I'm trying to implement arithmetic in a field modulo N. Here's a simplified example:
(struct field-element (number prime) #:transparent)
(define (field-element-add fe1 fe2)
(field-element (modulo (+ (field-element-number fe1)
(field-element-number fe2))
(field-element-prime fe1))
(field-element-prime fe1)))
(field-element-add (field-element 3 5) (field-element 4 5)) ; (1)
(field-element-add (field-element 3 5) (field-element 4 6)) ; (2)
(1) should return (field-element 2 5) because 3 + 4 = 7 = 2 mod 5
(2) should raise an error, because you can't add elements in fields with different prime modulus (5 and 6 in this example).
My question: how to use contracts that check all arguments to field-element-add share the same prime and raise errors when they don't?
All the contracts I've seen in the docs enforce constraints on each argument separately e.g. integer?. But I want to enforce a constraint across the arguments as a group: they must share a prime property.
And I know I could just check this manually without a contract -- but this seems like exactly the circumstance contracts were made for.
Thanks in advance!
In the page that you mentioned, take a look at section 7.3.6 for how to use ->i so that you can "mention" other arguments.
For your case:
(struct field-element (number prime) #:transparent)
(define field-binop/c
(->i ([a field-element?]
[b (a) (struct/c field-element
number?
(=/c (field-element-prime a)))])
[result field-element?]))
(define/contract (field-element-add fe1 fe2) field-binop/c
(field-element (modulo (+ (field-element-number fe1)
(field-element-number fe2))
(field-element-prime fe1))
(field-element-prime fe1)))
(field-element-add (field-element 3 5) (field-element 4 5)) ;=> (field-element 2 5)
(field-element-add (field-element 3 5) (field-element 4 6))
#|
../../Applications/Racket v7.2/collects/racket/contract/private/blame.rkt:347:0: field-element-add: contract violation
expected: (struct/c field-element number? (=/c 5))
given: (field-element 4 6)
in: the fe2 argument of
(->i
((fe1 field-element?)
(fe2
(fe1)
(struct/c
field-element
number?
(=/c (field-element-prime fe1)))))
(result field-element?))
contract from: (function field-element-add)
blaming: anonymous-module
(assuming the contract is correct)
at: unsaved-editor:5.18
|#
Related
How would I write a function in Dr. Racket which consumes a list of list of integers and produces a new list of list of integers with a transformation (sqr) applied to each element.
Note: There is an equal number of elements in each list.
Here are two examples to show what I am saying:
Example 1:
(list (list 1 2) (list 3 -2))
Should produce:
(list (list 1 4) (list 9 4))
Example 2:
(list (list 3 4 5) (list 2 1 3) (list 2 3 7) (list 0 -3 2))
Should produce:
(list (list 9 16 25) (list 4 1 9) (list 4 9 49) (list 0 9 4))
Here is my code so far:
(define (transform-to-sqr b)
(map sqr b))
If I type in:
(transform-to-sqr (list (list 1 2) (list 3 -2)))
I get an error message saying:
sqr: expected a number; given (list 1 2).
Why is this happening. Can someone please tell me what I am doing wrong.
Thanks for your help.
The map higher-order procedure applies a procedure over the elements of a list, but in this case the elements are lists themselves. To operate on the nested elements, we need to nest calls to map:
(define (transform-to-sqr matrix)
(map (λ (row) (map sqr row))
matrix))
It works as expected:
(transform-to-sqr '((1 2) (3 -2)))
=> '((1 4) (9 4))
(transform-to-sqr '((3 4 5) (2 1 3) (2 3 7) (0 -3 2)))
=> '((9 16 25) (4 1 9) (4 9 49) (0 9 4))
I want to define a functionality in common lisp which uses some words/symbols not known to lisp, for example having such a function/macro:
(my-func-or-macro lst key-word idx)
which returns items in the lst upto the idx if the key-word is to and from the idx to the end if the key-word is from.
So practically it should work like:
(my-func-or-macro '(1 2 3 4 5 6) from 3) => '(4 5 6)
and
(my-func-or-macro '(1 2 3 4 5 6) to 3) => '(1 2 3)
Since macros don't evaluate their arguments i think i should be using a macro which doesn't care about from and to (note i don't want to pass quoted args like 'from 'to).
Since every argument to a function is evaluated before the function is executed, you need a symbol that evaluates to itself.
Such symbols are already part of the language: all symbols in the special KEYWORD package evaluate to themselves. Symbols that are written with a leading colon, e. g. :foo are interned into that package.
Also part of the language are keyword arguments that use such keywords to identify parameters:
(defun my-func (list &key from)
(subseq list from))
(my-func '(0 1 2 3 4 5) :from 3)
=> (3 4 5)
You can give default values to such parameters:
(defun my-func (list &key (from 0) (to (length list)))
(subseq list from to))
(my-func '(0 1 2 3 4 5) :from 3)
=> (3 4 5)
(my-func '(0 1 2 3 4 5) :to 3)
=> (0 1 2)
(my-func '(0 1 2 3 4 5) :from 1 :to 4)
=> (1 2 3)
Keyword arguments can be given in any order:
(my-func '(0 1 2 3 4 5) :to 4 :from 1)
=> (1 2 3)
Given the code snippet that follows, is there any meaningful difference between example-func-A and example-func-B?
#lang racket/base
(require (only-in racket/function curry))
(define (((example-func-A x) y) z)
(+ x y z))
(define example-func-B
(curry
(lambda (x y z)
(+ x y z))))
Yes, example-func-A (which uses the MIT-style curried-procedure syntax) is less flexible than example-func-B, in that it expects to only be called with a single argument at a time:
> (((example-func-A 4) 5) 6)
15
> (example-func-A 4 5 6)
example-func-A: arity mismatch;
the expected number of arguments does not match the given number
expected: 1
given: 3
arguments...:
4
5
6
context...:
/opt/homebrew-cask/Caskroom/racket/6.4/Racket v6.4/collects/racket/private/misc.rkt:87:7
In contrast, example-func-B accommodates receiving multiple (or even zero!) arguments:
> (((example-func-B 4) 5) 6)
15
> (example-func-B 4 5 6)
15
> ((((example-func-B) 4)) 5 6)
15
(Presumably the flexibility of curry comes with a bit of a performance hit at runtime.)
Lets say I have two lists, ((1 2 3)) and (((1 2 3)) ((4 5))). I want to be able to tell if the first list is a member of the second list. I have tried to use subsetp, but it does not return true for this query. How can I accomplish this?
As Rainer Joswig mentioned in the comments, you're not checking for subsets, but for members, which you can do using the aptly named member function. Member returns a generalized boolean, i.e., nil for false, and something, not necessarily t, non-nil for true. Specifically, if an element is a member of the list, member returns the tail of the list whose first element is the element.
CL-USER> (member 3 '(1 2 3 4 5))
(3 4 5)
CL-USER> (member 7 '(1 2 3 4 5))
NIL
Of course, when checking membership in a list, there's a question of how to compare the given item with the elements of the list. Member's default comparison is eql, which works on things like numbers, as shown in the example above. For your case, however, you probably want to test with equal, since ((1 2 3)) might not be the same object as the first element of (((1 2 3)) ((4 5))):
CL-USER> (member '((1 2 3)) '(((1 2 3)) ((4 5))))
NIL
CL-USER> (member '((1 2 3)) '(((1 2 3)) ((4 5))) :test 'equal)
(((1 2 3)) ((4 5)))
CL-USER> (member '((4 5)) '(((1 2 3)) ((4 5))) :test 'equal)
(((4 5)))
CL-USER> (member '((1 2 4)) '(((1 2 3)) ((4 5))) :test 'equal)
NIL
If you want to have lists as elements of your sets for subsetp, you have to change the value of the :test keyword.
CL-USER 1 > (subsetp '(1 2 3) '(1 2 3 4 5))
T
CL-USER 2 > (subsetp '((1) (2) (3)) '((1) (2) (3) (4) (5)))
NIL
The first one gives T, the second one gives NIL. Why? Because equality is checked with #'eql which works for identical objects or numbers of the same value and of same type. Since two lists must not be identical objects, (eql '(1) '(1)) gives NIL. (That may depend on your CL implementation.) If you want to compare a tree of conses, tree-equal can help you.
CL-USER 3 > (subsetp '((1) (2) (3)) '((1) (2) (3) (4) (5)) :test #'tree-equal)
T
I don't understand the structure of the sets you gave as example completely, but I hope this helps.
I'm having a bit of trouble with Lisp. What i'm attempting to do, is keep track of the amount of times a number appears in x number of lists. However, running this over and over again, lisp isn't recreating the variable, but using the ending value from the last time I called the function. So I'm wondering how can I get past the 'binding' powers of let?
So, I've got some list like this
(((8 7) (3)) ((8 3) (2)) ((7 3) (6)) ((7 2) (8)) ((6 7) (4 1))
((6 6) (4 1)) ((6 2) (2)) ((5 6) (3)) ((5 3) (8 3)) ((4 6) (4))
((4 4) (6)) ((4 1) (7)) ((3 7) (5 3)) ((3 4) (1)) ((3 3) (3)) ((3 1) (9))
((2 7) (7)) ((2 5) (2)) ((2 2) (5 2)) ((1 7) (1)) ((1 6) (6 1))
((1 1) (2 1)) ((1 0) (3)) ((0 7) (8 1)) ((0 5) (6)) ((0 3) (9 6))
((0 1) (1)))
Then I'm calling some function like this, (declaring var here doesn't seem to do anything, past the initial function call)... I guess some kind of binding from let.
(defun counter (possibleValues)
(let ((var '(0 0 0 0 0 0 0 0 0 0)))
(loop for i from 0 to (list-length possibleValues) do
(loop for j in (cdr (nth i possibleValues)) do
(loop for k in j do
(incf (nth k var)))))
var))
So I can run my list through the function and get something like
(0 8 5 6 3 2 5 2 3 2)
Each position referring to the number found in the list. So the value 8 would refer to how many times 1 was found in all the lists (i'm considering the second list only). Now the problem.... run it twice and...
(0 16 10 12 6 4 10 4 6 4)
I was using an associative list earlier, but in trying to figure this out and keep things simple, i'm now using a list. I guess another question I have is, how can I create associative list elements on the fly? I don't like declaring 'var' like that, but I'm just trying to get around 'let' for the moment. I haven't had much luck with 'setq' or 'setf' either....
Thanks in advance for your help!
Change the initialization form for VAR to be an expression that creates new lists, such as (make-list 10 :initial-element 0) or even (list 0 0 0 0 0 0 0 0 0 0).
Basically, do not ever use quoted objects if you have intentions on modifying them, as the consequences are undefined if you do. In fact, evaluating that function definition gives a warning about that:
; in: LAMBDA NIL
; (INCF (NTH K VAR))
; --> LET*
; ==>
; (SB-KERNEL:%SETNTH #:TMP5 #:TMP4 #:NEW3)
;
; caught WARNING:
; Destructive function SB-KERNEL:%SETNTH called on constant data.
; See also:
; The ANSI Standard, Special Operator QUOTE
; The ANSI Standard, Section 3.2.2.3
;
; compilation unit finished
; caught 1 WARNING condition