Related
I want to make a hash of sets. Well, SetHashes, since they need to be mutable.
In fact, I would like to initialize my Hash with multiple identical copies of the same SetHash.
I have an array containing the keys for the new hash: #keys
And I have my SetHash already initialized in a scalar variable: $set
I'm looking for a clean way to initialize the hash.
This works:
my %hash = ({ $_ => $set.clone } for #keys);
(The parens are needed for precedence; without them, the assignment to %hash is part of the body of the for loop. I could change it to a non-postfix for loop or make any of several other minor changes to get the same result in a slightly different way, but that's not what I'm interested in here.)
Instead, I was kind of hoping I could use one of Raku's nifty hyper-operators, maybe like this:
my %hash = #keys »=>» $set;
That expression works a treat when $set is a simple string or number, but a SetHash?
Array >>=>>> SetHash can never work reliably: order of keys in SetHash is indeterminate
Good to know, but I don't want it to hyper over the RHS, in any order. That's why I used the right-pointing version of the hyperop: so it would instead replicate the RHS as needed to match it up to the LHS. In this sort of expression, is there any way to say "Yo, Raku, treat this as a scalar. No, really."?
I tried an explicit Scalar wrapper (which would make the values harder to get at, but it was an experiment):
my %map = #keys »=>» $($set,)
And that got me this message:
Lists on either side of non-dwimmy hyperop of infix:«=>» are not of the same length while recursing
left: 1 elements, right: 4 elements
So it has apparently recursed into the list on the left and found a single key and is trying to map it to a set on the right which has 4 elements. Which is what I want - the key mapped to the set. But instead it's mapping it to the elements of the set, and the hyperoperator is pointing the wrong way for that combination of sizes.
So why is it recursing on the right at all? I thought a Scalar container would prevent that. The documentation says it prevents flattening; how is this recursion not flattening? What's the distinction being drawn?
The error message says the version of the hyperoperator I'm using is "non-dwimmy", which may explain why it's not in fact doing what I mean, but is there maybe an even-less-dwimmy version that lets me be even more explicit? I still haven't gotten my brain aligned well enough with the way Raku works for it to be able to tell WIM reliably.
I'm looking for a clean way to initialize the hash.
One idiomatic option:
my %hash = #keys X=> $set;
See X metaoperator.
The documentation says ... a Scalar container ... prevents flattening; how is this recursion not flattening? What's the distinction being drawn?
A cat is an animal, but an animal is not necessarily a cat. Flattening may act recursively, but some operations that act recursively don't flatten. Recursive flattening stops if it sees a Scalar. But hyperoperation isn't flattening. I get where you're coming from, but this is not the real problem, or at least not a solution.
I had thought that hyperoperation had two tests controlling recursing:
Is it hyperoperating a nodal operation (eg .elems)? If so, just apply it like a parallel shallow map (so don't recurse). (The current doc quite strongly implies that nodal can only be usefully applied to a method, and only a List one (or augmentation thereof) rather than any routine that might get hyperoperated. That is much more restrictive than I was expecting, and I'm sceptical of its truth.)
Otherwise, is a value Iterable? If so, then recurse into that value. In general the value of a Scalar automatically behaves as the value it contains, and that applies here. So Scalars won't help.
A SetHash doesn't do the Iterable role. So I think this refusal to hyperoperate with it is something else.
I just searched the source and that yields two matches in the current Rakudo source, both in the Hyper module, with this one being the specific one we're dealing with:
multi method infix(List:D \left, Associative:D \right) {
die "{left.^name} $.name {right.^name} can never work reliably..."
}
For some reason hyperoperation explicitly rejects use of Associatives on either the right or left when coupled with the other side being a List value.
Having pursued the "blame" (tracking who made what changes) I arrived at the commit "Die on Associative <<op>> Iterable" which says:
This can never work due to the random order of keys in the Associative.
This used to die before, but with a very LTA error about a Pair.new()
not finding a suitable candidate.
Perhaps this behaviour could be refined so that the determining factor is, first, whether an operand does the Iterable role, and then if it does, and is Associative, it dies, but if it isn't, it's accepted as a single item?
A search for "can never work reliably" in GH/rakudo/rakudo issues yields zero matches.
Maybe file an issue? (Update I filed "RFC: Allow use of hyperoperators with an Associative that does not do Iterable role instead of dying with "can never work reliably".)
For now we need to find some other technique to stop a non-Iterable Associative being rejected. Here I use a Capture literal:
my %hash = #keys »=>» \($set);
This yields: {a => \(SetHash.new("b","a","c")), b => \(SetHash.new("b","a","c")), ....
Adding a custom op unwraps en passant:
sub infix:« my=> » ($lhs, $rhs) { $lhs => $rhs[0] }
my %hash = #keys »my=>» \($set);
This yields the desired outcome: {a => SetHash(a b c), b => SetHash(a b c), ....
my %hash = ({ $_ => $set.clone } for #keys);
(The parens seem to be needed so it can tell that the curlies are a block instead of a Hash literal...)
No. That particular code in curlies is a Block regardless of whether it's in parens or not.
More generally, Raku code of the form {...} in term position is almost always a Block.
For an explanation of when a {...} sequence is a Hash, and how to force it to be one, see my answer to the Raku SO Is that a Hash or a Block?.
Without the parens you've written this:
my %hash = { block of code } for #keys
which attempts to iterate #keys, running the code my %hash = { block of code } for each iteration. The code fails because you can't assign a block of code to a hash.
Putting parens around the ({ block of code } for #keys) part completely alters the meaning of the code.
Now it runs the block of code for each iteration. And it concatenates the result of each run into a list of results, each of which is a Pair generated by the code $_ => $set.clone. Then, when the for iteration has completed, that resulting list of pairs is assigned, once, to my %hash.
Most of the mainstream languages, including object-oriented programming (OOP) languages such as C#, Visual Basic, C++, and Java were designed to primarily support imperative (procedural) programming, whereas Haskell/gofer like languages are purely functional. Can anybody elaborate on what is the difference between these two ways of programming?
I know it depends on user requirements to choose the way of programming but why is it recommended to learn functional programming languages?
Here is the difference:
Imperative:
Start
Turn on your shoes size 9 1/2.
Make room in your pocket to keep an array[7] of keys.
Put the keys in the room for the keys in the pocket.
Enter garage.
Open garage.
Enter Car.
... and so on and on ...
Put the milk in the refrigerator.
Stop.
Declarative, whereof functional is a subcategory:
Milk is a healthy drink, unless you have problems digesting lactose.
Usually, one stores milk in a refrigerator.
A refrigerator is a box that keeps the things in it cool.
A store is a place where items are sold.
By "selling" we mean the exchange of things for money.
Also, the exchange of money for things is called "buying".
... and so on and on ...
Make sure we have milk in the refrigerator (when we need it - for lazy functional languages).
Summary: In imperative languages you tell the computer how to change bits, bytes and words in it's memory and in what order. In functional ones, we tell the computer what things, actions etc. are. For example, we say that the factorial of 0 is 1, and the factorial of every other natural number is the product of that number and the factorial of its predecessor. We don't say: To compute the factorial of n, reserve a memory region and store 1 there, then multiply the number in that memory region with the numbers 2 to n and store the result at the same place, and at the end, the memory region will contain the factorial.
Definition:
An imperative language uses a sequence of statements to determine how to reach a certain goal. These statements are said to change the state of the program as each one is executed in turn.
Examples:
Java is an imperative language. For example, a program can be created to add a series of numbers:
int total = 0;
int number1 = 5;
int number2 = 10;
int number3 = 15;
total = number1 + number2 + number3;
Each statement changes the state of the program, from assigning values to each variable to the final addition of those values. Using a sequence of five statements the program is explicitly told how to add the numbers 5, 10 and 15 together.
Functional languages:
The functional programming paradigm was explicitly created to support a pure functional approach to problem solving. Functional programming is a form of declarative programming.
Advantages of Pure Functions:
The primary reason to implement functional transformations as pure functions is that pure functions are composable: that is, self-contained and stateless. These characteristics bring a number of benefits, including the following:
Increased readability and maintainability. This is because each function is designed to accomplish a specific task given its arguments. The function does not rely on any external state.
Easier reiterative development. Because the code is easier to refactor, changes to design are often easier to implement. For example, suppose you write a complicated transformation, and then realize that some code is repeated several times in the transformation. If you refactor through a pure method, you can call your pure method at will without worrying about side effects.
Easier testing and debugging. Because pure functions can more easily be tested in isolation, you can write test code that calls the pure function with typical values, valid edge cases, and invalid edge cases.
For OOP People or
Imperative languages:
Object-oriented languages are good when you have a fixed set of operations on things and as your code evolves, you primarily add new things. This can be accomplished by adding new classes which implement existing methods and the existing classes are left alone.
Functional languages are good when you have a fixed set of things and as your code evolves, you primarily add new operations on existing things. This can be accomplished by adding new functions which compute with existing data types and the existing functions are left alone.
Cons:
It depends on the user requirements to choose the way of programming, so there is harm only when users don’t choose the proper way.
When evolution goes the wrong way, you have problems:
Adding a new operation to an object-oriented program may require editing many class definitions to add a new method
Adding a new kind of thing to a functional program may require editing many function definitions to add a new case.
Most modern languages are in varying degree both imperative and functional but to better understand functional programming, it will be best to take an example of pure functional language like Haskell in contrast of imperative code in not so functional language like java/C#. I believe it is always easy to explain by example, so below is one.
Functional programming: calculate factorial of n i.e n! i.e n x (n-1) x (n-2) x ...x 2 X 1
-- | Haskell comment goes like
-- | below 2 lines is code to calculate factorial and 3rd is it's execution
factorial 0 = 1
factorial n = n * factorial (n - 1)
factorial 3
-- | for brevity let's call factorial as f; And x => y shows order execution left to right
-- | above executes as := f(3) as 3 x f(2) => f(2) as 2 x f(1) => f(1) as 1 x f(0) => f(0) as 1
-- | 3 x (2 x (1 x (1)) = 6
Notice that Haskel allows function overloading to the level of argument value. Now below is example of imperative code in increasing degree of imperativeness:
//somewhat functional way
function factorial(n) {
if(n < 1) {
return 1;
}
return n * factorial(n-1);
}
factorial(3);
//somewhat more imperative way
function imperativeFactor(n) {
int f = 1;
for(int i = 1; i <= n; i++) {
f = f * i;
}
return f;
}
This read can be a good reference to understand that how imperative code focus more on how part, state of machine (i in for loop), order of execution, flow control.
The later example can be seen as java/C# lang code roughly and first part as limitation of the language itself in contrast of Haskell to overload the function by value (zero) and hence can be said it is not purist functional language, on the other hand you can say it support functional prog. to some extent.
Disclosure: none of the above code is tested/executed but hopefully should be good enough to convey the concept; also I would appreciate comments for any such correction :)
Functional Programming is a form of declarative programming, which describe the logic of computation and the order of execution is completely de-emphasized.
Problem: I want to change this creature from a horse to a giraffe.
Lengthen neck
Lengthen legs
Apply spots
Give the creature a black tongue
Remove horse tail
Each item can be run in any order to produce the same result.
Imperative Programming is procedural. State and order is important.
Problem: I want to park my car.
Note the initial state of the garage door
Stop car in driveway
If the garage door is closed, open garage door, remember new state; otherwise continue
Pull car into garage
Close garage door
Each step must be done in order to arrive at desired result. Pulling into the garage while the garage door is closed would result in a broken garage door.
//The IMPERATIVE way
int a = ...
int b = ...
int c = 0; //1. there is mutable data
c = a+b; //2. statements (our +, our =) are used to update existing data (variable c)
An imperative program = sequence of statements that change existing data.
Focus on WHAT = our mutating data (modifiable values aka variables).
To chain imperative statements = use procedures (and/or oop).
//The FUNCTIONAL way
const int a = ... //data is always immutable
const int b = ... //data is always immutable
//1. declare pure functions; we use statements to create "new" data (the result of our +), but nothing is ever "changed"
int add(x, y)
{
return x+y;
}
//2. usage = call functions to get new data
const int c = add(a,b); //c can only be assigned (=) once (const)
A functional program = a list of functions "explaining" how new data can be obtained.
Focus on HOW = our function add.
To chain functional "statements" = use function composition.
These fundamental distinctions have deep implications.
Serious software has a lot of data and a lot of code.
So same data (variable) is used in multiple parts of the code.
A. In an imperative program, the mutability of this (shared) data causes issues
code is hard to understand/maintain (since data can be modified in different locations/ways/moments)
parallelizing code is hard (only one thread can mutate a memory location at the time) which means mutating accesses to same variable have to be serialized = developer must write additional code to enforce this serialized access to shared resources, typically via locks/semaphores
As an advantage: data is really modified in place, less need to copy. (some performance gains)
B. On the other hand, functional code uses immutable data which does not have such issues. Data is readonly so there are no race conditions. Code can be easily parallelized. Results can be cached. Much easier to understand.
As a disadvantage: data is copied a lot in order to get "modifications".
See also: https://en.wikipedia.org/wiki/Referential_transparency
Imperative programming style was practiced in web development from 2005 all the way to 2013.
With imperative programming, we wrote out code that listed exactly what our application should do, step by step.
The functional programming style produces abstraction through clever ways of combining functions.
There is mention of declarative programming in the answers and regarding that I will say that declarative programming lists out some rules that we are to follow. We then provide what we refer to as some initial state to our application and we let those rules kind of define how the application behaves.
Now, these quick descriptions probably don’t make a lot of sense, so lets walk through the differences between imperative and declarative programming by walking through an analogy.
Imagine that we are not building software, but instead we bake pies for a living. Perhaps we are bad bakers and don’t know how to bake a delicious pie the way we should.
So our boss gives us a list of directions, what we know as a recipe.
The recipe will tell us how to make a pie. One recipe is written in an imperative style like so:
Mix 1 cup of flour
Add 1 egg
Add 1 cup of sugar
Pour the mixture into a pan
Put the pan in the oven for 30 minutes and 350 degrees F.
The declarative recipe would do the following:
1 cup of flour, 1 egg, 1 cup of sugar - initial State
Rules
If everything mixed, place in pan.
If everything unmixed, place in bowl.
If everything in pan, place in oven.
So imperative approaches are characterized by step by step approaches. You start with step one and go to step 2 and so on.
You eventually end up with some end product. So making this pie, we take these ingredients mix them, put it in a pan and in the oven and you got your end product.
In a declarative world, its different.In the declarative recipe we would separate our recipe into two separate parts, start with one part that lists the initial state of the recipe, like the variables. So our variables here are the quantities of our ingredients and their type.
We take the initial state or initial ingredients and apply some rules to them.
So we take the initial state and pass them through these rules over and over again until we get a ready to eat rhubarb strawberry pie or whatever.
So in a declarative approach, we have to know how to properly structure these rules.
So the rules we might want to examine our ingredients or state, if mixed, put them in a pan.
With our initial state, that doesn’t match because we haven’t yet mixed our ingredients.
So rule 2 says, if they not mixed then mix them in a bowl. Okay yeah this rule applies.
Now we have a bowl of mixed ingredients as our state.
Now we apply that new state to our rules again.
So rule 1 says if ingredients are mixed place them in a pan, okay yeah now rule 1 does apply, lets do it.
Now we have this new state where the ingredients are mixed and in a pan. Rule 1 is no longer relevant, rule 2 does not apply.
Rule 3 says if the ingredients are in a pan, place them in the oven, great that rule is what applies to this new state, lets do it.
And we end up with a delicious hot apple pie or whatever.
Now, if you are like me, you may be thinking, why are we not still doing imperative programming. This makes sense.
Well, for simple flows yes, but most web applications have more complex flows that cannot be properly captured by imperative programming design.
In a declarative approach, we may have some initial ingredients or initial state like textInput=“”, a single variable.
Maybe text input starts off as an empty string.
We take this initial state and apply it to a set of rules defined in your application.
If a user enters text, update text input. Well, right now that doesn’t apply.
If template is rendered, calculate the widget.
If textInput is updated, re render the template.
Well, none of this applies so the program will just wait around for an event to happen.
So at some point a user updates the text input and then we might apply rule number 1.
We may update that to “abcd”
So we just updated our text and textInput updates, rule number 2 does not apply, rule number 3 says if text input is update, which just occurred, then re render the template and then we go back to rule 2 thats says if template is rendered, calculate the widget, okay lets calculate the widget.
In general, as programmers, we want to strive for more declarative programming designs.
Imperative seems more clear and obvious, but a declarative approach scales very nicely for larger applications.
I think it's possible to express functional programming in an imperative fashion:
Using a lot of state check of objects and if... else/ switch statements
Some timeout/ wait mechanism to take care of asynchornousness
There are huge problems with such approach:
Rules/ procedures are repeated
Statefulness leaves chances for side-effects/ mistakes
Functional programming, treating functions/ methods like objects and embracing statelessness, was born to solve those problems I believe.
Example of usages: frontend applications like Android, iOS or web apps' logics incl. communication with backend.
Other challenges when simulating functional programming with imperative/ procedural code:
Race condition
Complex combination and sequence of events. For example, user tries to send money in a banking app. Step 1) Do all of the following in parallel, only proceed if all is good a) Check if user is still good (fraud, AML) b) check if user has enough balance c) Check if recipient is valid and good (fraud, AML) etc. Step 2) perform the transfer operation Step 3) Show update on user's balance and/ or some kind of tracking. With RxJava for example, the code is concise and sensible. Without it, I can imagine there'd be a lot of code, messy and error prone code
I also believe that at the end of the day, functional code will get translated into assembly or machine code which is imperative/ procedural by the compilers. However, unless you write assembly, as humans writing code with high level/ human-readable language, functional programming is the more appropriate way of expression for the listed scenarios
There seem to be many opinions about what functional programs and what imperative programs are.
I think functional programs can most easily be described as "lazy evaluation" oriented. Instead of having a program counter iterate through instructions, the language by design takes a recursive approach.
In a functional language, the evaluation of a function would start at the return statement and backtrack, until it eventually reaches a value. This has far reaching consequences with regards to the language syntax.
Imperative: Shipping the computer around
Below, I've tried to illustrate it by using a post office analogy. The imperative language would be mailing the computer around to different algorithms, and then have the computer returned with a result.
Functional: Shipping recipes around
The functional language would be sending recipes around, and when you need a result - the computer would start processing the recipes.
This way, you ensure that you don't waste too many CPU cycles doing work that is never used to calculate the result.
When you call a function in a functional language, the return value is a recipe that is built up of recipes which in turn is built of recipes. These recipes are actually what's known as closures.
// helper function, to illustrate the point
function unwrap(val) {
while (typeof val === "function") val = val();
return val;
}
function inc(val) {
return function() { unwrap(val) + 1 };
}
function dec(val) {
return function() { unwrap(val) - 1 };
}
function add(val1, val2) {
return function() { unwrap(val1) + unwrap(val2) }
}
// lets "calculate" something
let thirteen = inc(inc(inc(10)))
let twentyFive = dec(add(thirteen, thirteen))
// MAGIC! The computer still has not calculated anything.
// 'thirteen' is simply a recipe that will provide us with the value 13
// lets compose a new function
let doubler = function(val) {
return add(val, val);
}
// more modern syntax, but it's the same:
let alternativeDoubler = (val) => add(val, val)
// another function
let doublerMinusOne = (val) => dec(add(val, val));
// Will this be calculating anything?
let twentyFive = doubler(thirteen)
// no, nothing has been calculated. If we need the value, we have to unwrap it:
console.log(unwrap(thirteen)); // 26
The unwrap function will evaluate all the functions to the point of having a scalar value.
Language Design Consequences
Some nice features in imperative languages, are impossible in functional languages. For example the value++ expression, which in functional languages would be difficult to evaluate. Functional languages make constraints on how the syntax must be, because of the way they are evaluated.
On the other hand, with imperative languages can borrow great ideas from functional languages and become hybrids.
Functional languages have great difficulty with unary operators like for example ++ to increment a value. The reason for this difficulty is not obvious, unless you understand that functional languages are evaluated "in reverse".
Implementing a unary operator would have to be implemented something like this:
let value = 10;
function increment_operator(value) {
return function() {
unwrap(value) + 1;
}
}
value++ // would "under the hood" become value = increment_operator(value)
Note that the unwrap function I used above, is because javascript is not a functional language, so when needed we have to manually unwrap the value.
It is now apparent that applying increment a thousand times would cause us to wrap the value with 10000 closures, which is worthless.
The more obvious approach, is to actually directly change the value in place - but voila: you have introduced modifiable values a.k.a mutable values which makes the language imperative - or actually a hybrid.
Under the hood, it boils down to two different approaches to come up with an output when provided with an input.
Below, I'll try to make an illustration of a city with the following items:
The Computer
Your Home
The Fibonaccis
Imperative Languages
Task: Calculate the 3rd fibonacci number.
Steps:
Put The Computer into a box and mark it with a sticky note:
Field
Value
Mail Address
The Fibonaccis
Return Address
Your Home
Parameters
3
Return Value
undefined
and send off the computer.
The Fibonaccis will upon receiving the box do as they always do:
Is the parameter < 2?
Yes: Change the sticky note, and return the computer to the post office:
Field
Value
Mail Address
The Fibonaccis
Return Address
Your Home
Parameters
3
Return Value
0 or 1 (returning the parameter)
and return to sender.
Otherwise:
Put a new sticky note on top of the old one:
Field
Value
Mail Address
The Fibonaccis
Return Address
Otherwise, step 2, c/oThe Fibonaccis
Parameters
2 (passing parameter-1)
Return Value
undefined
and send it.
Take off the returned sticky note. Put a new sticky note on top of the initial one and send The Computer again:
Field
Value
Mail Address
The Fibonaccis
Return Address
Otherwise, done, c/o The Fibonaccis
Parameters
2 (passing parameter-2)
Return Value
undefined
By now, we should have the initial sticky note from the requester, and two used sticky notes, each having their Return Value field filled. We summarize the return values and put it in the Return Value field of the final sticky note.
Field
Value
Mail Address
The Fibonaccis
Return Address
Your Home
Parameters
3
Return Value
2 (returnValue1 + returnValue2)
and return to sender.
As you can imagine, quite a lot of work starts immediately after you send your computer off to the functions you call.
The entire programming logic is recursive, but in truth the algorithm happens sequentially as the computer moves from algorithm to algorithm with the help of a stack of sticky notes.
Functional Languages
Task: Calculate the 3rd fibonacci number. Steps:
Write the following down on a sticky note:
Field
Value
Instructions
The Fibonaccis
Parameters
3
That's essentially it. That sticky note now represents the computation result of fib(3).
We have attached the parameter 3 to the recipe named The Fibonaccis. The computer does not have to perform any calculations, unless somebody needs the scalar value.
Functional Javascript Example
I've been working on designing a programming language named Charm, and this is how fibonacci would look in that language.
fib: (n) => if (
n < 2 // test
n // when true
fib(n-1) + fib(n-2) // when false
)
print(fib(4));
This code can be compiled both into imperative and functional "bytecode".
The imperative javascript version would be:
let fib = (n) =>
n < 2 ?
n :
fib(n-1) + fib(n-2);
The HALF functional javascript version would be:
let fib = (n) => () =>
n < 2 ?
n :
fib(n-1) + fib(n-2);
The PURE functional javascript version would be much more involved, because javascript doesn't have functional equivalents.
let unwrap = ($) =>
typeof $ !== "function" ? $ : unwrap($());
let $if = ($test, $whenTrue, $whenFalse) => () =>
unwrap($test) ? $whenTrue : $whenFalse;
let $lessThen = (a, b) => () =>
unwrap(a) < unwrap(b);
let $add = ($value, $amount) => () =>
unwrap($value) + unwrap($amount);
let $sub = ($value, $amount) => () =>
unwrap($value) - unwrap($amount);
let $fib = ($n) => () =>
$if(
$lessThen($n, 2),
$n,
$add( $fib( $sub($n, 1) ), $fib( $sub($n, 2) ) )
);
I'll manually "compile" it into javascript code:
"use strict";
// Library of functions:
/**
* Function that resolves the output of a function.
*/
let $$ = (val) => {
while (typeof val === "function") {
val = val();
}
return val;
}
/**
* Functional if
*
* The $ suffix is a convention I use to show that it is "functional"
* style, and I need to use $$() to "unwrap" the value when I need it.
*/
let if$ = (test, whenTrue, otherwise) => () =>
$$(test) ? whenTrue : otherwise;
/**
* Functional lt (less then)
*/
let lt$ = (leftSide, rightSide) => () =>
$$(leftSide) < $$(rightSide)
/**
* Functional add (+)
*/
let add$ = (leftSide, rightSide) => () =>
$$(leftSide) + $$(rightSide)
// My hand compiled Charm script:
/**
* Functional fib compiled
*/
let fib$ = (n) => if$( // fib: (n) => if(
lt$(n, 2), // n < 2
() => n, // n
() => add$(fib$(n-2), fib$(n-1)) // fib(n-1) + fib(n-2)
) // )
// This takes a microsecond or so, because nothing is calculated
console.log(fib$(30));
// When you need the value, just unwrap it with $$( fib$(30) )
console.log( $$( fib$(5) ))
// The only problem that makes this not truly functional, is that
console.log(fib$(5) === fib$(5)) // is false, while it should be true
// but that should be solveable
https://jsfiddle.net/819Lgwtz/42/
I know this question is older and others already explained it well, I would like to give an example problem which explains the same in simple terms.
Problem: Writing the 1's table.
Solution: -
By Imperative style: =>
1*1=1
1*2=2
1*3=3
.
.
.
1*n=n
By Functional style: =>
1
2
3
.
.
.
n
Explanation in Imperative style we write the instructions more explicitly and which can be called as in more simplified manner.
Where as in Functional style, things which are self-explanatory will be ignored.
I ran into an unexpected code optimization recently, and wanted to check whether my interpretation of what I was observing was correct. The following is a much simplified example of the situation:
let demo =
let swap fst snd i =
if i = fst then snd else
if i = snd then fst else
i
[ for i in 1 .. 10000 -> swap 1 i i ]
let demo2 =
let swap (fst: int) snd i =
if i = fst then snd else
if i = snd then fst else
i
[ for i in 1 .. 10000 -> swap 1 i i ]
The only difference between the 2 blocks of code is that in the second case, I explicitly declare the arguments of swap as integers. Yet, when I run the 2 snippets in fsi with #time, I get:
Case 1 Real: 00:00:00.011, CPU: 00:00:00.000, GC gen0: 0, gen1: 0, gen2: 0
Case 2 Real: 00:00:00.004, CPU: 00:00:00.015, GC gen0: 0, gen1: 0, gen2: 0
i.e. the 2nd snippet runs 3 times faster than the first. The absolute performance difference here is obviously not an issue, but if I were to use the swap function a lot, it would pile up.
My assumption is that the reason for the performance hit is that in the first case, swap is generic and "requires equality", and checks whether int supports it, whereas the second case doesn't have to check anything. Is this the reason this is happening, or am I missing something else? And more generally, should I consider automatic generalization a double-edged sword, that is, an awesome feature which may have unexpected effects on performance?
I think this is generally the same case as in the question Why is this F# code so slow. In that question, the performance issue is caused by a constraint requiring comparison and in your case, it is caused by the equality constraint.
In both cases, the compiled generic code has to use interfaces (and boxing), while the specialized compiled code can directly use IL instructions for comparison or equality of integers or floating-point numbers.
The two ways to avoid the performance issue are:
Specialize the code to use int or float as you did
Mark the function as inline so that the compiler specializes it automatically
For smaller functions, the second approach is better, because it does not generate too much code and you can still write functions in a generic way. If you use function just for single type (by design), then using the first approach is probably appropriate.
The reason for the difference is that the compiler is generating calls to
IL_0002: call bool class [FSharp.Core]Microsoft.FSharp.Core.LanguagePrimitives/HashCompare::GenericEqualityIntrinsic<!!0> (!!0, !!0)
in the generic version, whilst the int version can just compare directly.
If you used inline I suspect that this problem would disappear as the compiler now has extra type information
So I'm trying to teach myself Haskell. I am currently on the 11th chapter of Learn You a Haskell for Great Good and am doing the 99 Haskell Problems as well as the Project Euler Problems.
Things are going alright, but I find myself constantly doing something whenever I need to keep track of "variables". I just create another function that accepts those "variables" as parameters and recursively feed it different values depending on the situation. To illustrate with an example, here's my solution to Problem 7 of Project Euler, Find the 10001st prime:
answer :: Integer
answer = nthPrime 10001
nthPrime :: Integer -> Integer
nthPrime n
| n < 1 = -1
| otherwise = nthPrime' n 1 2 []
nthPrime' :: Integer -> Integer -> Integer -> [Integer] -> Integer
nthPrime' n currentIndex possiblePrime previousPrimes
| isFactorOfAnyInThisList possiblePrime previousPrimes = nthPrime' n currentIndex theNextPossiblePrime previousPrimes
| otherwise =
if currentIndex == n
then possiblePrime
else nthPrime' n currentIndexPlusOne theNextPossiblePrime previousPrimesPlusCurrentPrime
where currentIndexPlusOne = currentIndex + 1
theNextPossiblePrime = nextPossiblePrime possiblePrime
previousPrimesPlusCurrentPrime = possiblePrime : previousPrimes
I think you get the idea. Let's also just ignore the fact that this solution can be made to be more efficient, I'm aware of this.
So my question is kind of a two-part question. First, am I going about Haskell all wrong? Am I stuck in the imperative programming mindset and not embracing Haskell as I should? And if so, as I feel I am, how do avoid this? Is there a book or source you can point me to that might help me think more Haskell-like?
Your help is much appreciated,
-Asaf
Am I stuck in the imperative programming mindset and not embracing
Haskell as I should?
You are not stuck, at least I don't hope so. What you experience is absolutely normal. While you were working with imperative languages you learned (maybe without knowing) to see programming problems from a very specific perspective - namely in terms of the van Neumann machine.
If you have the problem of, say, making a list that contains some sequence of numbers (lets say we want the first 1000 even numbers), you immediately think of: a linked list implementation (perhaps from the standard library of your programming language), a loop and a variable that you'd set to a starting value and then you would loop for a while, updating the variable by adding 2 and putting it to the end of the list.
See how you mostly think to serve the machine? Memory locations, loops, etc.!
In imperative programming, one thinks about how to manipulate certain memory cells in a certain order to arrive at the solution all the time. (This is, btw, one reason why beginners find learning (imperative) programming hard. Non programmers are simply not used to solve problems by reducing it to a sequence of memory operations. Why should they? But once you've learned that, you have the power - in the imperative world. For functional programming you need to unlearn that.)
In functional programming, and especially in Haskell, you merely state the construction law of the list. Because a list is a recursive data structure, this law is of course also recursive. In our case, we could, for example say the following:
constructStartingWith n = n : constructStartingWith (n+2)
And almost done! To arrive at our final list we only have to say where to start and how many we want:
result = take 1000 (constructStartingWith 0)
Note that a more general version of constructStartingWith is available in the library, it is called iterate and it takes not only the starting value but also the function that makes the next list element from the current one:
iterate f n = n : iterate f (f n)
constructStartingWith = iterate (2+) -- defined in terms of iterate
Another approach is to assume that we had another list our list could be made from easily. For example, if we had the list of the first n integers we could make it easily into the list of even integers by multiplying each element with 2. Now, the list of the first 1000 (non-negative) integers in Haskell is simply
[0..999]
And there is a function map that transforms lists by applying a given function to each argument. The function we want is to double the elements:
double n = 2*n
Hence:
result = map double [0..999]
Later you'll learn more shortcuts. For example, we don't need to define double, but can use a section: (2*) or we could write our list directly as a sequence [0,2..1998]
But not knowing these tricks yet should not make you feel bad! The main challenge you are facing now is to develop a mentality where you see that the problem of constructing the list of the first 1000 even numbers is a two staged one: a) define how the list of all even numbers looks like and b) take a certain portion of that list. Once you start thinking that way you're done even if you still use hand written versions of iterate and take.
Back to the Euler problem: Here we can use the top down method (and a few basic list manipulation functions one should indeed know about: head, drop, filter, any). First, if we had the list of primes already, we can just drop the first 1000 and take the head of the rest to get the 1001th one:
result = head (drop 1000 primes)
We know that after dropping any number of elements form an infinite list, there will still remain a nonempty list to pick the head from, hence, the use of head is justified here. When you're unsure if there are more than 1000 primes, you should write something like:
result = case drop 1000 primes of
[] -> error "The ancient greeks were wrong! There are less than 1001 primes!"
(r:_) -> r
Now for the hard part. Not knowing how to proceed, we could write some pseudo code:
primes = 2 : {-an infinite list of numbers that are prime-}
We know for sure that 2 is the first prime, the base case, so to speak, thus we can write it down. The unfilled part gives us something to think about. For example, the list should start at some value that is greater 2 for obvious reason. Hence, refined:
primes = 2 : {- something like [3..] but only the ones that are prime -}
Now, this is the point where there emerges a pattern that one needs to learn to recognize. This is surely a list filtered by a predicate, namely prime-ness (it does not matter that we don't know yet how to check prime-ness, the logical structure is the important point. (And, we can be sure that a test for prime-ness is possible!)). This allows us to write more code:
primes = 2 : filter isPrime [3..]
See? We are almost done. In 3 steps, we have reduced a fairly complex problem in such a way that all that is left to write is a quite simple predicate.
Again, we can write in pseudocode:
isPrime n = {- false if any number in 2..n-1 divides n, otherwise true -}
and can refine that. Since this is almost haskell already, it is too easy:
isPrime n = not (any (divides n) [2..n-1])
divides n p = n `rem` p == 0
Note that we did not do optimization yet. For example we can construct the list to be filtered right away to contain only odd numbers, since we know that even ones are not prime. More important, we want to reduce the number of candidates we have to try in isPrime. And here, some mathematical knowledge is needed (the same would be true if you programmed this in C++ or Java, of course), that tells us that it suffices to check if the n we are testing is divisible by any prime number, and that we do not need to check divisibility by prime numbers whose square is greater than n. Fortunately, we have already defined the list of prime numbers and can pick the set of candidates from there! I leave this as exercise.
You'll learn later how to use the standard library and the syntactic sugar like sections, list comprehensions, etc. and you will gradually give up to write your own basic functions.
Even later, when you have to do something in an imperative programming language again, you'll find it very hard to live without infinte lists, higher order functions, immutable data etc.
This will be as hard as going back from C to Assembler.
Have fun!
It's ok to have an imperative mindset at first. With time you will get more used to things and start seeing the places where you can have more functional programs. Practice makes perfect.
As for working with mutable variables you can kind of keep them for now if you follow the rule of thumb of converting variables into function parameters and iteration into tail recursion.
Off the top of my head:
Typeclassopedia. The official v1 of the document is a pdf, but the author has moved his v2 efforts to the Haskell wiki.
What is a monad? This SO Q&A is the best reference I can find.
What is a Monad Transformer? Monad Transformers Step by Step.
Learn from masters: Good Haskell source to read and learn from.
More advanced topics such as GADTs. There's a video, which does a great job explaining it.
And last but not least, #haskell IRC channel. Nothing can even come close to talk to real people.
I think the big change from your code to more haskell like code is using higher order functions, pattern matching and laziness better. For example, you could write the nthPrime function like this (using a similar algorithm to what you did, again ignoring efficiency):
nthPrime n = primes !! (n - 1) where
primes = filter isPrime [2..]
isPrime p = isPrime' p [2..p - 1]
isPrime' p [] = True
isPrime' p (x:xs)
| (p `mod` x == 0) = False
| otherwise = isPrime' p xs
Eg nthPrime 4 returns 7. A few things to note:
The isPrime' function uses pattern matching to implement the function, rather than relying on if statements.
the primes value is an infinite list of all primes. Since haskell is lazy, this is perfectly acceptable.
filter is used rather than reimplemented that behaviour using recursion.
With more experience you will find you will write more idiomatic haskell code - it sortof happens automatically with experience. So don't worry about it, just keep practicing, and reading other people's code.
Another approach, just for variety! Strong use of laziness...
module Main where
nonmults :: Int -> Int -> [Int] -> [Int]
nonmults n next [] = []
nonmults n next l#(x:xs)
| x < next = x : nonmults n next xs
| x == next = nonmults n (next + n) xs
| otherwise = nonmults n (next + n) l
select_primes :: [Int] -> [Int]
select_primes [] = []
select_primes (x:xs) =
x : (select_primes $ nonmults x (x + x) xs)
main :: IO ()
main = do
let primes = select_primes [2 ..]
putStrLn $ show $ primes !! 10000 -- the first prime is index 0 ...
I want to try to answer your question without using ANY functional programming or math, not because I don't think you will understand it, but because your question is very common and maybe others will benefit from the mindset I will try to describe. I'll preface this by saying I an not a Haskell expert by any means, but I have gotten past the mental block you have described by realizing the following:
1. Haskell is simple
Haskell, and other functional languages that I'm not so familiar with, are certainly very different from your 'normal' languages, like C, Java, Python, etc. Unfortunately, the way our psyche works, humans prematurely conclude that if something is different, then A) they don't understand it, and B) it's more complicated than what they already know. If we look at Haskell very objectively, we will see that these two conjectures are totally false:
"But I don't understand it :("
Actually you do. Everything in Haskell and other functional languages is defined in terms of logic and patterns. If you can answer a question as simple as "If all Meeps are Moops, and all Moops are Moors, are all Meeps Moors?", then you could probably write the Haskell Prelude yourself. To further support this point, consider that Haskell lists are defined in Haskell terms, and are not special voodoo magic.
"But it's complicated"
It's actually the opposite. It's simplicity is so naked and bare that our brains have trouble figuring out what to do with it at first. Compared to other languages, Haskell actually has considerably fewer "features" and much less syntax. When you read through Haskell code, you'll notice that almost all the function definitions look the same stylistically. This is very different than say Java for example, which has constructs like Classes, Interfaces, for loops, try/catch blocks, anonymous functions, etc... each with their own syntax and idioms.
You mentioned $ and ., again, just remember they are defined just like any other Haskell function and don't necessarily ever need to be used. However, if you didn't have these available to you, over time, you would likely implement these functions yourself when you notice how convenient they can be.
2. There is no Haskell version of anything
This is actually a great thing, because in Haskell, we have the freedom to define things exactly how we want them. Most other languages provide building blocks that people string together into a program. Haskell leaves it up to you to first define what a building block is, before building with it.
Many beginners ask questions like "How do I do a For loop in Haskell?" and innocent people who are just trying to help will give an unfortunate answer, probably involving a helper function, and extra Int parameter, and tail recursing until you get to 0. Sure, this construct can compute something like a for loop, but in no way is it a for loop, it's not a replacement for a for loop, and in no way is it really even similar to a for loop if you consider the flow of execution. Similar is the State monad for simulating state. It can be used to accomplish similar things as static variables do in other languages, but in no way is it the same thing. Most people leave off the last tidbit about it not being the same when they answer these kinds of questions and I think that only confuses people more until they realize it on their own.
3. Haskell is a logic engine, not a programming language
This is probably least true point I'm trying to make, but hear me out. In imperative programming languages, we are concerned with making our machines do stuff, perform actions, change state, and so on. In Haskell, we try to define what things are, and how are they supposed to behave. We are usually not concerned with what something is doing at any particular time. This certainly has benefits and drawbacks, but that's just how it is. This is very different than what most people think of when you say "programming language".
So that's my take how how to leave an imperative mindset and move to a more functional mindset. Realizing how sensible Haskell is will help you not look at your own code funny anymore. Hopefully thinking about Haskell in these ways will help you become a more productive Haskeller.
I'm implementing a trie for predictive text entry in VB.NET - basically autocompletion as far as the use of the trie is concerned. I've made my trie a recursive data structure based on the generic dictionary class.
It's basically:
class WordTree Inherits Dictionary(of Char, WordTree)
Each letter in a word (all upper cased) is used as a key to a new WordTrie. A null character on a leaf indicates the termination of a word. To find a word starting with a prefix I walk the trie as far as my prefix goes then collect all children words.
My question is basically on the implementation of the trie itself. I'm using the dictionary hash function to branch my tree. I could use a list and do a linear search over the list, or do something else. What's the smooth move here? Is this a reasonable way to do my branching?
Thanks.
Update:
Just to clarify, I'm basically asking if the dictionary branching approach is obviously inferior to some other alternative. The application in which I'm using this data structure only uses upper case letters, so maybe the array approach is the best. I might use the same data structure for a more complex typeahead situation in the future (more characters). In that case, it sounds like the dictionary is the right approach - up to the point where I need to use something more complex in general.
If it's just the 26 letters, as a 26 entry array. Then lookup is by index. It probably uses less space than the Dictionary if the bucket-list is longer than 26.
If you are worried about space, you can use bitmap compression on the valid byte transitions, assuming the 26char limit.
class State // could be struct or whatever
{
int valid; // can handle 32 transitions -- each bit set is valid
vector<State> transitions;
State getNextState( int ch )
{
int index;
int mask = ( 1 << ( toupper( ch ) - 'A' )) -1;
int bitsToCount = valid & mask;
for( index = 0; bitsToCount ; bitsToCount >>= 1)
{
index += bitsToCount & 1;
}
transitions.at( index );
}
};
There are other ways to do the bit counting Here, the index into the vector is the number of set bits in the valid bitset. the other alternative is the direct indexed array of states;
class State
{
State transitions[ 26 ]; // use the char as the index.
State getNextState( int ch )
{
return transitions[ ch ];
}
};
A good data structure that's efficient in space and potentially gives sub-linear prefix lookups is the ternary search tree. Peter Kankowski has a fantastic article about it. He uses C, but it's straightforward code once you understand the data structure. As he mentioned, this is the structure ispell uses for spelling correction.
I have done this (a trie implementation) in C with 8 bit chars, and simply used the array version (as alluded to by the "26 chars" answer).
HOWEVER, I am guessing that you want full unicode support (since a .NET char is unicode, among other reasons). Assuming you have to have support for unicode, the hash/map/dictionary lookup is probably your best bet, as a 64K entry array in each node won't really work very well.
About the only hack up I could think of on this is to store entire strings (suffixes or possibly "in-fixes") on branches that do not yet split, depending on how sparse the tree, er, trie, is. That adds a lot of logic to detect the multi-char strings, though, and to split them up when an alternate path is introduced.
What is the read vs update pattern?
---- update jul 2013 ---
If .NET strings have a function like java to get the bytes for a string (as UTF-8), then having an array in each node to represent the current position's byte value is probably a good way to go. You could even make the arrays variable size, with first/last bounds indicators in each node, since MANY nodes will have only lower case ASCII letters anyway, or only upper case letters or the digits 0-9 in some cases.
I've found burst trie's to be very space efficient. I wrote my own burst trie in Scala that also re-uses some ideas that I found in GWT's trie implementation. I used it in Stripe's Capture the Flag contest on a problem that was multi-node with a small amount of RAM.