Related
I am looking at Haskell elemIndex function:
elemIndex :: Eq a => a -> [a] -> Maybe Int
What does Maybe mean in this definition? Sometimes when I call it, the output has a Just or a Nothing What does it mean? How can I interpret this if I were to use folds?
First question:
What does it mean?
This means that the returned value is either an index (Int) or Nothing.
from the docs:
The elemIndex function returns the index of the first element in the given list which is equal (by ==) to the query element, or Nothing if there is no such element.
The second question:
How can I interpret this if I were to use folds?
I'm not sure there is enough context to the "were to use folds" part. But, there are at least 2 ways to use this function:
case analysis, were you state what to return in each case:
case elemIndex xs of
Just x -> f x -- apply function f to x.
Nothing -> undefined -- do something here, e.g. give a default value.
use function maybe:
maybe defaultValue f (elemIndex xs)
Maybe is a sum type.
Sum type is any type that has multiple possible representations.
For example:
data Bool = False | True
Bool can represented as True or False. The same goes with Maybe.
data Maybe a = Nothing | Just a
The Maybe type encapsulates an optional value. A value of type Maybe a either contains a value of type a (represented as Just a), or it is empty (represented as Nothing)
elemIndex :: Eq a => a -> [a] -> Maybe Int
The elemIndex function returns the index of the first element in the given list which is equal (by ==) to the query element, or Nothing if there is no such element.
Lets compare it to the indexOf function
What are the possible values of this method?
The index of the element in the array in case it was found (lets say 2).
-1 in case it was not found.
Another way to represent it:
Return a number in case it was found - Just 2.
Instead of returning magic numbers like -1 we can return a value that represents the
option of a failure - Nothing.
Regarding "How can I interpret this if I were to use folds", I do not have enough information to understand the question.
Maybe is a type constructor.
Int is a type. Maybe Int is a type.
String is a type. Maybe String is a type.
For any type a, Maybe a is a type. Its values come in two varieties: either Nothing or Just x where x is a value of type a (we write: x :: a):
x :: a
----------------- ------------------
Just x :: Maybe a Nothing :: Maybe a
In the first rule, the a in both the type of the value x :: a and the type of the value Just x :: Maybe a is the same. Thus if we know the type of x we know the type of Just x; and vice versa.
In the second rule, nothing in the value Nothing itself determines the a in its type. The determination will be made according to how that value is used, i.e. from the context of its usage, from its call site.
As to the fold implementation of elemIndex, it could be for example
elemIndex_asFold :: Eq a => a -> [a] -> Maybe Int
elemIndex_asFold x0 = foldr g Nothing
where
g x r | x == x0 = Just x
| else = r
I'm struggling a bit with this: I need a function that takes any function
of type fun(Any*) : Boolean as parameter, evaluates the function and returns true or
false, depending on the success of the function evaluation.
Essentially, what I need is a function type that allows any number and any type of parameter but the function must return Boolean.
Which would allow me to write functions like:
def checkLenght(str : String, length : Int) : Boolean ={
if (str.lenght == length)}
or
def ceckAB(a : Int, b : Int) : Boolean = {
if(a < b && a >= 23 && b < 42) }
so that, for example
eval(checkLenght(abc, 3)) //returns true
eval(ceckAB(4,1)) // returns false
I thought, a function type of:
type CheckFunction = (Any*) => Boolean
may does the trick but I struggle with writing the generic eval function.
Any advise?
Thank you
Solution:
The function requires
1) Another function of return type Boolean: "(func : => Boolean)"
2) Return type Boolean ": Boolean"
3) Returns the value of the passed function-parameter: " = func"
Altogether the function is:
def eval(func : => Boolean) : Boolean = func
It amazes me over again how simple simple things are in Scala.
As pointed out by the comments, this is a rather unusual function with no obvious
sense. Just a word about the underlying reasons.
Motivation:
There were a lot of question about the underlying motivation, so here a short
summary why such a function is needed.
Essentially, there are two reasons.
First one is about moving the failure handling away from the function itself
into a handler function. This preserves the purity of the check function and even allows
re-usage of generic checks.
Second, it's all about "pluggable failure handling". This means, the eval function only
tells if a failure happened (or not). In case of a failure, a handler is called through an interface. The implementation of the handler can be swapped using profiles as required.
Why?
Swapping profiles means, I code my checks and functions as usual but by switching the
profile, I switch the handler which means I can chose between full-stop, console print out, email alert, SNMP notification, push message... you name it. To do so, I need to decouple the check function from its evaluation and from its handling. That's the motivation for such a rather strange looking eval function.
And for the sake of completeness, I've already implemented all that stuff but was I facing the limitation of only handling trivial checks i.e. check(Boolean*) which is neat but often I would prefer to write a function to do more sophisticated checks.
Solved
The function is defined by returning the value of the passed function:
def eval(func : => Boolean) : Boolean = {func}
I can't say that I really understand your motivations for wanting to do what you want to do, but I guess that's beside the point. Maybe the eval function will check something before invoking the supplied function and not invoke that other function (like a fast fail) given some certain condition. Maybe you do some post checking after invoking the function and change the result based on something else. Either way, I suppose you could accomplish something similar to what you want with code looking like this:
def main(args: Array[String]) {
val str = "hello world"
println(eval(checkLength(str, 3)))
println(eval(intsEqual(1,1)))
}
def eval(func: => Boolean):Boolean = {
//Do whetever you want before invoking func, maybe
//not even invoke it if some other condition is present
val fres = func
//Maybe change something here before returning based on post conditions
fres
}
def checkLength(s:String, len:Int) = s.length() == len
def intsEqual(a:Int, b:Int) = a == b
If you really want the eval function to be able to support any function that takes any types of args and returns a Boolean, then using a by-name function like this, and then leveraging closure inside the by-name function to pass any params along to whatever actual function you want to invoke. A better way to demonstrate this is as follows:
def checkMyString(str:String, len:Int) = {
eval(str.length == len)
}
It's probably hard to see that the check str.length == len is not invoked unless eval decides to invoke it until you expand it to it's true form:
def checkMyString(str:String, len:Int) = {
def check = {
str.length == len
}
eval(check)
}
Here, the nested function check has access to str and len due to closure, and this will allow you to get around the requirement that eval must be able to invoke a function with any params that returns a Boolean.
This is just one way to solve your problem, and it might not even be suitable given your needs, but I just wanted to throw it out there.
If your input functions only have 2 arguments, like your two examples, you can write a semi generic function take takes all functions with two arguments of any type:
def eval[A,B](func: (A,B) => Boolean, arg1: A, arg2: B) = {
func(arg1, arg2)
}
def checkLength(str: String, length: Int) : Boolean = {
str.length == length
}
eval(checkLength, "ham", 4)
res0: Boolean = false
But if you want to support functions with more arguments, you would have to write one eval function for three arguments, four arguments, etc
Maybe there is a better way that can handle all cases?
I am trying to figure out the issue, and tried different styles that I have read on Scala, but none of them work. My code is:
....
val str = "(and x y)";
def stringParse ( exp: String, pos: Int, expreshHolder: ArrayBuffer[String], follow: Int )
var b = pos; //position of where in the expression String I am currently in
val temp = expreshHolder; //holder of expressions without parens
var arrayCounter = follow; //just counts to make sure an empty spot in the array is there to put in the strings
if(exp(b) == '(') {
b = b + 1;
while(exp(b) == ' '){b = b + 1} //point of this is to just skip any spaces between paren and start of expression type
if(exp(b) == 'a') {
temp(arrayCounter) = exp(b).toString;
b = b+1;
temp(arrayCounter)+exp(b).toString; b = b+1;
temp(arrayCounter) + exp(b).toString; arrayCounter+=1}
temp;
}
}
val hold: ArrayBuffer[String] = stringParse(str, 0, new ArrayBuffer[String], 0);
for(test <- hold) println(test);
My error is:
Driver.scala:35: error: type mismatch;
found : Unit
required: scala.collection.mutable.ArrayBuffer[String]
ho = stringParse(str, 0, ho, 0);
^one error found
When I add an equals sign after the arguments in the method declaration, like so:
def stringParse ( exp: String, pos: Int, expreshHolder: ArrayBuffer[String], follow: Int ) ={....}
It changes it to "Any". I am confused on how this works. Any ideas? Much appreciated.
Here's a more general answer on how one may approach such problems:
It happens sometimes that you write a function and in your head assume it returns type X, but somewhere down the road the compiler disagrees. This almost always happens when the function has just been written, so while the compiler doesn't give you the actual source (it points to the line where your function is called instead) you normally know that your function's return type is the problem.
If you do not see the type problem straight away, there is the simple trick to explicitly type your function. For example, if you thought your function should have returned Int, but somehow the compiler says it found a Unit, it helps to add : Int to your function. This way, you help the compiler to help you, as it will spot the exact place, where a path in your function returns a non-Int value, which is the actual problem you were looking for in the first place.
You have to add the equals sign if you want to return a value. Now, the reason that your function's return value is Any is that you have 2 control paths, each returning a value of a different type - 1 is when the if's condition is met (and the return value will be temp) and the other is when if's condition isn't (and the return value will be b=b+1, or b after it's incremented).
class Test(condition: Boolean) {
def mixed = condition match {
case true => "Hi"
case false => 100
}
def same = condition match {
case true => List(1,2,3)
case false => List(4,5,6)
}
case class Foo(x: Int)
case class Bar(x: Int)
def parent = condition match {
case true => Foo(1)
case false => Bar(1)
}
}
val test = new Test(true)
test.mixed // type: Any
test.same // type List[Int]
test.parent // type is Product, the case class super type
The compiler will do its best to apply the most specific type it can based on the possible set of result types returned from the conditional (match, if/else, fold, etc.).
In the Lua wiki I found a way to define default values for missing arguments:
function myfunction(a,b,c)
b = b or 7
c = c or 5
print (a,b,c)
end
Is that the only way? The PHP style myfunction (a,b=7,c=5) does not seem to work. Not that the Lua way doesn't work, I am just wondering if this is the only way to do it.
If you want named arguments and default values like PHP or Python, you can call your function with a table constructor:
myfunction{a,b=3,c=2}
(This is seen in many places in Lua, such as the advanced forms of LuaSocket's protocol modules and constructors in IUPLua.)
The function itself could have a signature like this:
function myfunction(t)
setmetatable(t,{__index={b=7, c=5}})
local a, b, c =
t[1] or t.a,
t[2] or t.b,
t[3] or t.c
-- function continues down here...
end
Any values missing from the table of parameters will be taken from the __index table in its metatable (see the documentation on metatables).
Of course, more advanced parameter styles are possible using table constructors and functions- you can write whatever you need. For example, here is a function that constructs a function that takes named-or-positional argument tables from a table defining the parameter names and default values and a function taking a regular argument list.
As a non-language-level feature, such calls can be changed to provide new behaviors and semantics:
Variables could be made to accept more than one name
Positional variables and keyword variables can be interspersed - and defining both can give precedence to either (or cause an error)
Keyword-only positionless variables can be made, as well as nameless position-only ones
The fairly-verbose table construction could be done by parsing a string
The argument list could be used verbatim if the function is called with something other than 1 table
Some useful functions for writing argument translators are unpack (moving to table.unpack in 5.2), setfenv (deprecated in 5.2 with the new _ENV construction), and select (which returns a single value from a given argument list, or the length of the list with '#').
In my opinion there isn't another way. That's just the Lua mentality: no frills, and except for some syntactic sugar, no redundant ways of doing simple things.
Technically, there's b = b == nil and 7 or b (which should be used in the case where false is a valid value as false or 7 evaluates to 7), but that's probably not what you're looking for.
The only way i've found so far that makes any sense is to do something like this:
function new(params)
params = params or {}
options = {
name = "Object name"
}
for k,v in pairs(params) do options[k] = v end
some_var = options.name
end
new({ name = "test" })
new()
If your function expects neither Boolean false nor nil to be passed as parameter values, your suggested approach is fine:
function test1(param)
local default = 10
param = param or default
return param
end
--[[
test1(): [10]
test1(nil): [10]
test1(true): [true]
test1(false): [10]
]]
If your function allows Boolean false, but not nil, to be passed as the parameter value, you can check for the presence of nil, as suggested by Stuart P. Bentley, as long as the default value is not Boolean false:
function test2(param)
local default = 10
param = (param == nil and default) or param
return param
end
--[[
test2(): [10]
test2(nil): [10]
test2(true): [true]
test2(false): [false]
]]
The above approach breaks when the default value is Boolean false:
function test3(param)
local default = false
param = (param == nil and default) or param
return param
end
--[[
test3(): [nil]
test3(nil): [nil]
test3(true): [true]
test3(false): [false]
]]
Interestingly, reversing the order of the conditional checks does allow Boolean false to be the default value, and is nominally more performant:
function test4(param)
local default = false
param = param or (param == nil and default)
return param
end
--[[
test4(): [false]
test4(nil): [false]
test4(true): [true]
test4(false): [false]
]]
This approach works for reasons that seem counter-intuitive until further examination, upon which they are discovered to be kind of clever.
If you want default parameters for functions that do allow nil values to be passed, you'll need to do something even uglier, like using variadic parameters:
function test5(...)
local argN = select('#', ...)
local default = false
local param = default
if argN > 0 then
local args = {...}
param = args[1]
end
return param
end
--[[
test5(): [false]
test5(nil): [nil]
test5(true): [true]
test5(false): [false]
]]
Of course, variadic parameters completely thwart auto-completion and linting of function parameters in functions that use them.
Short answer is that it's simplest and best way . in lua , variables by default equal with nil . this means if we don't pass argument to lua functions ,the argument is exits but is nil and lua programmers uses of this lua attribute for set the default value .
also it's not a way for set default value but you can use following function
this function create a error is you don't pass values to arguments
function myFn(arg1 , arg2)
err = arg1 and arg2
if not err then error("argument") end
-- or
if not arg1 and arg2 then error("msg") end
but it's not a good way and better is don't use of this function
and in diagrams shows optional argument in [,arg]
function args(a1 [,a2])
-- some
end
function args ( a1 [,a2[,a3]])
-- some
end
As always, "Lua gives you the power, you build the mechanisms". The first distinction to make here is that between named parameters and the commonly used parameter list.
The parameter list
Assuming all your args are given in the parameter list as follows, they will all be initialized. At this point, you can't distinguish between "wasn't passed" and "was passed as nil" - both will simply be nil. Your options for setting defaults are:
Using the or operator if you expect a truthy value (not nil or false). Defaulting to something even if false is given might be a feature in this case.
Using an explicit nil check param == nil, used either as if param == nil then param = default end or the typical Lua ternary construct param == nil and default or param.
If you find yourself frequently repeating the patterns from point (2), you might want to declare a function:
function default(value, default_value)
if value == nil then return default_value end
return value
end
(whether to use global or local scope for this function is another issue I won't get into here).
I've included all three ways the following example:
function f(x, y, z, w)
x = x or 1
y = y == nil and 2 or y
if z == nil then z == 3 end
w = default(w, 4
print(x, y, z, w)
end
f()
f(1)
f(1, 2)
f(1, 2, 3)
f(1, 2, 3, 4)
note that this also allows omitting arguments inbetween; trailing nil arguments will also be treated as absent:
f(nil)
f(nil, 2, 3)
f(nil, 2, nil, 4)
f(1, 2, 3, nil)
Varargs
A lesser known feature of Lua is the ability to actually determine how many arguments were passed, including the ability to distinguish between explicitly passed nil arguments and "no argument" through the select function. Let's rewrite our function using this:
function f(...)
local n_args = select("#", ...) -- number of arguments passed
local x, y, z, w = ...
if n_args < 4 then w = 4 end
if n_args < 3 then z = 3 end
if n_args < 2 then y = 2 end
if n_args < 1 then x = 1 end
print(x, y, z, w)
end
f() -- prints "1 2 3 4"
f(nil) -- prints "nil 2 3 4"
f(1, nil) -- prints "1 nil 3 4"
f(1, nil, 3) -- prints "1 nil 3 4"
f(nil, nil, nil, nil) -- prints 4x nil
Caveat: (1) the argument list got dragged into the function, hurting readability (2) this is rather cumbersome to write manually, and should probably be abstracted away, perhaps time using a wrapper function wrap_defaults({1, 2, 3, 4}, f) that supplies the defaults as appropriate. Implementation of this is left up to the reader as an exercise (hint: the straightforward way would first collect the args into a garbage table, then unpack that after setting the defaults).
Table calls
Lua provides syntactic sugar for calling functions with a single table as the only argument: f{...} is equivalent to f({...}). Furthermore, {f(...)} can be used to capture a vararg returned by f (caveat: if f returns nils, the table will have holes in it's list part).
Tables also allow implementing named "arguments" as table fields: Tables allow mixing a list and a hash part, making f{1, named_arg = 2} perfectly valid Lua.
In terms of limitations, the advantage of table call is that it only leaves a single argument - the table - on the stack rather than multiple arguments. For recursive functions, this allows hitting the stack overflow later. Since PUC Lua drastically increased the stack limit to ~1M this isn't much of an issue anymore; LuaJIT still has a stack limit of ~65k however, and PUC Lua 5.1 is even lower at around 15k.
In terms of performance & memory consumption, the table call is obviously worse: It requires Lua to build a garbage table, which will then waste memory until the GC gets rid of it. Garbage parameter tables should therefore probably not be used in hotspots where plenty of calls happen. Indexing a hashmap is also obviously slower than getting values straight off the stack.
That said, let's examine the ways to implement defaults for tables:
Unpacking / Destructuring
unpack (table.unpack in later versions (5.2+)) can be used to convert a table into a vararg, which can be treated like a parameter list; note however that in Lua the list part can't have trailing nil values, not allowing you to distinguish "no value" and nil. Unpacking / destructuring to locals also helps performance since it gets rid of repeated table indexing.
function f(params)
local x, y, z, w = unpack(params)
-- use same code as if x, y, z, w were regular params
end
f{1, 2, nil}
if you use named fields, you'll have to explicitly destructure those:
function f(params)
local x, y, z, w = params.x, params.y, params.z, params.w
-- use same code as if x, y, z, w were regular params
end
f{x = 1, w = 4}
mix & match is possible:
function f(params)
local x, y, z = unpack(params)
local w = params.w
-- use same code as if x, y, z, w were regular params
end
f{1, 2, w = 4}
Metatables
The __index metatable field can be used to set a table which is indexed with name if params.name is nil, providing defaults for nil values. One major drawback of setting a metatable on a passed table is that the passed table's metatable will be lost, perhaps leading to unexpected behavior on the caller's end. You could use getmetatable and setmetatable to restore the metatable after you're done operating with the params, but that would be rather dirty, hence I would recommend against it.
Bad
function f(params)
setmetatable(params, {__index = {x = 1, y = 2, z = 3, w = 4}})
-- use params.[xyzw], possibly unpacking / destructuring
end
f{x = 1}
in addition to the presumably garbage params table, this will create (1) a garbage metatable and (2) a garbage default table every time the function is called. This is pretty bad. Since the metatable is constant, simply drag it out of the function, making it an upvalue:
Okay
local defaults_metatable = {__index = {x = 1, y = 2, z = 3, w = 4}}
function f(params)
setmetatable(params, defaults_metatable)
-- use params.[xyzw], possibly unpacking / destructuring
end
Avoiding metatables
If you want a default table without the hackyness of metatables, consider once again writing yourself a helper function to complete a table with default values:
local function complete(params, defaults)
for param, default in pairs(defaults) do
if params[param] == nil then
params[param] = default
end
end
end
this will change the params table, properly setting the defaults; use as params = complete(params, defaults). Again, remember to drag the defaults table out of the function.
I quite often see on the Internet various complaints that other peoples examples of currying are not currying, but are actually just partial application.
I've not found a decent explanation of what partial application is, or how it differs from currying. There seems to be a general confusion, with equivalent examples being described as currying in some places, and partial application in others.
Could someone provide me with a definition of both terms, and details of how they differ?
Currying is converting a single function of n arguments into n functions with a single argument each. Given the following function:
function f(x,y,z) { z(x(y));}
When curried, becomes:
function f(x) { lambda(y) { lambda(z) { z(x(y)); } } }
In order to get the full application of f(x,y,z), you need to do this:
f(x)(y)(z);
Many functional languages let you write f x y z. If you only call f x y or f(x)(y) then you get a partially-applied function—the return value is a closure of lambda(z){z(x(y))} with passed-in the values of x and y to f(x,y).
One way to use partial application is to define functions as partial applications of generalized functions, like fold:
function fold(combineFunction, accumulator, list) {/* ... */}
function sum = curry(fold)(lambda(accum,e){e+accum}))(0);
function length = curry(fold)(lambda(accum,_){1+accum})(empty-list);
function reverse = curry(fold)(lambda(accum,e){concat(e,accum)})(empty-list);
/* ... */
#list = [1, 2, 3, 4]
sum(list) //returns 10
#f = fold(lambda(accum,e){e+accum}) //f = lambda(accumulator,list) {/*...*/}
f(0,list) //returns 10
#g = f(0) //same as sum
g(list) //returns 10
The easiest way to see how they differ is to consider a real example. Let's assume that we have a function Add which takes 2 numbers as input and returns a number as output, e.g. Add(7, 5) returns 12. In this case:
Partial applying the function Add with a value 7 will give us a new function as output. That function itself takes 1 number as input and outputs a number. As such:
Partial(Add, 7); // returns a function f2 as output
// f2 takes 1 number as input and returns a number as output
So we can do this:
f2 = Partial(Add, 7);
f2(5); // returns 12;
// f2(7)(5) is just a syntactic shortcut
Currying the function Add will give us a new function as output. That function itself takes 1 number as input and outputs yet another new function. That third function then takes 1 number as input and returns a number as output. As such:
Curry(Add); // returns a function f2 as output
// f2 takes 1 number as input and returns a function f3 as output
// i.e. f2(number) = f3
// f3 takes 1 number as input and returns a number as output
// i.e. f3(number) = number
So we can do this:
f2 = Curry(Add);
f3 = f2(7);
f3(5); // returns 12
In other words, "currying" and "partial application" are two totally different functions. Currying takes exactly 1 input, whereas partial application takes 2 (or more) inputs.
Even though they both return a function as output, the returned functions are of totally different forms as demonstrated above.
Note: this was taken from F# Basics an excellent introductory article for .NET developers getting into functional programming.
Currying means breaking a function with many arguments into a series
of functions that each take one argument and ultimately produce the
same result as the original function. Currying is probably the most
challenging topic for developers new to functional programming, particularly because it
is often confused with partial application. You can see both at work
in this example:
let multiply x y = x * y
let double = multiply 2
let ten = double 5
Right away, you should see behavior that is different from most
imperative languages. The second statement creates a new function
called double by passing one argument to a function that takes two.
The result is a function that accepts one int argument and yields the
same output as if you had called multiply with x equal to 2 and y
equal to that argument. In terms of behavior, it’s the same as this
code:
let double2 z = multiply 2 z
Often, people mistakenly say that multiply is curried to form double.
But this is only somewhat true. The multiply function is curried, but
that happens when it is defined because functions in F# are curried by
default. When the double function is created, it’s more accurate to
say that the multiply function is partially applied.
The multiply function is really a series of two functions. The first
function takes one int argument and returns another function,
effectively binding x to a specific value. This function also accepts
an int argument that you can think of as the value to bind to y. After
calling this second function, x and y are both bound, so the result is
the product of x and y as defined in the body of double.
To create double, the first function in the chain of multiply
functions is evaluated to partially apply multiply. The resulting
function is given the name double. When double is evaluated, it uses
its argument along with the partially applied value to create the
result.
Interesting question. After a bit of searching, "Partial Function Application is not currying" gave the best explanation I found. I can't say that the practical difference is particularly obvious to me, but then I'm not an FP expert...
Another useful-looking page (which I confess I haven't fully read yet) is "Currying and Partial Application with Java Closures".
It does look like this is widely-confused pair of terms, mind you.
I have answered this in another thread https://stackoverflow.com/a/12846865/1685865 . In short, partial function application is about fixing some arguments of a given multivariable function to yield another function with fewer arguments, while Currying is about turning a function of N arguments into a unary function which returns a unary function...[An example of Currying is shown at the end of this post.]
Currying is mostly of theoretical interest: one can express computations using only unary functions (i.e. every function is unary). In practice and as a byproduct, it is a technique which can make many useful (but not all) partial functional applications trivial, if the language has curried functions. Again, it is not the only means to implement partial applications. So you could encounter scenarios where partial application is done in other way, but people are mistaking it as Currying.
(Example of Currying)
In practice one would not just write
lambda x: lambda y: lambda z: x + y + z
or the equivalent javascript
function (x) { return function (y){ return function (z){ return x + y + z }}}
instead of
lambda x, y, z: x + y + z
for the sake of Currying.
Currying is a function of one argument which takes a function f and returns a new function h. Note that h takes an argument from X and returns a function that maps Y to Z:
curry(f) = h
f: (X x Y) -> Z
h: X -> (Y -> Z)
Partial application is a function of two(or more) arguments which takes a function f and one or more additional arguments to f and returns a new function g:
part(f, 2) = g
f: (X x Y) -> Z
g: Y -> Z
The confusion arises because with a two-argument function the following equality holds:
partial(f, a) = curry(f)(a)
Both sides will yield the same one-argument function.
The equality is not true for higher arity functions because in this case currying will return a one-argument function, whereas partial application will return a multiple-argument function.
The difference is also in the behavior, whereas currying transforms the whole original function recursively(once for each argument), partial application is just a one step replacement.
Source: Wikipedia Currying.
Simple answer
Curry: lets you call a function, splitting it in multiple calls, providing one argument per-call.
Partial: lets you call a function, splitting it in multiple calls, providing multiple arguments per-call.
Simple hints
Both allow you to call a function providing less arguments (or, better, providing them cumulatively). Actually both of them bind (at each call) a specific value to specific arguments of the function.
The real difference can be seen when the function has more than 2 arguments.
Simple e(c)(sample)
(in Javascript)
We want to run the following process function on different subjects (e.g. let's say our subjects are "subject1" and "foobar" strings):
function process(context, successCallback, errorCallback, subject) {...}
why always passing the arguments, like context and the callbacks, if they will be always the same?
Just bind some values for the the function:
processSubject = _.partial(process, my_context, my_success, my_error)
// assign fixed values to the first 3 arguments of the `process` function
and call it on subject1 and foobar, omitting the repetition of the first 3 arguments, with:
processSubject('subject1');
processSubject('foobar');
Comfy, isn't it? 😉
With currying you'd instead need to pass one argument per time
curriedProcess = _.curry(process); // make the function curry-able
processWithBoundedContext = curriedProcess(my_context);
processWithCallbacks = processWithBoundedContext(my_success)(my_error); // note: these are two sequential calls
result1 = processWithCallbacks('subject1');
// same as: process(my_context, my_success, my_error, 'subject1');
result2 = processWithCallbacks('foobar');
// same as: process(my_context, my_success, my_error, 'foobar');
Disclaimer
I skipped all the academic/mathematical explanation. Cause I don't know it. Maybe it helped 🙃
EDIT:
As added by #basickarl, a further slight difference in use of the two functions (see Lodash for examples) is that:
partial returns a pre-cooked function that can be called once with the missing argument(s) and return the final result;
while curry is being called multiple times (one for each argument), returning a pre-cooked function each time; except in the case of calling with the last argument, that will return the actual result from the processing of all the arguments.
With ES6:
here's a quick example of how immediate Currying and Partial-application are in ECMAScript 6.
const partialSum = math => (eng, geo) => math + eng + geo;
const curriedSum = math => eng => geo => math + eng + geo;
The difference between curry and partial application can be best illustrated through this following JavaScript example:
function f(x, y, z) {
return x + y + z;
}
var partial = f.bind(null, 1);
6 === partial(2, 3);
Partial application results in a function of smaller arity; in the example above, f has an arity of 3 while partial only has an arity of 2. More importantly, a partially applied function would return the result right away upon being invoke, not another function down the currying chain. So if you are seeing something like partial(2)(3), it's not partial application in actuality.
Further reading:
Functional Programming in 5 minutes
Currying: Contrast with Partial Function Application
I had this question a lot while learning and have since been asked it many times. The simplest way I can describe the difference is that both are the same :) Let me explain...there are obviously differences.
Both partial application and currying involve supplying arguments to a function, perhaps not all at once. A fairly canonical example is adding two numbers. In pseudocode (actually JS without keywords), the base function may be the following:
add = (x, y) => x + y
If I wanted an "addOne" function, I could partially apply it or curry it:
addOneC = curry(add, 1)
addOneP = partial(add, 1)
Now using them is clear:
addOneC(2) #=> 3
addOneP(2) #=> 3
So what's the difference? Well, it's subtle, but partial application involves supplying some arguments and the returned function will then execute the main function upon next invocation whereas currying will keep waiting till it has all the arguments necessary:
curriedAdd = curry(add) # notice, no args are provided
addOne = curriedAdd(1) # returns a function that can be used to provide the last argument
addOne(2) #=> returns 3, as we want
partialAdd = partial(add) # no args provided, but this still returns a function
addOne = partialAdd(1) # oops! can only use a partially applied function once, so now we're trying to add one to an undefined value (no second argument), and we get an error
In short, use partial application to prefill some values, knowing that the next time you call the method, it will execute, leaving undefined all unprovided arguments; use currying when you want to continually return a partially-applied function as many times as necessary to fulfill the function signature. One final contrived example:
curriedAdd = curry(add)
curriedAdd()()()()()(1)(2) # ugly and dumb, but it works
partialAdd = partial(add)
partialAdd()()()()()(1)(2) # second invocation of those 7 calls fires it off with undefined parameters
Hope this helps!
UPDATE: Some languages or lib implementations will allow you to pass an arity (total number of arguments in final evaluation) to the partial application implementation which may conflate my two descriptions into a confusing mess...but at that point, the two techniques are largely interchangeable.
For me partial application must create a new function where the used arguments are completely integrated into the resulting function.
Most functional languages implement currying by returning a closure: do not evaluate under lambda when partially applied. So, for partial application to be interesting, we need to make a difference between currying and partial application and consider partial application as currying plus evaluation under lambda.
I could be very wrong here, as I don't have a strong background in theoretical mathematics or functional programming, but from my brief foray into FP, it seems that currying tends to turn a function of N arguments into N functions of one argument, whereas partial application [in practice] works better with variadic functions with an indeterminate number of arguments. I know some of the examples in previous answers defy this explanation, but it has helped me the most to separate the concepts. Consider this example (written in CoffeeScript for succinctness, my apologies if it confuses further, but please ask for clarification, if needed):
# partial application
partial_apply = (func) ->
args = [].slice.call arguments, 1
-> func.apply null, args.concat [].slice.call arguments
sum_variadic = -> [].reduce.call arguments, (acc, num) -> acc + num
add_to_7_and_5 = partial_apply sum_variadic, 7, 5
add_to_7_and_5 10 # returns 22
add_to_7_and_5 10, 11, 12 # returns 45
# currying
curry = (func) ->
num_args = func.length
helper = (prev) ->
->
args = prev.concat [].slice.call arguments
return if args.length < num_args then helper args else func.apply null, args
helper []
sum_of_three = (x, y, z) -> x + y + z
curried_sum_of_three = curry sum_of_three
curried_sum_of_three 4 # returns a function expecting more arguments
curried_sum_of_three(4)(5) # still returns a function expecting more arguments
curried_sum_of_three(4)(5)(6) # returns 15
curried_sum_of_three 4, 5, 6 # returns 15
This is obviously a contrived example, but notice that partially applying a function that accepts any number of arguments allows us to execute a function but with some preliminary data. Currying a function is similar but allows us to execute an N-parameter function in pieces until, but only until, all N parameters are accounted for.
Again, this is my take from things I've read. If anyone disagrees, I would appreciate a comment as to why rather than an immediate downvote. Also, if the CoffeeScript is difficult to read, please visit coffeescript.org, click "try coffeescript" and paste in my code to see the compiled version, which may (hopefully) make more sense. Thanks!
I'm going to assume most people who ask this question are already familiar with the basic concepts so their is no need to talk about that. It's the overlap that is the confusing part.
You might be able to fully use the concepts, but you understand them together as this pseudo-atomic amorphous conceptual blur. What is missing is knowing where the boundary between them is.
Instead of defining what each one is, it's easier to highlight just their differences—the boundary.
Currying is when you define the function.
Partial Application is when you call the function.
Application is math-speak for calling a function.
Partial application requires calling a curried function and getting a function as the return type.
A lot of people here do not address this properly, and no one has talked about overlaps.
Simple answer
Currying: Lets you call a function, splitting it in multiple calls, providing one argument per-call.
Partial Application: Lets you call a function, splitting it in multiple calls, providing multiple arguments per-call.
One of the significant differences between the two is that a call to a
partially applied function returns the result right away, not another
function down the currying chain; this distinction can be illustrated
clearly for functions whose arity is greater than two.
What does that mean? That means that there are max two calls for a partial function. Currying has as many as the amount of arguments. If the currying function only has two arguments, then it is essentially the same as a partial function.
Examples
Partial Application and Currying
function bothPartialAndCurry(firstArgument) {
return function(secondArgument) {
return firstArgument + secondArgument;
}
}
const partialAndCurry = bothPartialAndCurry(1);
const result = partialAndCurry(2);
Partial Application
function partialOnly(firstArgument, secondArgument) {
return function(thirdArgument, fourthArgument, fifthArgument) {
return firstArgument + secondArgument + thirdArgument + fourthArgument + fifthArgument;
}
}
const partial = partialOnly(1, 2);
const result = partial(3, 4, 5);
Currying
function curryOnly(firstArgument) {
return function(secondArgument) {
return function(thirdArgument) {
return function(fourthArgument ) {
return function(fifthArgument) {
return firstArgument + secondArgument + thirdArgument + fourthArgument + fifthArgument;
}
}
}
}
}
const curryFirst = curryOnly(1);
const currySecond = curryFirst(2);
const curryThird = currySecond(3);
const curryFourth = curryThird(4);
const result = curryFourth(5);
// or...
const result = curryOnly(1)(2)(3)(4)(5);
Naming conventions
I'll write this when I have time, which is soon.
There are other great answers here but I believe this example (as per my understanding) in Java might be of benefit to some people:
public static <A,B,X> Function< B, X > partiallyApply( BiFunction< A, B, X > aBiFunction, A aValue ){
return b -> aBiFunction.apply( aValue, b );
}
public static <A,X> Supplier< X > partiallyApply( Function< A, X > aFunction, A aValue ){
return () -> aFunction.apply( aValue );
}
public static <A,B,X> Function< A, Function< B, X > > curry( BiFunction< A, B, X > bif ){
return a -> partiallyApply( bif, a );
}
So currying gives you a one-argument function to create functions, where partial-application creates a wrapper function that hard codes one or more arguments.
If you want to copy&paste, the following is noisier but friendlier to work with since the types are more lenient:
public static <A,B,X> Function< ? super B, ? extends X > partiallyApply( final BiFunction< ? super A, ? super B, X > aBiFunction, final A aValue ){
return b -> aBiFunction.apply( aValue, b );
}
public static <A,X> Supplier< ? extends X > partiallyApply( final Function< ? super A, X > aFunction, final A aValue ){
return () -> aFunction.apply( aValue );
}
public static <A,B,X> Function< ? super A, Function< ? super B, ? extends X > > curry( final BiFunction< ? super A, ? super B, ? extends X > bif ){
return a -> partiallyApply( bif, a );
}
In writing this, I confused currying and uncurrying. They are inverse transformations on functions. It really doesn't matter what you call which, as long as you get what the transformation and its inverse represent.
Uncurrying isn't defined very clearly (or rather, there are "conflicting" definitions that all capture the spirit of the idea). Basically, it means turning a function that takes multiple arguments into a function that takes a single argument. For example,
(+) :: Int -> Int -> Int
Now, how do you turn this into a function that takes a single argument? You cheat, of course!
plus :: (Int, Int) -> Int
Notice that plus now takes a single argument (that is composed of two things). Super!
What's the point of this? Well, if you have a function that takes two arguments, and you have a pair of arguments, it is nice to know that you can apply the function to the arguments, and still get what you expect. And, in fact, the plumbing to do it already exists, so that you don't have to do things like explicit pattern matching. All you have to do is:
(uncurry (+)) (1,2)
So what is partial function application? It is a different way to turn a function in two arguments into a function with one argument. It works differently though. Again, let's take (+) as an example. How might we turn it into a function that takes a single Int as an argument? We cheat!
((+) 0) :: Int -> Int
That's the function that adds zero to any Int.
((+) 1) :: Int -> Int
adds 1 to any Int. Etc. In each of these cases, (+) is "partially applied".
Currying
Wikipedia says
Currying is the technique of converting a function that takes multiple arguments into a sequence of functions that each takes a single argument.
Example
const add = (a, b) => a + b
const addC = (a) => (b) => a + b // curried function. Where C means curried
Partial application
Article Just Enough FP: Partial Application
Partial application is the act of applying some, but not all, of the arguments to a function and returning a new function awaiting the rest of the arguments. These applied arguments are stored in closure and remain available to any of the partially applied returned functions in the future.
Example
const add = (a) => (b) => a + b
const add3 = add(3) // add3 is a partially applied function
add3(5) // 8
The difference is
currying is a technique (pattern)
partial application is a function with some predefined arguments (like add3 from the previous example)