I am trying experiment with CVC4 a bit.
(set-option :produce-models true)
(set-option :produce-assignments true)
(set-logic QF_UFDT)
(declare-datatypes ()
(Color (Red) (Black))
)
(declare-const x C)
(declare-const y C)
(assert (not (= x y)))
(check-sat)
(get-value (x y))
(assert (distinct x y))
(check-sat)
(get-value (x y))
When I run this using CVC4 I am getting the following output
sat
((x R) (y R))
sat
((x R) (y R))
I am confused by this behaviour by this output.
If I am asserting x and y should not be equal their values must be different right?
Same is the case with distinct assertion.
Is CVC4 treating x and y as two different "objects" and hence giving the output it is giving?
I don't see the same results. This is the message I get with the latest development version of CVC4 (http://cvc4.cs.stanford.edu/downloads/):
(error "Parse Error: stack.smt2:5.8: Sequence terminated early by token: 'Color'.
(Color (Red) (Black))
^
")
There are a few syntax errors in your example, here is a corrected version:
(set-option :produce-models true)
(set-option :produce-assignments true)
(set-logic QF_UFDT)
(declare-datatypes () (
(Color (Red) (Black))
))
(declare-const x Color)
(declare-const y Color)
(assert (not (= x y)))
(check-sat)
(get-value (x y))
(assert (distinct x y))
(check-sat)
(get-value (x y))
On this input, cvc4 with the option "--incremental" (which enables multiple queries), gives this response:
sat
((x Red) (y Black))
sat
((x Red) (y Black))
Hope this helps,
Andy
Related
I am learning Common Lisp using clisp and have entered following code:
(defun ordered (x y)
(if (< x y)
(list x y)
(list y x)))
(setq l (ordered 28 49))
(print l)
(setq l (ordered 49 28))
(print l)
Expected these answers:
(28 49)
(49 28)
Got these answers:
(28 49)
(28 49)
In the solutions of this book I have found the same function definition.
What could be wrong?
Your code
(defun
defines a function,
ordered
named "ordered",
(x y)
that expects two arguments which will be known as "x" and "y" in its body, whereupon on receiving the arguments (i.e. having been called with two values, e.g. (ordered 49 28))
(if (< x y)
it will compare them, and in case the first was smaller than the second, it will produce
(list x y)
the same two values repackaged in a list (i.e. '(49 28)); or otherwise, if the first value was not smaller than the second,
(list y x)))
it will produce the list containing the second value first, and then the first argument value (i.e. '(28 49)).
So, which was the case here, of comparing the 49 and 28?
Reading this code generally, we can say that if it receives the smaller number as its first argument, it will produce the smaller number first and the bigger number second, in the result list;
and in case it receives the smaller number as its second argument, it will produce the smaller number first and the bigger number second, in the result list.
Reading this back, we can see that this description can be simplified further into one simple statement: it will always produce ______ number first, and ______ second, in the resulting list.
Another way to attack this, is to write down the function created by that definition,
( lambda (x y) (if (< x y) (list x y) (list y x) ) )
Then follow its application symbolically:
( ( lambda (x y) (if (< x y) (list x y) (list y x) ) )
49
28 )
==
(let ( (x 49)
(y 28)
)
(if (< x y) (list x y) (list y x) ) )
==
(let ( (x 49)
(y 28)
)
(if (< 49 28) (list x y) (list y x) ) )
==
(let ( (x 49)
(y 28)
)
(if FALSE (list x y) (list y x) ) )
==
(let ( (x 49)
(y 28)
)
(list y x) )
==
(let ( (x 49)
(y 28)
)
(list 28 49) )
==
(list 28 49)
I am trying to write a recursive code to do x^y but the problem no mater how I update the code it gives me an error.
The Code:
(defun power(x y) (if(> y 0) (* x (power(x (- y 1)))) (1)))
Error:
CL-USER 11 : 5 >Power 2 3
Error: Undefined operator X in form (X (- Y 1)).
Error:
CL-USER 11 : 5 >power(2 3)
Illegal argument in functor position: 2 in (2 3).
You're calling the function in the wrong way. In lisps function calls have the form:
(f a b c)
not
f(a b c)
You had (power (x (- y 1))) in your recursive definition, which in turn had (x (- y 1)) hence the error: x is not a function.
Use (power x (- y 1)) so your definition becomes:
(defun power (x y)
(if (> y 0)
(* x
(power x (- y 1)))
1))
and call it as (power 2 3)
To expand slightly on the previous (correct) answer, this version uses some idiomatic functions:
(defun power (x y)
(if (plusp y)
(* x (power x (1- y)))
1))
You cannot use parenthesis for grouping since CL thinks you want to call function x and function 1. Remove the excess like this:
(defun power(x y)
(if (> y 0)
(* x (power x (- y 1)))
1))
Parenthesis goes on the outside, just as in your function:
(power 2 3) ;==> 8
When you write (X ...) in a Lisp expression, you are asserting that X is a function to be called on the arguments ....
Your problem is you have too many parentheses in your expression. When you write (power (x ..
you've made this assertion. Write (power x ... instead.
You're calling, among others, this code:
(power (x (- y 1)))
So power is called with (x (- y 1)) as a parameter. Are you sure you want to call x as a function?
This works fine:
[1]> ((lambda (x) (/ x x)) 5)
1
but this:
[2]> ((lambda (x y) (/ x y)) 5 2)
5/2
give me '5/2' instead of 2.5. How can I fix it?
Common Lisp performs rational arithmetic whenever possible. If you want floating point, you either have to supplying at least one float as input to the arithmetic function, or use an explicit coercion function on the result.
((lambda (x y) (float (/ x y)) 5 2)
or
((lambda (x y) (/ x y)) 5.0 2)
Rational arithmetic is generally more exact than floating point. Consider this:
(setf x1 (/ 1 3)) => 1/3
(setf x2 (float (/ 1 3)) => 0.33333333
(* x1 3) => 1
(* x2 3) => 0.99999999
The prompt is to define a procedure that returns the sum of the squares of the two largest of three numbers.
I know this isn't exactly an elegant solution, but this is what I hacked together:
(define (largest-of-two-sum-of-squares x y z)
(cond ((and (< x y) (< x z)) (sum-of-squares y z))
((and (< y z) (< y x)) (sum-of-squares x z))
((and (< z x) (< z y)) (sum-of-squares x y)))))
What I'm wondering is why I'm getting an error.
;The object 85 is not applicable
The number that follows the word object is always the correct answer, btw. I am a scheme beginner, it must be something in my syntax?
Thanks
Here's another possible solution, this one works even in the cases where all three numbers are equal or if two are equal and lower than the other:
(define (sum-max a b c)
(define (sum x y)
(+ (* x x) (* y y)))
(if (>= a b)
(if (>= b c)
(sum a b)
(sum a c))
(if (>= a c)
(sum b a)
(sum b c))))
As sindikat pointed out, an excess closing bracket. Sorry about that.
What about
(define (largest-of-two-sum-of-squares x y z)
(+ (square x) (square y) (square z)
(- (square (min x y z)))))
?
Question:
((lambda (x y) (x y)) (lambda (x) (* x x)) (* 3 3))
This was #1 on the midterm, I put "81 9" he thought I forgot to cross one out lawl, so I cross out 81, and he goes aww. Anyways, I dont understand why it's 81.
I understand why (lambda (x) (* x x)) (* 3 3) = 81, but the first lambda I dont understand what the x and y values are there, and what the [body] (x y) does.
So I was hoping someone could explain to me why the first part doesn't seem like it does anything.
This needs some indentation to clarify
((lambda (x y) (x y))
(lambda (x) (* x x))
(* 3 3))
(lambda (x y) (x y)); call x with y as only parameter.
(lambda (x) (* x x)); evaluate to the square of its parameter.
(* 3 3); evaluate to 9
So the whole thing means: "call the square function with the 9 as parameter".
EDIT: The same thing could be written as
((lambda (x) (* x x))
(* 3 3))
I guess the intent of the exercise is to highlight how evaluating a scheme form involves an implicit function application.
Let's look at this again...
((lambda (x y) (x y)) (lambda (x) (* x x)) (* 3 3))
To evaluate a form we evaluate each part of it in turn. We have three elements in our form. This one is on the first (function) position:
(lambda (x y) (x y))
This is a second element of a form and a first argument to the function:
(lambda (x) (* x x))
Last element of the form, so a second argument to the function.
(* 3 3)
Order of evaluation doesn't matter in this case, so let's just start from the left.
(lambda (x y) (x y))
Lambda creates a function, so this evaluates to a function that takes two arguments, x and y, and then applies x to y (in other words, calls x with a single argument y). Let's call this call-1.
(lambda (x) (* x x))
This evaluates to a function that takes a single argument and returns a square of this argument. So we can just call this square.
(* 3 3)
This obviously evaluates to 9.
OK, so after this first run of evaluation we have:
(call-1 square 9)
To evaluate this, we call call-1 with two arguments, square and 9. Applying call-1 gives us:
(square 9)
Since that's what call-1 does - it calls its first argument with its second argument. Now, square of 9 is 81, which is the value of the whole expression.
Perhaps translating that code to Common Lisp helps clarify its behaviour:
((lambda (x y) (funcall x y)) (lambda (x) (* x x)) (* 3 3))
Or even more explicitly:
(funcall (lambda (x y) (funcall x y))
(lambda (x) (* x x))
(* 3 3))
Indeed, that first lambda doesn't do anything useful, since it boils down to:
(funcall (lambda (x) (* x x)) (* 3 3))
which equals
(let ((x (* 3 3)))
(* x x))
equals
(let ((x 9))
(* x x))
equals
(* 9 9)
equals 81.
The answers posted so far are good, so rather than duplicating what they already said, perhaps here is another way you could look at the program:
(define (square x) (* x x))
(define (call-with arg fun) (fun arg))
(call-with (* 3 3) square)
Does it still look strange?