Related
I'm trying to complete the activity at the bottom of this page, where I need to print the index of each element as well as the value. I'm starting from the code
use std::fmt; // Import the `fmt` module.
// Define a structure named `List` containing a `Vec`.
struct List(Vec<i32>);
impl fmt::Display for List {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
// Extract the value using tuple indexing
// and create a reference to `vec`.
let vec = &self.0;
write!(f, "[")?;
// Iterate over `vec` in `v` while enumerating the iteration
// count in `count`.
for (count, v) in vec.iter().enumerate() {
// For every element except the first, add a comma.
// Use the ? operator, or try!, to return on errors.
if count != 0 { write!(f, ", ")?; }
write!(f, "{}", v)?;
}
// Close the opened bracket and return a fmt::Result value
write!(f, "]")
}
}
fn main() {
let v = List(vec![1, 2, 3]);
println!("{}", v);
}
I'm brand new to coding and I'm learning Rust by working my way through the Rust docs and Rust by Example. I'm totally stuck on this.
In the book you can see this line:
for (count, v) in vec.iter().enumerate()
If you look at the documentation, you can see a lot of useful functions for Iterator and enumerate's description states:
Creates an iterator which gives the current iteration count as well as the next value.
The iterator returned yields pairs (i, val), where i is the current index of iteration and val is the value returned by the iterator.
enumerate() keeps its count as a usize. If you want to count by a different sized integer, the zip function provides similar functionality.
With this, you have the index of each element in your vector. The simple way to do what you want is to use count:
write!(f, "{}: {}", count, v)?;
This is a simple example to print the index and value of a vector:
fn main() {
let vec1 = vec![1, 2, 3, 4, 5];
println!("length is {}", vec1.len());
for x in 0..vec1.len() {
println!("{} {}", x, vec1[x]);
}
}
This program output is -
length is 5
0 1
1 2
2 3
3 4
4 5
Assuming I have a bunch of functions of arity 2: f: a b -> x, g: c d -> y,
etc. up to unary function u: a -> a. What I would like to do is to chain them in such a way:
f(_, g(_, .... z(_, u(_))...)
where inside _ placeholders consecutive values from given input array will be injected. I'm trying to solve this using Ramda library.
Another, very similar problem I have is chaining the functions the same way but the _ placeholder being filled with the same value against which this composition is being executed.
To be more specific:
// 1st problem
someComposition( f(v[0], g(v[1], ..... z(v[n-1], u(v[n]))...) )(v);
// 2nd problem
someComposition2( f(v, g(v, ..... z(v, u(v))...) )(v);
Best what I could came up with for 2nd problem was, assuming all function are currable, following piece of code (hate it because of the (v) repetitions):
compose(
z(v),
...
g(v),
f(v),
u
)(v);
I tried solving it with compose, composeK, pipe, ap but none of them seem to applied to this situation or I just simply am not able to see the solution. Any help is more then welcome.
There's nothing directly built into Ramda for either of these. (Disclaimer: I'm one of the Ramda authors.) You can create composition functions like these, if you like, though:
const {tail, compose, reduce, identity, reverse} = R;
const f = (x, y) => `f(${x}, ${y})`;
const g = (x, y) => `g(${x}, ${y})`;
const h = (x, y) => `h(${x}, ${y})`;
const i = (x, y) => `i(${x}, ${y})`;
const j = (x) => `j(${x})`;
const multApply = (fns) => (...vals) => fns.length < 2
? fns[0].apply(null, vals)
: fns[0](vals[0], multApply(tail(fns))(...tail(vals)));
console.log(multApply([f, g, h, i, j])('a', 'b', 'c', 'd', 'e'));
//=> f(a, g(b, h(c, i(d, j(e)))))
const nest = compose(reduce((g, f) => (v) => f(v, g(v)), identity), reverse);
console.log(nest([f, g, h, i, j])('v')) //=> f(v, g(v, h(v, i(v, j(v)))));
<script src="//cdnjs.cloudflare.com/ajax/libs/ramda/0.25.0/ramda.js"></script>
Neither of these does any error checking for empty lists, or for an arguments list shorter than the function list (in the first case.) But other than that, they seem to fit the bill.
There's sure to be a recursive version of the second one to match the first, but this implementation is already fairly simple. I didn't readily see a version of the first as simple as the second, but it might well exist.
There's probably some handy Ramda function that I don't know of, or some super functional combinator-thingy I don't understand that makes this easy, but anyway:
You could create your own composition function to compose a list of binary functions and inject values. This function takes a list of functions and a list of arguments. It partially applies the first function it gets to the first argument and keeps on doing so until it's out of arguments, at which it returns a final composed (unary) function:
// Utils
const { add, subtract, multiply, identity, compose, isNil } = R;
const square = x => x * x;
// Our own compose method
const comp2_1 = ([f2, ...f2s ], [x, ...xs], f = identity) =>
isNil(x)
? compose(f2, f)
: comp2_1(f2s, xs, compose(f2(x), f));
// An example
const myFormula = comp2_1(
[add, subtract, multiply, square],
[10, 5, 2]);
// 3 + 10 = 13
// 13 - 5 = 8
// 8 * 2 = 16
// 16 * 16 = 256
console.log(myFormula(3));
<script src="//cdnjs.cloudflare.com/ajax/libs/ramda/0.25.0/ramda.js"></script>
This example will only work for xs.length === fs.length + 1. You might want it to be a bit more flexible by, for instance, continuing the composition even when we're out of arguments:
/* ... */
isNil(x)
? isNil(f2)
? f
: comp2_1(f2s, [], compose(f2, f))
: /* ... */
I have the following function, which takes a vector as argument and returns a vector of its pairs of elements:
fn to_pairs(flat: Vec<u64>) -> Vec<(u64, u64)> {
assert!(flat.len() % 2 == 0);
let mut pairs = Vec::new();
pairs.reserve(flat.len() / 2);
for pair in flat.chunks(2) {
assert!(pair.len() == 2);
pairs.push((pair.get(0).unwrap().clone(), pair.get(1).unwrap().clone()));
}
pairs
}
I want consume the vector flat so I don't have to clone its elements when constructing the pair.
Is it possible to do so without reimplementing a variation of Vec::chunks() myself?
I want consume the vector flat so I don't have to clone its elements when constructing the pair.
Convert the input Vec into an iterator, then take two things from the iterator at a time. Essentially, you want the same thing as processing a Range (an iterator) in chunks:
fn to_pairs<T>(flat: Vec<T>) -> Vec<(T, T)> {
let len = flat.len();
assert!(len % 2 == 0);
let mut pairs = Vec::with_capacity(len / 2);
let mut input = flat.into_iter().peekable();
while input.peek().is_some() {
match (input.next(), input.next()) {
(Some(a), Some(b)) => pairs.push((a, b)),
_ => unreachable!("Cannot have an odd number of values"),
}
}
pairs
}
fn main() {
assert_eq!(vec![(1,2), (3,4)], to_pairs(vec![1,2,3,4]));
assert_eq!(vec![(true,true), (false,false)], to_pairs(vec![true,true,false,false]));
}
The assert!(len % 2 == 0); is quite important here, as Iterator makes no guarantees about what happens after the first time next returns None. Since we call next twice without checking the first value, we could be triggering that case. In other cases, you'd want to use fuse.
As pointed out by Kha, you could simplify the while loop a bit:
let mut input = flat.into_iter();
while let (Some(a), Some(b)) = (input.next(), input.next()) {
pairs.push((a, b));
}
I'm trying to write some code in a functional paradigm for practice. There is one case I'm having some problems wrapping my head around. I am trying to create an array of 5 unique integers from 1, 100. I have been able to solve this without using functional programming:
let uniqueArray = [];
while (uniqueArray.length< 5) {
const newNumber = getRandom1to100();
if (uniqueArray.indexOf(newNumber) < 0) {
uniqueArray.push(newNumber)
}
}
I have access to lodash so I can use that. I was thinking along the lines of:
const uniqueArray = [
getRandom1to100(),
getRandom1to100(),
getRandom1to100(),
getRandom1to100(),
getRandom1to100()
].map((currentVal, index, array) => {
return array.indexOf(currentVal) > -1 ? getRandom1to100 : currentVal;
});
But this obviously wouldn't work because it will always return true because the index is going to be in the array (with more work I could remove that defect) but more importantly it doesn't check for a second time that all values are unique. However, I'm not quite sure how to functionaly mimic a while loop.
Here's an example in OCaml, the key point is that you use accumulators and recursion.
let make () =
Random.self_init ();
let rec make_list prev current max accum =
let number = Random.int 100 in
if current = max then accum
else begin
if number <> prev
then (number + prev) :: make_list number (current + 1) max accum
else accum
end
in
make_list 0 0 5 [] |> Array.of_list
This won't guarantee that the array will be unique, since its only checking by the previous. You could fix that by hiding a hashtable in the closure between make and make_list and doing a constant time lookup.
Here is a stream-based Python approach.
Python's version of a lazy stream is a generator. They can be produced in various ways, including by something which looks like a function definition but uses the key word yield rather than return. For example:
import random
def randNums(a,b):
while True:
yield random.randint(a,b)
Normally generators are used in for-loops but this last generator has an infinite loop hence would hang if you try to iterate over it. Instead, you can use the built-in function next() to get the next item in the string. It is convenient to write a function which works something like Haskell's take:
def take(n,stream):
items = []
for i in range(n):
try:
items.append(next(stream))
except StopIteration:
return items
return items
In Python StopIteration is raised when a generator is exhausted. If this happens before n items, this code just returns however much has been generated, so perhaps I should call it takeAtMost. If you ditch the error-handling then it will crash if there are not enough items -- which maybe you want. In any event, this is used like:
>>> s = randNums(1,10)
>>> take(5,s)
[6, 6, 8, 7, 2]
of course, this allows for repeats.
To make things unique (and to do so in a functional way) we can write a function which takes a stream as input and returns a stream consisting of unique items as output:
def unique(stream):
def f(s):
items = set()
while True:
try:
x = next(s)
if not x in items:
items.add(x)
yield x
except StopIteration:
raise StopIteration
return f(stream)
this creates an stream in a closure that contains a set which can keep track of items that have been seen, only yielding items which are unique. Here I am passing on any StopIteration exception. If the underlying generator has no more elements then there are no more unique elements. I am not 100% sure if I need to explicitly pass on the exception -- (it might happen automatically) but it seems clean to do so.
Used like this:
>>> take(5,unique(randNums(1,10)))
[7, 2, 5, 1, 6]
take(10,unique(randNums(1,10))) will yield a random permutation of 1-10. take(11,unique(randNums(1,10))) will never terminate.
This is a very good question. It's actually quite common. It's even sometimes asked as an interview question.
Here's my solution to generating 5 integers from 0 to 100.
let rec take lst n =
if n = 0 then []
else
match lst with
| [] -> []
| x :: xs -> x :: take xs (n-1)
let shuffle d =
let nd = List.map (fun c -> (Random.bits (), c)) d in
let sond = List.sort compare nd in
List.map snd sond
let rec range a b =
if a >= b then []
else a :: range (a+1) b;;
let _ =
print_endline
(String.concat "\t" ("5 random integers:" :: List.map string_of_int (take (shuffle (range 0 101)) 5)))
How's this:
const addUnique = (ar) => {
const el = getRandom1to100();
return ar.includes(el) ? ar : ar.concat([el])
}
const uniqueArray = (numberOfElements, baseArray) => {
if (numberOfElements < baseArray.length) throw 'invalid input'
return baseArray.length === numberOfElements ? baseArray : uniqueArray(numberOfElements, addUnique(baseArray))
}
const myArray = uniqueArray(5, [])
It is by now a well known theorem of the lambda calculus that any function taking two or more arguments can be written through currying as a chain of functions taking one argument:
# Pseudo-code for currying
f(x,y) -> f_curried(x)(y)
This has proven to be extremely powerful not just in studying the behavior of functions but in practical use (Haskell, etc.).
Functions returning values, however, seem to not be discussed. Programmers typically deal with their inability to return more than one value from a function by returning some meta-object (lists in R, structures in C++, etc.). It has always struck me as a bit of a kludge, but a useful one.
For instance:
# R code for "faking" multiple return values
uselessFunc <- function(dat) {
model1 <- lm( y ~ x , data=dat )
return( list( coef=coef(model1), form=formula(model1) ) )
}
Questions
Does the lambda calculus have anything to say about a multiplicity of return values? If so, do any surprising conclusions result?
Similarly, do any languages allow true multiple return values?
According to the Wikipedia page on lambda calculus:
Lambda calculus, also written as λ-calculus, is a formal system for function
definition, function application and recursion
And a function, in the mathematical sense:
Associates one quantity, the argument of the function, also known as the input,
with another quantity, the value of the function, also known as the output
So answering your first question no, lambda calculus (or any other formalism based on mathematical functions) can not have multiple return values.
For your second question, as far as I know, programming languages that implement multiple return values do so by packing multiple results in some kind of data structure (be it a tuple, an array, or even the stack) and then unpacking it later - and that's where the differences lie, as some programming languages make the packing/unpacking part transparent for the programmer (for instance Python uses tuples under the hood) while other languages make the programmer do the job explicitly, for example Java programmers can simulate multiple return values to some extent by packing multiple results in a returned Object array and then extracting and casting the returned result by hand.
A function returns a single value. This is how functions are defined in mathematics. You can return multiple values by packing them into one compound value. But then it is still a single value. I'd call it a vector, because it has components. There are vector functions in mathematics there, so there are also in programming languages. The only difference is the support level from the language itself and does it facilitate it or not.
Nothing prevents you from having multiple functions, each one returning one of the multiple results that you would like to return.
For example, say, you had the following function in python returning a list.
def f(x):
L = []
for i in range(x):
L.append(x * i)
return L
It returns [0, 3, 6] for x=3 and [0, 5, 10, 15, 20] for x=5. Instead, you can totally have
def f_nth_value(x, n):
L = []
for i in range(x):
L.append(x * i)
if n < len(L):
return L[n]
return None
Then you can request any of the outputs for a given input, and get it, or get None, if there aren't enough outputs:
In [11]: f_nth_value(3, 0)
Out[11]: 0
In [12]: f_nth_value(3, 1)
Out[12]: 3
In [13]: f_nth_value(3, 2)
Out[13]: 6
In [14]: f_nth_value(3, 3)
In [15]: f_nth_value(5, 2)
Out[15]: 10
In [16]: f_nth_value(5, 5)
Computational resources may be wasted if you have to do some of the same work, as in this case. Theoretically, it can be avoided by returning another function that holds all the results inside itself.
def f_return_function(x):
L = []
for i in range(x):
L.append(x * i)
holder = lambda n: L[n] if n < len(L) else None
return holder
So now we have
In [26]: result = f_return_function(5)
In [27]: result(3)
Out[27]: 15
In [28]: result(4)
Out[28]: 20
In [29]: result(5)
Traditional untyped lambda calculus is perfectly capable of expressing this idea. (After all, it is Turing complete.) Whenever you want to return a bunch of values, just return a function that can give the n-th value for any n.
In regard to the second question, python allows for such a syntax, if you know exactly, just how many values the function is going to return.
def f(x):
L = []
for i in range(x):
L.append(x * i)
return L
In [39]: a, b, c = f(3)
In [40]: a
Out[40]: 0
In [41]: b
Out[41]: 3
In [42]: c
Out[42]: 6
In [43]: a, b, c = f(2)
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-43-5480fa44be36> in <module>()
----> 1 a, b, c = f(2)
ValueError: need more than 2 values to unpack
In [44]: a, b, c = f(4)
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-44-d2c7a6593838> in <module>()
----> 1 a, b, c = f(4)
ValueError: too many values to unpack
Lastly, here is an example from this Lisp tutorial:
;; in this function, the return result of (+ x x) is not assigned so it is essentially
;; lost; the function body moves on to the next form, (* x x), which is the last form
;; of this function body. So the function call only returns (* 10 10) => 100
* ((lambda (x) (+ x x) (* x x)) 10)
=> 100
;; in this function, we capture the return values of both (+ x x) and (* x x), as the
;; lexical variables SUM and PRODUCT; using VALUES, we can return multiple values from
;; a form instead of just one
* ((lambda (x) (let ((sum (+ x x)) (product (* x x))) (values sum product))) 10)
=> 20 100
I write this as a late response to the accepted answer since it is wrong!
Lambda Calculus does have multiple return values, but it takes a bit to understand what returning multiple values mean.
Lambda Calculus has no inherent definition of a collection of stuff, but it does allow you to invent it using products and church numerals.
pure functional JavaScript will be used for this example.
let's define a product as follows:
const product = a => b => callback => callback(a)(b);
then we can define church_0, and church_1 aka true, false, aka left, right, aka car, cdr, aka first, rest as follows:
const church_0 = a => b => a;
const church_1 = a => b => b;
let's start with making a function that returns two values, 20, and "Hello".
const product = a => b => callback => callback(a)(b);
const church_0 = a => b => a;
const church_1 = a => b => b;
const returns_many = () => product(20)("Hello");
const at_index_zero = returns_many()(church_0);
const at_index_one = returns_many()(church_1);
console.log(at_index_zero);
console.log(at_index_one);
As expected, we got 20 and "Hello".
To return more than 2 values, it gets a bit tricky:
const product = a => b => callback => callback(a)(b);
const church_0 = a => b => a;
const church_1 = a => b => b;
const returns_many = () => product(20)(
product("Hello")(
product("Yes")("No")
)
);
const at_index_zero = returns_many()(church_0);
const at_index_one = returns_many()(church_1)(church_0);
const at_index_two = returns_many()(church_1)(church_1)(church_0);
console.log(at_index_zero);
console.log(at_index_one);
console.log(at_index_two);
As you can see, a function can return an arbitrary number of return values, but to access these values, a you cannot simply use result()[0], result()[1], or result()[2], but you must use functions that filter out the position you want.
This is mindblowingly similar to electrical circuits, in that circuits have no "0", "1", "2", "3", but they do have means to make decisions, and by abstracting away our circuitry with byte(reverse list of 8 inputs), word(reverse list of 16 inputs), in this language, 0 as a byte would be [0, 0, 0, 0, 0, 0, 0, 0] which is equivalent to:
const Byte = a => b => c => d => e => f => g => h => callback =>
callback(a)(b)(c)(d)(e)(f)(g)(h);
const Byte_one = Byte(0)(0)(0)(0)(0)(0)(0)(1); // preserves
const Bit_zero = Byte_one(b7 => b6 => b5 => b4 => b3 => b2 => b1 => b0 => b0);
After inventing a number, we can make an algorithm to, given a byte-indexed array, and a byte representing index we want from this array, it will take care of the boilerplate.
Anyway, what we call arrays is nothing more than the following, expressed in higher level to show the point:
// represent nested list of bits(addresses)
// to nested list of bits(bytes) interpreted as strings.
const MyArray = function(index) {
return (index == 0)
? "0th"
: (index == 1)
? "first"
: "second"
;
};
except it doesnt do 2^32 - 1 if statements, it only does 8 and recursively narrows down the specific element you want. Essentially it acts exactly like a multiplexor(except the "single" signal is actually a fixed number of bits(coproducts, choices) needed to uniquely address elements).
My point is that is Arrays, Maps, Associative Arrays, Lists, Bits, Bytes, Words, are all fundamentally functions, both at circuit level(where we can represent complex universes with nothing but wires and switches), and mathematical level(where everything is ultimately products(sequences, difficult to manage without requiring nesting, eg lists), coproducts(types, sets), and exponentials(free functors(lambdas), forgetful functors)).