[Haskell-cafe] Just how unsafe is unsafe

[Jake McArthur]

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Peter Verswyvelen wrote:
| I do have asked myself the question whether a "really random generating"
| function could be regarded as "pure" somehow (actually would a true
| random function still be a mathematical function?)
|
| E.g. the function would return a true (not pseudo) random number,
| practically unpredictable (e.g. hardware assisted, using some physical
| phenomenon, e.g. using atmospheric noise or something). So you surely
| won't get referential transparency but since the function is really
| random, this would be correct behavior?

An informal definition of a function might be something like a black box
that takes and input and produces an output, and for each possible
input, the output must be the same. Taking this to be a function, there
is really no such thing as a random function, and if there was, it
wouldn't even need to be a function. (What would the input to it be?)

If you wanted to mathematically represent a random number, it would, in
most cases I can think of, best be represented as a free variable. In a
program, such a free variable could be filled in by the runtime.
Conveniently, (and by no coincidence) this is something the IO monad can
provide for us! :)

| Of course you could just put this random generator in the IO monad, but
| certain algorithms- like Monte Carlo - intuitively don't seem to operate
| in a IO monad to me.

Why not?

A Random monad might be more appropriate in this case anyway. Such a
monad is a State monad that hold a random seed. Every time a random
number is needed, the seed is passed to a deterministic psuedo-random
number generator, and a new seed is put as the next state.

If a truly random number is ever needed, either IO or unsafeInterleaveIO
will be needed. The use of unsafeInterleaveIO would be a (rightly)
controversial choice though.

- - Jake
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