section-header (s level stream)
(format stream "~V,0T[~A]~%"
(* level *test-indent*)
(test-section-header s)))
(defun display-test (test level stream)
(etypecase test
(test-item (display-test-item test level stream))
(test-section
(display-test-section-header test level stream)
(dolist (i (test-section-items test))
(display-test i (1+ level) stream)))))
(defun display-result (total passed stream)
(format stream "Results: ~D test~:P passed, ~D test~:P failed.~%" passed (- total passed)))
All the code is licenced under WTFPL.

Using scheme/racket to return specific items from a list

What I would like to do is create a function that takes in a list of values and a list of characters and coalesce the corresponding characters("atoms" I think they would technically be called) into a new list.
Here is what I have so far;
#lang racket
(define (find num char)
(if (= num 1)
(car char) ;Problem here perhaps?
(find (- num 1) (cdr char))))
(define (test num char)
(if (null? num)
'("Done")
(list (find (car num) (test (cdr num) char)))))
This however gives me an error, which for the most part I understand what it is saying but I don't see what is wrong to create the error. Given the following simple test input, this is what I get
> (test '(2 1) '(a b c))
car: contract violation
expected: pair?
given: '()
Essentially the output should be '(b a) instead of the error obviously.
A little help and guidance for a new scheme user would be appreciated!
EDIT:
Here is the code that I was able to get running.
#lang racket
(define (find num char)
(cond ((empty? char) #f)
((= num 1) (car char))
(else (find (- num 1) (cdr char)))))
(define (project num char)
(if (empty? num)
'()
(cons (find (car num) char) (project (cdr num) char))))
The find procedure is mostly right (although it's basically reinventing the wheel and doing the same that list-ref does, but well...) just be careful, and don't forget to consider the case when the list is empty:
(define (find num char)
(cond ((empty? char) #f)
((= num 1) (car char))
(else (find (- num 1) (cdr char)))))
The project procedure, on the other hand, is not quite right. You should know by now how to write the recipe for iterating over a list and creating a new list as an answer. I'll give you some tips, fill-in the blanks:
(define (project num char)
(if <???> ; if num is empty
<???> ; then we're done, return the empty list
(cons ; otherwise cons
<???> ; the desired value, hint: use find
(project <???> char)))) ; and advance the recursion
That should do the trick:
(test '(2 1) '(a b c))
=> '(b a)
Better late than never:
(define (coalesce nums chars)
(map (lambda (num) (list-ref chars (- num 1))) nums))
With higher order functions
#lang racket
(define (find num chars)
(cond ((empty? chars) #f)
((= num 1) (car chars))
(else (find (- num 1) (cdr chars)))))
(define (project nums chars)
(let ((do-it (lambda (num) (find num chars))))
(map do-it nums)))