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Challenges by default ask for submissions that are either functions or complete programs. Historically Brain-Flak submissions have been complete programs because there is no way to define functions like in other languages.

However code Snippets in Brain-Flak can be thought of as functions because they do return a value.

For example:

In Brain-Flak,

()()()()

is arguably the same thing as

lambda:4

in Python.

The latter would be a valid answer if the question was a question to output 4 so why not the former?

The argument for functions with input is a little more tenuous since the Stack is more like a global variable than a input, but one might say that

{({})({}[()])}{}

and

lambda x:x**2

are equivalent and thus the former is also a function. To what extent can snippets written in Brain-Flak (and other Flaks such as Brain-Flueue or Micro-Flak) be considered functions for PPCG submissions?

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    \$\begingroup\$ I don't see why it is lambda: 4 rather than just 4. There is no way to reference the function without using the entire thing so it's much rather a code snippet \$\endgroup\$ – Downgoat Jan 4 '17 at 6:38
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However code Snippets in Brain-Flak can be thought of as functions because they do return a value.

I would disagree with that. Code snippets in brain-flak don't return a value, they simply evaluate to a certain value. To reiterate what some other users have already said,

()()()()

is not equivalent to

lambda: 4

in python, it's equivalent to

4

They both produce a value, and have no side effect. You can do things with this value, such as

print(4)
a=4

in python, or

(()()()())
(((()()()()))<>)

in brain-flak, but it's not a function by itself. Similarly, your other example is equivalent to:

input() ** 2

not

lambda x:x**2

The crucial difference here is that in the python example, it defines a block of code that can be saved and reused later, while the brain-flak code is just a snippet that evaluates to a certain value. Since brain-flak has no ability to save and reuse a piece of code, I would say it has no functions. The same would apply to the various flak-variations (mini-flak, brain-fleue), brainfuck, and other similar tarpits.

So I would propose that brain-flak has no functions, and treating snippets as functions should not be allowed.

On a related note, I found the following proposed default IO methods on meta while I was thinking over this answer:

Given the way brain-flak implicitly pushes all input to the stack, and implicitly prints all values left on the stack, if brain-flak had functions it wouldn't make any difference. A hypothetical function in brain-flak would be the same length as the full program with standard IO.

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