How lexical scope affects lambda function? - racket

This is an example of the Racket tutorial.
(define (square n)
(filled-rectangle n n))
(define series
(lambda (mk)
(hc-append 4 (mk 5)(mk 10)(mk 20))))
(define (rgb-series mk)
(vc-append
(series (lambda (sz) (colorize (mk sz) "red")))
(series (lambda (sz) (colorize (mk sz) "green")))
(series (lambda (sz) (colorize (mk sz) "blue")))))
(define (rgb-maker mk)
(lambda (sz)
(vc-append (colorize (mk sz) "red")
(colorize (mk sz) "green")
(colorize (mk sz) "blue"))))
I think the function rgb-series and rgb-maker are doing the same thing. However, their outputs are quite different.
I could not figure out why. Could anyone explain what's the difference between two functions? Thank you

The difference lies in how vc-append and hc-append are applied.
When you create a row of picts using hc-append, these picts are arranged [h]orizontally, [c]entre aligned. For example:
Now you can stack three such rows into a column using vc-append, forming the following final pict:
This is what is happening in rgb-series, whereby rows are first created, then stacked into a column.
On the other hand, (series (rgb-maker circle)) first creates a column of circles, then arranges these columns into a row, which would look as follows:

Related

Custom pattern-matching facility for Chez Scheme

I am trying to make my own pattern-matching system in Scheme. To begin I am making a parser for s-expressions that divides them into tokens like this:
'(1 2 b (3 4)) => '(number number symbol (number number))
It should be noted that I have not used define-syntax before in Scheme so that may be where I am messing up. Chez Scheme throws me this error:
Exception: invalid syntax classify at line 21, char 4 of pmatch.scm. Note that the line numbers won't correspond exactly to the snippet here. Does anyone know what I am doing wrong?
(define-syntax classify
(syntax-rules ()
((_ checker replacement)
((checker (car sexpr)) (cons replacement (classify-sexpr (cdr sexpr)))))))
(define (classify-sexpr sexpr)
(cond
((null? sexpr) sexpr)
(classify list? (classify-sexpr (car sexpr)))
(classify number? 'number)
(classify symbol? 'symbol)
(else
(cons 'symbol (classify-sexpr (cdr sexpr))))))
(display (classify-sexpr '(1 (b 3) (4 5) 6)))
Your code is hugely confused. In fact it's so confused I'm not sure what you're trying to do completely: I've based my answer on what you say the classifier should produce at the start of your question.
First of all your macro refers to sexpr which has no meaning in the macro, and because Scheme macros are hygienic it will definitely not refer to the sexpr which is the argument to classify-sexpr.
Secondly you don't need a macro at all here. I suspect that you may be thinking that because you are trying to write a macro you must use macros in its construction: that's not necessarily true and often a bad idea.
Thirdly the syntax of your cond is botched beyond repair: I can't work out what it's trying to do.
Finally the list classification will never be needed: if you want to classify (1 2 3 (x)) as (number number number (symbol)) then you'll simply never reach a case where you have a list which you want to classify since you must walk into it to classify its elements.
Instead just write the obvious functions do do what you want:
(define classification-rules
;; an alist of predicate / replacement which drives classigy
`((,number? number)
(,symbol? symbol)))
(define (classify thing)
;; classify thing using classification-rules
(let loop ([tail classification-rules])
(cond [(null? tail)
'something]
[((first (first tail)) thing)
(second (first tail))]
[else
(loop (rest tail))])))
(define (classify-sexpr sexpr)
;; classify a sexpr using classify.
(cond
[(null? sexpr) '()]
[(cons? sexpr) (cons (classify-sexpr (car sexpr))
(classify-sexpr (cdr sexpr)))]
[else (classify sexpr)]))
And now
> (classify-sexpr '(1 2 3 (x 2) y))
'(number number number (symbol number) symbol)
It may be that what you really want is something which classifies (1 2 (x 2)) as (list number number (list symbol number)) say. You can do this fairly easily:
(define atomic-classification-rules
;; an alist of predicate / replacements for non-conses
`((,number? number)
(,symbol? symbol)))
(define (classify-sexpr sexpr)
(cond
[(null? sexpr) '()]
[(list? sexpr)
`(list ,#(map classify-sexpr sexpr))]
[(cons? sexpr)
`(cons ,(classify-sexpr (car sexpr))
,(classify-sexpr (cdr sexpr)))]
[else
(let caloop ([rtail atomic-classification-rules])
(cond [(null? rtail)
'unknown]
[((first (first rtail)) sexpr)
(second (first rtail))]
[else
(caloop (rest rtail))]))]))
And now
> (classify-sexpr '(1 2 3 (x 2) y))
'(list number number number (list symbol number) symbol)
> (classify-sexpr '(1 2 3 (x 2) . y))
'(cons number (cons number (cons number (cons (list symbol number) symbol))))

How to insert literal identifier from input pattern as symbol in syntax-rules macro

I have code like this:
(define-syntax macron
(syntax-rules ()
((_ name)
(lambda (x)
(eval (cons 'name x) (interaction-environment))))))
(define x (map (macron lambda)
'(((x) (display x)) ((a b) (+ a b)))))
(let ((square (car x))
(sum (cadr x)))
(display (square 10))
(newline)
(display (sum 1 2 3))
(newline))
the code is working it use macro as value by wrapping it with lambda. My question is how can I put inside syntax-rule macro literal symbol 'name instead of (cons 'lambda ...) so the output code is:
(lambda (x)
(eval (cons 'name x) (interaction-environment)))
so it work with code like this:
(define (name x)
(display x)
(newline))
(for-each (macron lambda) ;; lambda can be anything
'((1) (2) (3)))
and it print all the numbers.
I know that I can change the name in pattern into something else, but I want to know more about syntax-rules and it's edge cases. So is it possible to have name if I use it as input pattern?
I'm looking for answers with R7RS, that have more of this type of edge cases covered.
All macros happens in compile time so runtime stuff might not exist. That means that you should think of it as syntax sugar and use it as susch. eg.
(for-each (macron something) '((1) (2) (3)))
Should then have an expansion based on that. Your current expansion is that it turns into this:
(for-each (lambda (x)
(eval (cons 'someting x) (interaction-environment))
'((1) (2) (3)))
For something being a macro this will apply the macro in runtime. It is bad. It also removes the need for the macro in the first place. You could do this instead:
(define (macron-proc name)
(lambda (x)
(eval (cons name x) (interaction-environment))))
(for-each (macron-proc 'something) '((1) (2) (3)))
I made a programming language that had passable macros:
(define xor (flambda (a b) `(if ,a (not ,b) ,b)))
(define (fold comb init lst)
(if (null? lst)
init
(fold comb (comb (car lst) init) (cdr lst))))
(fold xor #f '(#t #t)) ; ==> #f
It's not a very good approach if you are targeting an efficient compiled end product. The first macros were indeed like this and they removed it in LISP 1.5 before Common Lisp. Scheme avoided macros for many years and opted for syntax-rules in R4RS as an optional feature. R6RS is the only version that has full power macros.
With a procedure instead of macros this is actually the same as the following code with the bad eval removed:
(for-each (lambda (x)
(apply something x))
'((1) (2) (3)))
Which means you can implement macron much easier:
(define-syntax macron
(syntax-rules ()
((_ name)
(lambda (x)
(apply name x)))))
But from looking at this now you don't need a macro at all. This is partial application.
(define (partial proc arg)
(lambda (lst)
(apply proc arh lst)))
(map (partial + 3) '((1 2) (3 4) (4 5)))
; ==> (6 10 12)
There is actually a SRFI-26 called cut/cute which allows us to do something similar where it wraps it in a lambda:
(map (cut apply + 3 <>) '((1 2) (3 4) (4 5)))
The syntax-rules are the macros with the least power. You cannot do anything unhygienic and you cannot make new identifiers based on other ones. Eg. it' impossible to implement a racket style struct where you can do (struct complex [real imag]) and have the macro create complex?, complex-real, and complex-imag as procedures. You need to do as SRFI-57 does and require th euser to specify all the names such that you don't need to concatenate to new identifiers.
Right now R7RS-small only has syntax-rules. I think it was a mistake not to have a more powerful macro as an alternative since now the R7RS-large cannot be implemented with R7RS-small.

Turning a vector into a list and then into an image in Racket

So, my brain is fried and in class we are working on Conway's Game of Life in DrRacket. This is an Intro to CS class so this is proving to be difficult for me, since coding is very new to me.
I have used lists in animation before but I am lost as to how to turn a vector into an image. Our prof gave us the hint of turning a vector into a list and then we should be able to create the image. I can turn the vector into a list but then I get lost. Any help, guidance or advice would be so greatly appreciated...greatly greatly appreciated.
This isn't all of the code, just a sample.
(define small-board (vector
(vector 1 0)
(vector 0 1))
)
(define live-square (square 10 "solid" "blue"))
(define dead-square (square 10 "solid" "red"))
;Purpose: Create a function that turns board into an image
;Signature: Vector of Vectors -> Image
;Example
(check-expect (board->image small-board)
(above (beside live-square dead-square)
(beside dead-square live-square))
)
;Code
(define (board->image brd)
...
Since you can turn the 2d vector into a 2d list, I can show you how to turn the 2d list into an image.
(require 2htdp/image)
(define small-board (vector (vector 1 0) (vector 0 1)))
(define small-board-as-list (list (list 1 0) (list 0 1)))
(define live-square (square 10 "solid" "blue"))
(define dead-square (square 10 "solid" "red"))
(define MT empty-image)
Recur over the board and put every rendered row above the rest of the rendered board. Within a helper, recur over the row and put each rendered cell beside the rendered "rest" of the row.
; [List-of [List-of (U 1 0)]] -> Image
(define (board->image b)
(cond [(empty? b) MT]
[else (above (row->image (first b))
(board->image (rest b)))]))
; [List-of (U 1 0)] -> Image
(define (row->image r)
(cond [(empty? r) MT]
[else (beside (cell->image (first r))
(row->image (rest r)))]))
; Cell -> Image
(define (cell->image c)
(if (= 1 c) live-square dead-square))
The recursive structure can be abstracted using foldr:
; [List-of [List-of (U 1 0)]] -> Image
(define (board->image-abs.v1 b)
(foldr (λ (r b) (above (foldr (λ (c r) (beside (cell->image c) r)) MT r) b)) MT b))
We can also use map and apply
; [List-of [List-of (U 1 0)]] -> Image
(define (board->image-abs.v2 b)
(apply above (map (λ (r) (apply beside (map (λ (c) (cell->image c)) r))) b)))
The result
(board->image small-board-as-list)
(board->image-abs.v1 small-board-as-list)
(board->image-abs.v2 small-board-as-list)

for/list vs custom for/bytes in Racket

I'm playing around with Racket and missed a byte-string comprehension. When I found for/fold/derived with examples in the documentation, I decided to roll my own byte-string comprehension macro, as any beginner would:
(define-syntax (for/bytes stx)
(syntax-case stx ()
((_ clauses . defs+exprs)
(with-syntax ((original stx))
#'(let-values
(((bstr i max-length)
(for/fold/derived original ((bstr (make-bytes 16)) (c 0) (ln-incr 32)) clauses
(define el (let () . defs+exprs))
(let-values (((new-bstr new-ln-incr)
(if (eq? c (bytes-length bstr))
(values (bytes-append bstr (make-bytes ln-incr)) (* ln-incr 2))
(values bstr ln-incr))))
(bytes-set! new-bstr c el)
(values new-bstr (+ c 1) new-ln-incr)))))
(subbytes bstr 0 i))))))
I've got a few related questions:
Is this the Racket way anyhow?
Is the macro ok? Basically I combined the examples from the for/fold/derived documentation with a macro-expaned for/vector
Are there any obvious performance optimizations?
Sadly, it's not really faster than (list->bytes (for/list ... This micro-benchmark:
(define size 50000)
(define (custom-byte-test) (for/bytes ((i (in-range size))) (modulo i 256)))
(define (standard-list-test) (list->bytes (for/list ((i (in-range size))) (modulo i 256))))
(profile-thunk custom-byte-test #:repeat 1000)
(profile-thunk standard-list-test #:repeat 1000)
gives 3212ms vs 3690ms. For sizes much smaller than 50000 my for/bytes loses, for sizes bigger than that it wins.
My answers:
Is this the Racket way anyhow?
Yes.
Is the macro ok? Basically I combined the examples from the for/fold/derived documentation with a macro-expand for/vector
Yes, I think it looks good.
Are there any obvious performance optimizations? Sadly, it's not really faster than (list->bytes (for/list ...
I'm not aware of how to do it faster. The "win" here is that the complexity of buffer resizing is hidden from users of for/bytes.
I sped your code up a little.
1) The bytes-length calculation in the inner loop is unneeded since you already know the current length. I replaced your ln-incr with a bstr-len that represents both the current length and the amount to increase the length.
This gave ~15% improvement.
2) Since you already do length checking, you can safely use unsafe-bytes-set!, which speeds things up another ~10%.
On my machine, custom-byte-test is now ~1200ms vs ~1750ms for standard-list-test.
#lang racket
(require racket/unsafe/ops profile)
(define-syntax (for/bytes stx)
(syntax-case stx ()
[(_ clauses . defs+exprs)
(with-syntax ([original stx])
#'(let ([init-bstr-len 32])
(let-values
([(bstr i max-length)
(for/fold/derived
original
([bstr (make-bytes init-bstr-len)]
[c 0]
[bstr-len init-bstr-len]) ; <-- use as curr len + extend len
clauses
(define el (let () . defs+exprs))
(let-values
([(new-bstr new-bstr-len)
(if (= c bstr-len) ; <-- remove len calculation
(values
(bytes-append bstr (make-bytes bstr-len))
(* bstr-len 2))
(values bstr bstr-len))])
(unsafe-bytes-set! new-bstr c el) ; <-- unsafe op
(values new-bstr (add1 c) new-bstr-len)))])
(subbytes bstr 0 i))))]))
(define size 50000)
(define (custom-byte-test)
(for/bytes ([i (in-range size)]) (modulo i 256)))
(define (standard-list-test)
(list->bytes (for/list ([i (in-range size)]) (modulo i 256))))
(profile-thunk custom-byte-test #:repeat 1000)
(profile-thunk standard-list-test #:repeat 1000)

(define (average ....)) in Lisp

I'm just playing around with scheme/lisp and was thinking about how I would right my own definition of average. I'm not sure how to do some things that I think are required though.
define a procedure that takes an arbitrary number of arguments
count those arguments
pass the argument list to (+) to sum them together
Does someone have an example of defining average? I don't seem to know enough about LISP to form a web search that gets back the results I'm looking for.
The definition would be a very simple one-liner, but without spoiling it, you should look into:
a "rest" argument -- this (define (foo . xs) ...xs...) defines foo as a function that takes any number of arguments and they're available as a list which will be the value of xs.
length returns the length of a list.
apply takes a function and a list of values and applies the function to these values.
When you get that, you can go for more:
see the foldl function to avoid applying a list on a potentially very big list (this can matter in some implementations where the length of the argument list is limited, but it wouldn't make much difference in Racket).
note that Racket has exact rationals, and you can use exact->inexact to make a more efficient floating-point version.
And the spoilers are:
(define (average . ns) (/ (apply + ns) (length ns)))
Make it require one argument: (define (average n . ns) (/ (apply + n ns) (add1 (length ns))))
Use foldl: (define (average n . ns) (/ (foldl + 0 (cons n ns)) (add1 (length ns))))
Make it use floating point: (define (average n . ns) (/ (foldl + 0.0 (cons n ns)) (add1 (length ns))))
In Common Lisp, it looks like you can do:
(defun average (&rest args)
(when args
(/ (apply #'+ args) (length args))))
although I have no idea if &rest is available on all implementations of Lisp. Reference here.
Putting that code into GNU CLISP results in:
[1]> (defun average (&rest args)
(when args
(/ (apply #'+ args) (length args))))
AVERAGE
[2]> (average 1 2 3 4 5 6)
7/2
which is 3.5 (correct).
Two versions in Common Lisp:
(defun average (items)
(destructuring-bind (l . s)
(reduce (lambda (c a)
(incf (car c))
(incf (cdr c) a)
c)
items
:initial-value (cons 0 0))
(/ s l)))
(defun average (items &aux (s 0) (l 0))
(dolist (i items (/ s l))
(incf s i)
(incf l)))
In Scheme, I prefer using a list instead of the "rest" argument because rest argument makes implementing procedures like the following difficult:
> (define (call-average . ns)
(average ns))
> (call-average 1 2 3) ;; => BANG!
Packing arbitrary number of arguments into a list allows you to perform any list operation on the arguments. You can do more with less syntax and confusion. Here is my Scheme version of average that take 'n' arguments:
(define (average the-list)
(let loop ((count 0) (sum 0) (args the-list))
(if (not (null? args))
(loop (add1 count) (+ sum (car args)) (cdr args))
(/ sum count))))
Here is the same procedure in Common Lisp:
(defun average (the-list)
(let ((count 0) (sum 0))
(dolist (n the-list)
(incf count)
(incf sum n))
(/ sum count)))
In Scheme R5RS:
(define (average . numbers)
(/ (apply + numbers) (length numbers)))