``functional'' vs imperative programming

If all of the ``functional programming'' programs that ever existed disappeared, nobody would notice except for the people who work on ``functional programming'' compilers.

If all of the imperative programs that ever existed disappeared, there would be no more programs, including critical parts of ``functional programming'' software.

Check em

Lambda calculus is inherently functional programming. Lambda calculus is the mathematical basis of all computing.

>>3
Lambda calculus has nothing to do with mathematics or computing.

>>4
What does it have anything to do with, then? Your anus?

For example, the function
sqsum(x, y) = x^2 + y^2
can be rewritten in anonymous form as
@(x, y) -> x^2 + y^2
(read as "the pair of x and y is mapped to x^2 + y^2

For example,
@(x, y) -> x^2 + y^2

can be reworked into

@(x) -> ( @(y) -> x^2 + y^2) ?

This method, known as currying, transforms a function that takes multiple arguments into a chain of functions each with a single argument.

I don't quite see how it is one argument though, there are obviously still two

Nice way to make the addition function more complicated than the square / square root function

>>5
https://en.wikipedia.org/wiki/Deductive_lambda_calculus

Alonzo Church invented the lambda calculus in the 1930s, originally to provide a new and simpler basis for mathematics.[1][2] However soon after inventing it major logic problems were identified with the definition of the lambda abstraction: The Kleene–Rosser paradox is an implementation of Richard's paradox in the lambda calculus.[3] Haskell Curry found that the key step in this paradox could be used to implement the simpler Curry's paradox. The existence of these paradoxes meant that the lambda calculus could not be both consistent and complete as a deductive system.[4]

This was the original reason for lambda calculus. It was a failure there too, but it's still useful as a money sink for getting grants. Every time they ``patch'' lambda calculus to solve some problem that normal math already solves, it gets more and more complicated.

Can anyone honestly say homotopy type theory (or whatever the latest version is called) is a ``simpler basis for mathematics'' than set theory?

>>8
You're confusing the original intent of a mathematician's work and the application of that work. Lambda calculus is a branch of mathematics that is used the form the mathematical foundation of computation.

Under set theory, natural numbers are defined in terms of sets. Zero is defined to be the empty set, and n + 1 as {n}. Thus, the concept of a number ultimately relies on one's intuition of an object, or a ``being.'' Under the lambda calculus, on the other hand, natural numbers are defined in terms of function application. The number zero is defined as a function f which is applied zero times, and n + 1 as f applied to n. Unlike set theory, the concept of a number relies on one's intuition of a process, or a ``doing.'' In a manner of speaking, natural numbers occupy space when defined using set theory, but they occupy time when defined using the lambda calculus. If anything, the lambda calculus provides a refreshing perspective on the natural numbers.

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