The Monad Challenges

A set of challenges for jump starting your understanding of monads.

Outline

Set 1: Random Numbers

Set 2: Failing Computations

Set 3: Combinations

Set 4: Common Abstraction

Set 5: Do Notation

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Threading the random number state

In the previous exercise we wrote something that handled the threading of state through a list of generators. A simpler idea is to have a function that does one step of two generators and the necessary state threading. Now write a function called genTwo that does this. Its first argument will be a generator. Its second argument will be a function that takes the result of the first generator and returns a second generator. The type signature looks like this:

genTwo :: Gen a -> (a -> Gen b) -> Gen b

Implement this function.

Now look at the implementation of your repRandom function. It probably has one clause handling the empty list case. That case probably looks something like this:

repRandom [] s = ([], s)

repRandom was expecting a list of generators and it’s supposed to return a generator. In the empty list case it has no incoming generators to work with but it still has to return one. Esentially what’s happening here is it has to construct a Gen out of thin air. It turns out that this is a really common pattern. So let’s make a function for it. We’ll call this function mkGen. It has to return a Gen a. But it has to get the a from somewhere, so that will have to be the argument.

Implement mkGen. Try to figure out the type signature yourself, but if you need help here it is hex-encoded: 6D6B47656E203A3A2061202D3E2047656E2061.

You can decode it with this online hex decoder.

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