Dear Benjamin,

I'm not sure I quite get your problem. My guess: you want a type-level guarantee that `turnOff'` function will only be applied to the terms of type `State True`, and so, you expect a compile-time error from `turnOff' off`. Am I get it right?

In your solution you seem to over engineer the solution. You try to relate type-level informaton (the value of of the type parameter `s` of `State`) to the term-level one (the value of the field stored in the `State` datatype). I think you'd better read how this task is solved with the technique known as singletons (https://cs.brynmawr.edu/~rae/papers/2012/singletons/paper.pdf).

But I bet you don't need to solve that task to just address the problem at hand, if I understand the problem correctly. Please, tell me if the simpler solution below suits you: it doesn't use term-level (field of State) information at all.

{-# LANGUAGE DataKinds, TypeFamilies #-}

data State (s :: Bool) = State deriving Show

off :: State False
off = State

type family TurnOff s where
  TurnOff True = False

turnOff :: State True -> State False
turnOff State = State

bad = turnOff off  --  <-- error: Couldn't match type ‘'False’ with ‘'True’

main = print bad

https://ideone.com/boWN1q

--

Best, Artem

On Fri, 22 Jun 2018 at 12:46 Benjamin Franksen <ben.franksen@online.de> wrote:

I have observed that type functions seem to be lazy. A type function
that is partial does not give me a type error when it is called with an
argument for which it is not defined.

Is there a 'seq' at the type level?

Here is my use case, simplified of course. Suppose we want to statically
track the state of a switch with a phantom type parameter:

> {-# LANGUAGE DataKinds, TypeFamilies #-}
>
> data State (s :: Bool) = State Bool deriving Show
>
> off :: State False
> off = State False

We want user code to be able to call the function 'turnOff' only if the
switch is currently on:

> turnOff :: State True -> State False
> turnOff (State True) = State False

This works fine:

*Main> turnOff off

<interactive>:1:9: error:
    ? Couldn't match type ?'False? with ?'True?
      Expected type: State 'True
        Actual type: State 'False

But now I want to abstract this pattern and write a (closed) type function

> type family TurnOff s where
>   TurnOff True = False

> turnOff' :: State x -> State (TurnOff x)
> turnOff' (State True) = State False

> bad = turnOff' off

*Main> :t bad
bad :: State (TurnOff 'False)
*Main> bad
*** Exception: TypeLevelSeq.lhs:37:3-37: Non-exhaustive patterns in
function turnOff'

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