Hi Oleg, Thanks for the links! These are quite interesting. 1. Here is one situation that occurs in evolutionary biology where I would want to have the full range of Haskell syntax available to me. Consider a binary tree, where each tree node has an integer name in [1..num_nodes tree]. The function (parent tree n) gives the parent of node n and (root tree) gives the root node. -- the expected value for a node is the value at its parent mean node tree x | node == root tree = 0 | otherwise = x!!parent tree node -- given a tree, simulate down the tree, simulate_on_tree tree = let x = [sample $ normal (mean node tree x) 1 | node <- [1..num_nodes tree]] My understanding is that you cannot refer to the result of a computation while performing a computation, as in: do {x <- simulate_on_tree tree x} Am I missing something? On 01/11/2018 12:02 PM, Oleg Grenrus wrote:
(a) Non-determism is an effect, e.g. simple list is non-determinism monad, for small discrete distributions!
(b) Yes. We can write effectful code "implicitly" - You might look into *Automatically Escaping Monads* - https://www.youtube.com/watch?v=wG8AErq6Bbo, slides: http://benl.ouroborus.net/talks/2016-HIW-Escape.pdf - http://disciple.ouroborus.net/ or https://github.com/DDCSF/ddc
Interstingly, while searching for the paper, I stumbled upon Oleg Kiselyov's (not me) paper from *Effects Without Monads: Non-determinism*, which is a different approach. Maybe that's what you are looking after http://okmij.org/ftp/tagless-final/nondet-paper.pdf
2. Why would we want to consider non-determinism (in the sense of returning an unpredictable value) as an effect? Certainly running a non-deterministic function does not change global state like modifying an IORef would. I'm also thinking of functions that are (somehow) TRULY random, so they are not keeping a hidden state around somewhere. I'm calling them "non-deterministic" instead of "random" because I want to ignore (for the moment) the probability distribution, and just say that the result is arbitrary. 3. Sampling from a normal distribution gives ONE value, and the list of possible values is .... large :-) [i.e. it would include all Double values.] 4. Interesting - I like his approach to making the box / run instructions implicit. 5. In this paper, it seems that non-determinism means returning ALL possible outcomes. However, what I meant is arbitrarily choosing ONE possible outcome. My terminology is probably being imported from statistics - is there a different word I should use here? -BenRI