functional dependencies vs type families

Question

I'm developing a framework for running experiments with artificial life, and I'm trying to use type families instead of functional dependencies. Type families seems to be the preferred approach among Haskellers, but I've run into a situation where functional dependencies seem like a better fit. Am I missing a trick? Here's the design using type families. (This code compiles OK.)

{-# LANGUAGE TypeFamilies, FlexibleContexts #-}

import Control.Monad.State (StateT)

class Agent a where
  agentId :: a -> String
  liveALittle :: Universe u => a -> StateT u IO a
  -- plus other functions

class Universe u where
  type MyAgent u :: *
  withAgent :: (MyAgent u -> StateT u IO (MyAgent u)) -> 
    String -> StateT u IO ()
  -- plus other functions

data SimpleUniverse = SimpleUniverse
  {
    mainDir :: FilePath
    -- plus other fields
  }

defaultWithAgent :: (MyAgent u -> StateT u IO (MyAgent u)) -> String -> 
  StateT u IO ()
defaultWithAgent = undefined -- stub

-- plus default implementations for other functions

--
-- In order to use my framework, the user will need to create a typeclass
-- that implements the Agent class...
--

data Bug = Bug String deriving (Show, Eq)

instance Agent Bug where
  agentId (Bug s) = s
  liveALittle bug = return bug -- stub

--
-- .. and they'll also need to make SimpleUniverse an instance of Universe
-- for their agent type.
--

instance Universe SimpleUniverse where
  type MyAgent SimpleUniverse = Bug
  withAgent = defaultWithAgent     -- boilerplate
  -- plus similar boilerplate for other functions

Is there a way to avoid forcing my users to write those last two lines of boilerplate? Compare with the version using fundeps, below, which seems to make things simpler for my users. (The use of UndecideableInstances may be a red flag.) (This code also compiles OK.)

{-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies, FlexibleInstances,
    UndecidableInstances #-}

import Control.Monad.State (StateT)

class Agent a where
  agentId :: a -> String
  liveALittle :: Universe u a => a -> StateT u IO a
  -- plus other functions

class Universe u a | u -> a where
  withAgent :: Agent a => (a -> StateT u IO a) -> String -> StateT u IO ()
  -- plus other functions

data SimpleUniverse = SimpleUniverse
  {
    mainDir :: FilePath
    -- plus other fields
  }

instance Universe SimpleUniverse a where
  withAgent = undefined -- stub
  -- plus implementations for other functions

--
-- In order to use my framework, the user will need to create a typeclass
-- that implements the Agent class...
--

data Bug = Bug String deriving (Show, Eq)

instance Agent Bug where
  agentId (Bug s) = s
  liveALittle bug = return bug -- stub

--
-- And now my users only have to write stuff like...
--

u :: SimpleUniverse
u = SimpleUniverse "mydir"

Edit: In trying to present a simple example, I omitted part of the motivation for my design.

The #1 role that the Universe class plays is serialising and deserialising agents, so I think it has to be linked to the Agent class. It also has readAgent and writeAgent functions. However, I wanted to ensure that the user couldn't accidentally forget to write an agent after modifying it, so instead of exporting those functions, I provide a withAgent function that takes care of everything. The withAgent function takes two parameters: a function that runs on an agent, and the name (unique ID) of the agent to run the program on. It reads the file containing that agent, runs the program, and writes the updated agent back out to the file. (I could instead just export the readAgent and writeAgent functions.)

There is also a Daemon class that is responsible for giving each agent its fair share of the CPU. So inside the daemon's main loop, it queries the universe for a current list of agents. Then, for each agent, it invokes the withAgent function to run the liveAlittle program for that agent. The daemon doesn't care what type the agent is.

There is one other user of the withAgent function: the agent itself. Inside the agent's liveALittle function, it might query the universe for a list of agents, in order a possible mating partner. It will invoke the withAgent function to run some sort of mating function. Obviously an agent can only mate with another agent of the same species (typeclass).

EDIT: Here's the solution I think I will use. Not type families or functional dependencies, but now I have to do something so that the compiler will know which liveALittle to call. The way I've done that is to have the user supply the correct liveALittle as a parameter.

{-# LANGUAGE DeriveGeneric #-}

import Control.Monad.State (StateT)
import Data.Serialize (Serialize)
import GHC.Generics (Generic)

class Agent a where
  agentId :: a -> String
  liveALittle :: Universe u => a -> StateT u IO a
  -- plus other functions

class Universe u where
  -- Given the name of an agent, read it from a file, and let it run.
  withAgent :: (Agent a, Serialize a) => 
    (a -> StateT u IO a) -> String -> StateT u IO ()
  -- plus other functions

-- This method will be called by a daemon
daemonTask :: (Universe u, Agent a, Serialize a) => 
  (a -> StateT u IO a) -> StateT u IO ()
daemonTask letAgentLiveALittle = do
  -- do some stuff
  withAgent letAgentLiveALittle "a"
  -- do some other stuff

data SimpleUniverse = SimpleUniverse
  {
    mainDir :: FilePath
    -- plus other fields
  }

instance Universe SimpleUniverse where
  withAgent = undefined -- stub
  -- plus implementations for other functions

--
-- And now my users only have to write stuff like...
--

data Bug = Bug String deriving (Show, Eq, Generic)

instance Serialize Bug

instance Agent Bug where
  agentId (Bug s) = s
  liveALittle bug = return bug -- stub

Can every actor be used in every universe, or is it, as your code says, that each universe only is usable by one type of actor? — dflemstr
I don't mind if each universe is only usable by one instance of Agent, because the user can take advantage of algebraic data types to support more than one species of agent. I had an approach using existential types that would allow multiple Agent instances to be used in a universe. However, that approach was criticised (justifiably, I think) for being un-Haskellish. — mhwombat

AndrewC AndrewC · Accepted Answer · 2012-10-18T18:15:26

Type Families vs Multi Parameter Type Classes with Functional Dependencies

To answer the question in the title, Functional dependencies tend to be rather counter-intuitive, so it's more of a headache to get them working. Type Families are much easier to use, and so much more intuitive for a functional programmer, that I would recommend you always try using them first (unless you absolutely need the extra type parameter for making instances of some other class over which you have no control).

In your case, I'm not sure you need either, which is, I believe, why you're running into problems.

What do your Universe classes and instances say?

Both the class definitions tie the user to using each universe once, whereas they might like to reuse a universe with a different agent type.

Let's look at what's going on in your Universe instances:

Type Families: You make an instance by writing a lot of boilerplate just reusing a standard set of functions wholesale. This suggests you didn't need to know the particular type of MyAgent to deal with it. There doesn't seem to be an Agent context on any of the functions. Hmmm.
Functional Dependencies: you use instance Universe SimpleUniverse a where... and magically your Agent Bug instance gives you a working Universe. That's because your instance declaration used the type a so at the matching end of the equation, didn't use any facts about a.

This leads me to suspect you don't need to link the universe and the agents so strongly. Suggestion 1: Is it possible to have two separate but linked classes:

class Universe u where
   withAgents :: Agents a => (a -> StateT u IO a) -> String -> StateT u IO ()

Here you're saying the universe has to accept any Agents type, not one specific Agents type. I've renamed Agent to Agents to suggest to the users that they use it to represent all their agent types in a union type as you pointed out.

class Agents a where
   agentId :: a -> String
   liveALittle :: Universe u => a -> StateT u IO a

Here you're saying an Agents type has to be able to interact with any sort of universe.

The nature of the universe

The fact that you feel you can write default declarations like

defaultWithAgent :: (MyAgent u -> StateT u IO (MyAgent u)) -> String -> StateT u IO ()

or declare an instance that doesn't use any information about Bug:

instance Universe SimpleUniverse a where
    withAgent = ...

suggests you can write withAgent without reference to the types u or a.

Suggestion 2: Can you ditch the Universe class altogether in favour of either a TheUniverse type so you define

withAgent :: (Agents a => a -> StateT TheUniverse IO a) -> String -> StateT TheUniverse IO ()

which I'm not convinced will suit you, or...

Suggestion 3: Ditch the Universe class restriction altogether, and make withAgent work with any type.

withAgent :: (Agents a => a -> StateT u IO a) -> String -> StateT u IO ()

It's hard to say what's best without knowing what other functions you need, but hopefully one of these might help. I only make suggestions 2 and 3 because you seemed to be saying a default definition always works. Maybe in reality some functions need to be in the Universe class becuase they use the structure of the universe but not the internal details of the Agents. Maybe others belong in Agents because although they use a Universe, they just use class functions, not the internal details. In any case we have:

Overarching suggestion:

Think carefully about what level of detail about a Agents or the Universe the function needs. If it's both, maybe you could refactor into two separate helper functions, so no function needs to know the inner workings of both the Universe and Agents. That way you don't need a type class that has both types. There'd be no need for either TypeFamilies or FunDeps.