Here's the briefest explanation:
A Turing Complete system means a system in which a program can be written that will find an answer (although with no guarantees regarding runtime or memory).
So, if somebody says "my new thing is Turing Complete" that means in principle (although often not in practice) it could be used to solve any computation problem.
Sometimes it's a joke... a guy wrote a Turing Machine simulator in vi, so it's possible to say that vi is the only computational engine ever needed in the world.
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 $add5 = adder(5);
print &$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 => y => 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<int, Func<int, int>> adder =
(int x) => (int y) => x + y; // `int` declarations optional
Func<int, int> 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<int, int> addWithClosure =
(x) => x + yEnclosed;
Debug.Assert(addWithClosure(2) == 3);
Swift
func adder(x: Int) -> (Int) -> Int{
return { y in x + y }
}
let add5 = adder(5)
add5(1)
6
PHP
$a = 1;
$b = 2;
$lambda = fn () => $a + $b;
echo $lambda();
Haskell
(\x y -> 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<Integer> pred = x -> 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 -> 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)
-> y { x + y }
end
R
adder <- function(x) {
function(y) x + y
}
add5 <- adder(5)
add5(1)
#> [1] 6
Best Solution
Imagine you're in a queue to purchase food at a restaurant, for which pregnant women have priority. And there's just a whole bunch of pregnant women arriving all the time.
You'll soon be starving. ;)
Now imagine you are a low-priority process and the pregnant women are higher priority ones. =)