What is a lambda function

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For a person without a comp-sci background  what is a lambda in the world of Computer Science

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For a person without a comp-sci background, what is a lambda in the world of Computer Science?

I will illustrate it intuitively step by step in simple and readable python codes.

In short, a lambda is just an anonymous and inline function.

Let's start from assignment to understand lambdas as a freshman with background of basic arithmetic.

The blueprint of assignment is 'the name = value', see:

In [1]: x = 1
   ...: y = 'value'
In [2]: x
Out[2]: 1
In [3]: y
Out[3]: 'value'

'x', 'y' are names and 1, 'value' are values. Try a function in mathematics

In [4]: m = n**2 + 2*n + 1
NameError: name 'n' is not defined

Error reports,
you cannot write a mathematic directly as code,'n' should be defined or be assigned to a value.

In [8]: n = 3.14
In [9]: m = n**2 + 2*n + 1
In [10]: m
Out[10]: 17.1396

It works now,what if you insist on combining the two seperarte lines to one. There comes lambda

In [13]: j = lambda i: i**2 + 2*i + 1
In [14]: j
Out[14]: <function __main__.<lambda>>

No errors reported.

This is a glance at lambda, it enables you to write a function in a single line as you do in mathematic into the computer directly.

We will see it later.

Let's continue on digging deeper on 'assignment'.

As illustrated above, the equals symbol = works for simple data(1 and 'value') type and simple expression(n**2 + 2*n + 1).

Try this:

In [15]: x = print('This is a x')
This is a x
In [16]: x
In [17]: x = input('Enter a x: ')
Enter a x: x

It works for simple statements,there's 11 types of them in python 7. Simple statements — Python 3.6.3 documentation

How about compound statement,

In [18]: m = n**2 + 2*n + 1 if n > 0
SyntaxError: invalid syntax
#or
In [19]: m = n**2 + 2*n + 1, if n > 0
SyntaxError: invalid syntax

There comes def enable it working

In [23]: def m(n):
    ...:     if n > 0:
    ...:         return n**2 + 2*n + 1
    ...:
In [24]: m(2)
Out[24]: 9

Tada, analyse it, 'm' is name, 'n**2 + 2*n + 1' is value.: is a variant of '='.
Find it, if just for understanding, everything starts from assignment and everything is assignment.

Now return to lambda, we have a function named 'm'

Try:

In [28]: m = m(3)
In [29]: m
Out[29]: 16

There are two names of 'm' here, function m already has a name, duplicated.

It's formatting like:

In [27]: m = def m(n):
    ...:         if n > 0:
    ...:             return n**2 + 2*n + 1
    SyntaxError: invalid syntax

It's not a smart strategy, so error reports

We have to delete one of them,set a function without a name.

m = lambda n:n**2 + 2*n + 1

It's called 'anonymous function'

In conclusion,

lambda in an inline function which enable you to write a function in one straight line as does in mathematics
lambda is anonymous

Hope, this helps.

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The lambda calculus is a consistent mathematical theory of substitution  In school mathematics one sees for example x y 5 paired with x-y 1  Along with ways to manipulate individual equations it s also possible to put the information from these two together  provided cross-equation substitutions are done logically  Lambda calculus codifies the correct way to do these substitutions   Given that y   x-1 is a valid rearrangement of the second equation  this    y   x-1 means a function substituting the symbols x-1 for the symbol y  Now imagine applying   y to each term in the first equation  If a term is y then perform the substitution  otherwise do nothing  If you do this out on paper you ll see how applying that   y will make the first equation solvable   That s an answer without any computer science or programming   The simplest programming example I can think of comes from http   en wikipedia org wiki Joy  programming language  How it works      here is how the square function might be defined in an imperative   programming language  C    int square int x        return x   x          The variable x is a formal parameter which is replaced by the actual   value to be squared when the function is called  In a functional   language  Scheme  the same function would be defined    define square    lambda  x          x x          This is different in many ways  but it still uses the formal parameter   x in the same way      Added  http   imgur com a XBHub

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An example of a lambda in Ruby is as follows   hello   lambda do     puts  Hello       puts  I am inside a proc   end  hello call   Will genereate the following output   Hello I am inside a proc

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Just because I cant see a C  11 example here  I ll go ahead and post this nice example from here  After searching  it is the clearest language specific example that I could find   Hello  Lambdas  version 1  template lt typename F gt   void Eval  const F amp  f                f      void foo                Eval      printf  Hello  Lambdas n             Hello  Lambdas  version 2   void bar            auto f       printf  Hello  Lambdas n              f

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Lambda explained for everyone  Lambda is an annonymous function  This means lambda is a function objekt in Python that doesnt require a reference before  Let s concider this bit of code here  def name of func         command instruction     print  hello    print type name of func      the name of the function is a reference                              the reference contains a function Objekt with command instruction  To proof my proposition I print out the type of name of func which returns us   lt class  function  gt   A function must have a interface  but a interface dosent needs to contain something  What does this mean  Let s look a little bit closer to our function and we may notice that out of the name of the functions there are some more details we need to explain to understand what a function is  A regular function will be defined with the syntax  quot def quot   then we type in the name and settle the interface with  quot    quot  and ending our definition by the syntax  quot   quot   Now we enter the functions body with our instructions commands  So let s consider this bit of code here  def print my argument x       print x    print my argument  Hello    In this case we run our function  named  quot print my argument quot  and passing a parameter argument through the interface  The Output will be  Hello  So now that we know what a function is and how the architecture works for a function  we can take a look to an annonymous function  Let s consicder this bit of code here  def name of func        print  Hello      lambda  print  Hello    these function objekts are pretty much the same except of the fact that the upper  regular function have a name and the other function is an annonymous one  Let s take a closer look on our annonymous function  to understand how to use it  So let s concider this bit of code here  def delete last char arg1 None       print arg1  -1    string    Hello World  delete last char string   f   lambda arg1 None  print arg1  -1   f string   So what we have done in the above code is to write once againg  a regular function and an anonymous function  Our anonymous function we had assignd to a var  which is pretty much the same as to give this function a name  Anyway  the output will be  Hello Worl Hello Worl  To fully proof that lambda is a function object and doesnt just mimik a function we run this bit of code here  string    Hello World  f   lambda arg1 string  print arg1  -1   f   print type f    and the Output will be  Hello Worl  lt class  function  gt   Last but not least you should know that every function in python needs to return something  If nothing is defined in the body of the function  None will be returned by default  look at this bit of code here  def delete last char arg1       print arg1  -1    string    Hello World  x   delete last char string   f   lambda arg1 string  print arg1  -1   x2   f    print x  print x2   Output will be  Hello Worl Hello Worl None None

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A Lambda Function  or a Small Anonymous Function  is a self-contained block of functionality that can be passed around and used in your code  Lambda has different names in different programming languages     Lambda in Python and Kotlin  Closure in Swift  or Block in C and Objective-C  Although lambda s meaning is quite similar for these languages it has slight distinctions sometimes    Let s see how Lambda  Closure  works in Swift 4 2 with sorted   method     from normal function till the shortest expression   let coffee   String      Cappuccino    Espresso    Latte    Ristretto     1  Normal Function  func backward   n1  String    n2  String  - gt  Bool       return n1  gt  n2   var reverseOrder   coffee sorted by  backward       RESULT    Ristretto    Latte    Espresso    Cappuccino     2  Closure Expression  reverseOrder   coffee sorted by     n1  String  n2  String  - gt  Bool in     return n1  gt  n2      3  Inline Closure Expression  reverseOrder   coffee sorted by     n1  String  n2  String  - gt  Bool in return n1  gt  n2       4  Inferring Type From Context  reverseOrder   coffee sorted by    n1  n2 in return n1  gt  n2       5  Implicit Returns from Single-Expression Closures  reverseOrder   coffee sorted by    n1  n2 in n1  gt  n2       6  Shorthand Argument Names  reverseOrder   coffee sorted by     0  gt   1          0 and  1 are closure   s first and second String arguments    7  Operator Methods  reverseOrder   coffee sorted by   gt       RESULT    Ristretto    Latte    Espresso    Cappuccino     Hope this helps

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In computer programming  lambda is a piece of code  statement  expression or a group of them  which takes some arguments from an external source  It must not always be an anonymous function - we have many ways to implement them   We have clear separation between expressions  statements and functions  which mathematicians do not have   The word  function  in programming is also different - we have  function is a series of steps to do   from Latin  perform    In math it is something about correlation between variables   Functional languages are trying to be as similar to math formulas as possible  and their words mean almost the same  But in other programming languages we have it different

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You can think of it as an anonymous function - here s some more info  Wikipedia - Anonymous Function

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The question has been answered fully  I don t want to go into details  I want to share the usage when writing numerical computation in rust   There is an example of a lambda anonymous function   let f    x  f32  - gt  f32   x   x - 2 0    let df    x  f32  - gt  f32   2 0   x      When I was writing a module of Newton   Raphson method  it was used as first and second order derivative   If you want to know what is Newton   Raphson method  please visit  https   en wikipedia org wiki Newton 27s method     The output as the following  println   f    6       df    6    f 10 0   df 10 0    f 98 000000       df 20 000000

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It refers to lambda calculus  which is a formal system that just has lambda expressions  which represent a function that takes a function for its sole argument and returns a function  All functions in the lambda calculus are of that type  i e               Lisp used the lambda concept to name its anonymous function literals  This lambda represents a function that takes two arguments  x and y  and returns their product    lambda  x y     x y      It can be applied in-line like this  evaluates to 50      lambda  x y     x y   5 10

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I have trouble wrapping my head around lambda expressions because I work in Visual FoxPro  which has Macro substitution and the ExecScript   and Evaluate   functions  which seem to serve much the same purpose     Calculator 10  23   a   b     Calculator 10  23   a - b     FUNCTION Calculator a  b  op  RETURN Evaluate op    One definite benefit to using formal lambdas is  I assume  compile-time checking  Fox won t know if you typo the text string above until it tries to run it   This is also useful for data-driven code  you can store entire routines in memo fields in the database and then just evaluate them at run-time  This lets you tweak part of the application without actually having access to the source   But that s another topic altogether

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Imagine that you have a restaurant with a delivery option and you have an order that needs to be done in under 30 minutes  The point is clients usually don t care if you send their food by bike with a car or barefoot as long as you keep the meal warm and tied up  So lets convert this idiom to Javascript with anonymous and defined transportation functions   Below we defined the way of our delivering aka we define a name to a function      ES5  var food   function withBike kebap  coke    return  kebap   coke         What if we would use arrow lambda functions to accomplish this transfer      ES6     const food    kebap  coke    gt    return kebap   coke      You see there is no difference for client and no time wasting to think about how to send food  Just send it   Btw  I don t recommend the kebap with coke this is why upper codes will give you errors  Have fun

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In Javascript  for example  functions are treated as the same mixed type as everything else  int  string  float  bool   As such  you can create functions on the fly  assign them to things  and call them back later  It s useful but  not something you want to over use or you ll confuse everyone who has to maintain your code after you     This is some code I was playing with to see how deep this rabbit hole goes   var x   new Object  x thingy   new Array    x thingy 0    function    return function    return function    alert  index 0 pressed            x thingy 1    function    return function    return function    alert  index 1 pressed            x thingy 2    function    return function    return function    alert  index 2 pressed             for var i 0  i lt 3  i        x thingy i

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The question is formally answered greatly  so I will not try to add more on this   In very simple  informal words to someone that knows very little or nothing on math or programming  I would explain it as a small  machine  or  box  that takes some input  makes some work and produces some output  has no particular name  but we know where it is and by just this knowledge  we use it   Practically speaking  for a person that knows what a function is  I would tell them that it is a function that has no name  usually put to a point in memory that can be used just by referencing to that memory  usually via the usage of a variable - if they have heard about the concept of the function pointers  I would use them as a similar concept  - this answer covers the pretty basics  no mention of closures etc  but one can get the point easily

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It is a function that has no name  For e g  in c  you can use  numberCollection GetMatchingItems lt int gt  number   gt  number  gt  5     to return the numbers that are greater than 5   number   gt  number  gt  5   is the lambda part here  It represents a function which takes a parameter  number  and returns a boolean value  number   5   GetMatchingItems method uses this lambda on all the items in the collection and returns the matching items

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In context of CS a lambda function is an abstract mathematical concept that tackles a problem of symbolic evaluation of mathematical expressions  In that context a lambda function is the same as a lambda term   But in programming languages it s something different  It s a piece of code that is declared  in place   and that can be passed around as a  first-class citizen   This concept appeared to be useful so that it came into almost all popular modern programming languages  see lambda functions everwhere post

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A lambda function can take any number of arguments  but they contain only a single expression      Lambda functions can be used to return function objects  Syntactically  lambda functions are restricted to only a single expression

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Brian I use lambdas all the time in C   in LINQ and non-LINQ operators  Example   string   GetCustomerNames IEnumerable lt Customer gt  customers     return customers Select c  gt c Name        Before C   I used anonymous functions in JavaScript for callbacks to AJAX functions  before the term Ajax was even coined   getXmlFromServer function result     success     function error    fail        The interesting thing with C  s lambda syntax  though  is that on their own their type cannot be infered  i e   you can t type var foo    x y     x   y  but depending on which type they re assigned to  they ll be compiled as delegates or abstract syntax trees representing the expression  which is how LINQ object mappers do their  language-integrated  magic    Lambdas in LISP can also be passed to a quotation operator and then traversed as a list of lists  Some powerful macros are made this way

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A lambda is a type of function  defined inline  Along with a lambda you also usually have some kind of variable type that can hold a reference to a function  lambda or otherwise   For instance  here s a C  piece of code that doesn t use a lambda   public Int32 Add Int32 a  Int32 b        return a   b     public Int32 Sub Int32 a  Int32 b        return a - b     public delegate Int32 Op Int32 a  Int32 b    public void Calculator Int32 a  Int32 b  Op op        Console WriteLine  Calculator  op     a          b            op a  b       public void Test         Calculator 10  23  Add       Calculator 10  23  Sub       This calls Calculator  passing along not just two numbers  but which method to call inside Calculator to obtain the results of the calculation   In C  2 0 we got anonymous methods  which shortens the above code to   public delegate Int32 Op Int32 a  Int32 b    public void Calculator Int32 a  Int32 b  Op op        Console WriteLine  Calculator  op     a          b            op a  b       public void Test         Calculator 10  23  delegate Int32 a  Int32 b                return a   b              Calculator 10  23  delegate Int32 a  Int32 b                return a - b              And then in C  3 0 we got lambdas which makes the code even shorter   public delegate Int32 Op Int32 a  Int32 b    public void Calculator Int32 a  Int32 b  Op op        Console WriteLine  Calculator  op     a          b            op a  b       public void Test         Calculator 10  23   a  b    gt  a   b       Calculator 10  23   a  b    gt  a - b

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Lambda comes from the Lambda Calculus and refers to anonymous functions in programming   Why is this cool  It allows you to write quick throw away functions without naming them  It also provides a nice way to write closures  With that power you can do things like this   Python  def adder x       return lambda y  x   y add5   adder 5  add5 1  6   As you can see from the snippet of Python  the function adder takes in an argument x  and returns an anonymous function  or lambda  that takes another argument y  That anonymous function allows you to create functions from functions  This is a simple example  but it should convey the power lambdas and closures have   Examples in other languages  Perl 5  sub adder       my   x            return sub           my   y                 x    y          my  add5   adder 5   print  amp  add5 1     6    ok n     not ok n     JavaScript  var adder   function  x        return function  y            return x   y            add5   adder 5   add5 1     6   JavaScript  ES6   const adder   x   gt  y   gt  x   y  add5   adder 5   add5 1     6   Scheme   define adder      lambda  x           lambda  y                x y      define add5      adder 5    add5 1  6   C  3 5 or higher  Func lt int  Func lt int  int gt  gt  adder         int x    gt   int y    gt  x   y      int  declarations optional Func lt int  int gt  add5   adder 5   var add6   adder 6      Using implicit typing Debug Assert add5 1     6   Debug Assert add6 -1     5       Closure example int yEnclosed   1  Func lt int  int gt  addWithClosure         x    gt  x   yEnclosed  Debug Assert addWithClosure 2     3     Swift  func adder x  Int  - gt   Int  - gt  Int     return   y in x   y     let add5   adder 5  add5 1  6   PHP   a   1   b   2    lambda   fn      gt   a    b   echo  lambda      Haskell    x y - gt  x   y     Java see this post     The following is an example of Predicate       a functional interface that takes an argument     and returns a boolean primitive type   Predicate lt Integer gt  pred   x - gt  x   2    0     Tests if the parameter is even  boolean result   pred test 4      true   Lua  adder   function x      return function y          return x   y     end end add5   adder 5  add5 1     6        -- true   Kotlin  val pred     x  Int - gt  x   2    0   val result   pred 4     true   Ruby  Ruby is slightly different in that you cannot call a lambda using the exact same syntax as calling a function  but it still has lambdas   def adder x    lambda    y  x   y   end add5   adder 5  add5 1     6   Ruby being Ruby  there is a shorthand for lambdas  so you can define adder this way   def adder x    - gt  y   x   y   end   R    adder  lt - function x      function y  x   y   add5  lt - adder 5  add5 1    gt   1  6

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I like the explanation of Lambdas in this article  The Evolution Of LINQ And Its Impact On The Design Of C   It made a lot of sense to me as it shows a real world for Lambdas and builds it out as a practical example   Their quick explanation  Lambdas are a way to treat code  functions  as data

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The name  lambda  is just a historical artifact  All we re talking about is an expression whose value is a function   A simple example  using Scala for the next line  is   args foreach arg   gt  println arg     where the argument to the foreach method is an expression for an anonymous function  The above line is more or less the same as writing something like this  not quite real code  but you ll get the idea    void printThat Object that      println that        args foreach printThat    except that you don t need to bother with    Declaring the function somewhere else  and having to look for it when you revisit the code later   Naming something that you re only using once    Once you re used to function values  having to do without them seems as silly as being required to name every expression  such as   int tempVar   2   a   b     println tempVar    instead of just writing the expression where you need it   println 2   a   b    The exact notation varies from language to language  Greek isn t always required    -

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Slightly oversimplified  a lambda function is one that can be passed round to other functions and it s logic accessed   In C  lambda syntax is often compiled to simple methods in the same way as anonymous delegates  but it can also be broken down and its logic read   For instance  in C 3    LinqToSqlContext Where       row   gt  row FieldName  gt  15      LinqToSql can read that function  x   15  and convert it to the actual SQL to execute using expression trees   The statement above becomes   select     from  tablename   where  FieldName   gt  15      --this line was  read  from the lambda function   This is different from normal methods or anonymous delegates  which are just compiler magic really  because they cannot be read   Not all methods in C  that use lambda syntax can be compiled to expression trees  i e  actual lambda functions   For instance   LinqToSqlContext Where       row   gt  SomeComplexCheck  row FieldName        Now the expression tree cannot be read - SomeComplexCheck cannot be broken down  The SQL statement will execute without the where  and every row in the data will be put through SomeComplexCheck   Lambda functions should not be confused with anonymous methods  For instance   LinqToSqlContext Where       delegate   DataRow row              return row FieldName  gt  15              This also has an  inline  function  but this time it s just compiler magic - the C  compiler will split this out to a new instance method with an autogenerated name    Anonymous methods can t be read  and so the logic can t be translated out as it can for lambda functions

[lambda] What is a lambda (function)?

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