Adding the results of two functions in Scheme - scheme

I try to make a function in Scheme that adds the squares of two numbers.
(define (sum-of-two-squares X Y)
(+ square(X) square(Y)))
(sum-of-two-squares 3 5)
As error it tells me that "5 is not a function". How do you add the results of this two functions without giving you error?

just write (square X) instead of square(X).
In Scheme, (X) means "call X as a function, without any arguments".
And (square X) means "call square as a function, with X as its argument".

I think what you want is:
(define (sum-of-two-squares X Y)
(+ (square X) (square Y)))

Related

Racket: Trying to subtract numbers, getting list

I'm currently learning Racket/Scheme for a course (I'm not sure what's the difference, actually, and I'm not sure if the course covered that). I'm trying a basic example, implementing the Newton method to find a square root of a number; however, I ran into a problem with finding the distance between two numbers.
It seems that for whatever reason, when I'm trying to apply the subtraction operator between two numbers, it returns a list instead.
#lang racket
(define distance
(lambda (x y) (
(print (real? x))
(print (real? y))
(abs (- x y))
)
)
)
(define abs
(lambda x (
(print (list? x))
(if (< x 0) (- x) x)
)
)
)
(distance 2 5)
As you can see, I've added printing of the types of variables to make sure the problem is what I think it is, and the output of all those prints is #t. So:
In calling distance, x and y are both real.
In calling abs, x is a list.
So, the conclusion is that (- x y) returns a list, but why?
I double-checked with the documentation and it seems I'm using the subtraction operator correctly; I've typed (- 2 5) and then (real? (- 2 5)) into the same REPL I'm using to debug my program (Dr. Racket, to be specific), and I'm getting the expected results (-3 and #t, respectively).
Is there any wizard here that can tell me what kind of sorcery is this?
Thanks in advance!
How about this...
(define distance
(lambda (x y)
(print (real? x))
(print (real? y))
(abs (- x y))))
(define abs
(lambda (x) ;; instead of (lambda x ...), we are using (lambda (x) ...) form which is more strict in binding with formals
(print (list? x))
(if (< x 0) (- x) x)))
Read further about various lambda forms and their binding with formals.

Dr racket define error in student language. define: expected only one expression for the function body, but found 3 extra parts

When I write code in Dr Racket, I got error message
unsaved-editor:8:2: define: expected only one expression for the
function body, but found 3 extra parts in: (define (improve guess x)
(average guess (/ x guess)))
But this code can run in Racket or repl.it.
I want to know why error is happening in Dr Racket and is my code really wrong?
My code is this:
(define (average x y) (/ (+ x y) 2))
(define (square x) (* x x))
(define (sqrt1 x)
(define (good-enough? guess x)
(< (abs (- (square guess) x)) 0.001))
(define (improve guess x)
(average guess (/ x guess)))
(define (sqrt-iter guess x)
(if (good-enough? guess x)
guess
(sqrt-iter (improve guess x) x)))
(sqrt-iter 1.0 x))
(sqrt1 9)
Your code is OK for Scheme/Racket. However Student Language is a subset of Scheme, highly limited so it's easier for beginners. It's also used in How To Design Programs book. You can read more about Student Languages (actually there is five of them) on https://docs.racket-lang.org/htdp-langs/index.html.
In case of define there are important limitations:
You can have only one expression in the function body.
In function body you can only use expressions, not definitions (so no define inside define).
To make your code valid for Student Language, depending on Level (Beginner, Intermediate etc), you can:
use letrec* or local instead of define for all local definitions
or
define good-enough, improve and sqrt-iter as top level functions.

Function Definitions After Expressions in Scheme

I understand I can't define a function inside an expression, but I'm getting errors defining one after an expression within the same nested function. I'm using R5RS with DrScheme.
For example, this throws an error, 'define: not allowed in an expression context':
(define (cube x)
(if (= x 0) 0) ;just for example, no reason to do this
(define (square x) (* x x))
(* x (square x)))
In R5RS you can only use define in rather specific places: in particular you can use it at the beginning (only) of forms which have a <body>. This is described in 5.2.2. That means in particular that internal defines can never occur after any other expression, even in a <body>.
Native Racket (or whatever the right name is for what you get with#lang racket) is much more flexible in this regard: what you are trying to do would (apart from the single-armed if) be legal in Racket.
You can use define inside another definition. Some Schemes won't allow you to have an if without the else part, though. This works for me:
(define (cube x)
(if (= x 0) 0 1) ; just for example, no reason to do this
(define (square x) (* x x))
(* x (square x)))
Have you tried making the definition at the beginning? maybe that could be a problem with your interpreter.
define inside a procedure body (that includes all forms that are syntactic sugar for procedures, like let, let*, and letrec) are only legal before other expressions and never after the first expression and it can not be the last form.
Your example shows no real reason for why you would want to have an expression before definitions. There is no way you can get anything more than moving all define up to the beginning. eg.
(define (cube x)
;; define moved to top
(define (square x) (* x x))
;; dead code moved under define and added missing alternative
(if (= x 0) 0 'undefined)
(* x (square x)))
If the code isn't dead. eg. it's the tail expression you can use let to make a new body:
(define (cube x)
(if (= x 0)
0
(let ()
;; this is top level in the let
(define (square x) (* x x))
;; required expression
(* x (square x)))))
I think perhaps we would need an example where you think it would be warranted to have the define after the expression and we'll be happy to show how to scheme it up.

What causes an unbound variable error in Scheme?

I've started out with SICP and I'm new to Scheme. I've tried debugging this piece of code and even compared it to similar solutions.
(def (myFunc x y z)
(cond ((and (<= x y) (<= x z)) (+ (* y y) (* z z)))
((and (<= y x) (<= y z)) (+ (* x x) (* z z)))
(else (+ (* x x) (* y y)))))
This function returns the sum of the squares of two largest numbers.
When I run this, the interpreter gives out ";Unbound variable: y". Could you please explain the cause behind this error?
Help is greatly appreciated :)
The function-defining primitive in Scheme is called define, not def.
As it is, the whole (def ...) expression was treated as a function call to def. So its arguments' values needed to be found. The first argument (myFunc x y z) is a function call so its argument values needed to be found. Apparently your implementation wanted to find out the value of y first.
The R5RS standard says "The operator and operand expressions are evaluated (in an unspecified order) and the resulting procedure is passed the resulting arguments."
It is likely your implementation chooses the rightmost argument first, which leads to (<= x y) being evaluated first (because of special rules of evaluating the cond and and special forms), with y in its rightmost position.

Scheme, higher order functions, and curried functions

I need to write a Scheme higher-order function that takes a function of two parameters as its parameter and returns a curried version of the function. I understand this much so far in terms of curried functions:
(define curriedFunction (lambda (x)
(if (positive? x)
(lambda (y z) (+ x y z))
(lambda (y z) (- x y z)))))
(display ((curriedFunction -5) 4 7))
(display "\n")
(display ((curriedFunction 5) 4 7))
If x is negative, it subtracts x y and z. If x is positive, it adds x, y, and z.
In terms of higher order functions I understand this:
(display (map (lambda (x y) (* x y)) '(1 2 3) '(3 4 5)))
And thirdly I understand this much in terms of passing functions in as arguments:
(define (function0 func x y)
(func x y))
(define myFunction (lambda (x y)
(* x y)))
(display (function0 myFunction 10 4))
In the code directly above, I understand that the function "myFunction" could have also been written as this:
(define (myFunction x y)
(* x y))
So now you know where I am at in terms of Scheme programming and syntax.
Now back to answering the question of writing a Scheme higher-order function that takes a function of two parameters as its parameter and returns a curried version of the function. How do I connect these concepts together? Thank you in advance, I truly appreciate it.
Here is a possible solution:
(define (curry f)
(lambda (x)
(lambda (y)
(f x y))))
The function curry takes the function f and returns a function with a single argument x. That function, given a value for its argument, returns another function that takes an argument y and returns the result of applying the original function f to x and y. So, for instance, (curry +) returns a curried version of +:
(((curry +) 3) 4) ; produces 7

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