Creating New Effects

We have now seen several side-effecting operations provided by the Effects library, and examples of their use in Section Simple Effects. We have also seen how operations may modify the available effects by changing state in Section Dependent Effects. We have not, however, yet seen how these operations are implemented. In this section, we describe how a selection of the available effects are implemented, and show how new effectful operations may be provided.

State

Effects are described by algebraic data types, where the constructors describe the operations provided when the effect is available. Stateful operations are described as follows:

data State : Effect where
     Get :      State a  a (\x => a)
     Put : b -> State () a (\x => b)

Effect itself is a type synonym, giving the required type for an effect signature:

Effect : Type
Effect = (result : Type) ->
         (input_resource : Type) ->
         (output_resource : result -> Type) -> Type

Each effect is associated with a resource. The second argument to an effect signature is the resource type on input to an operation, and the third is a function which computes the resource type on output. Here, it means:

• Get takes no arguments. It has a resource of type a, which is not updated, and running the Get operation returns something of type a.
• Put takes a b as an argument. It has a resource of type a on input, which is updated to a resource of type b. Running the Put operation returns the element of the unit type.

The effects library provides an overloaded function sig which can make effect signatures more concise, particularly when the result has no effect on the resource type. For State, we can write:

data State : Effect where
     Get :      sig State a  a
     Put : b -> sig State () a b

There are four versions of sig, depending on whether we are interested in the resource type, and whether we are updating the resource. Idris will infer the appropriate version from usage.

NoResourceEffect.sig : Effect -> Type -> Type
NoUpdateEffect.sig   : Effect -> (ret : Type) ->
                                 (resource : Type) -> Type
UpdateEffect.sig     : Effect -> (ret : Type) ->
                                 (resource_in : Type) ->
                                 (resource_out : Type) -> Type
DepUpdateEffect.sig  : Effect -> (ret : Type) ->
                                 (resource_in : Type) ->
                                 (resource_out : ret -> Type) -> Type

In order to convert State (of type Effect) into something usable in an effects list, of type EFFECT, we write the following:

STATE : Type -> EFFECT
STATE t = MkEff t State

MkEff constructs an EFFECT by taking the resource type (here, the t which parameterises STATE) and the effect signature (here, State). For reference, EFFECT is declared as follows:

data EFFECT : Type where
     MkEff : Type -> Effect -> EFFECT

Recall that to run an effectful program in Eff, we use one of the run family of functions to run the program in a particular computation context m. For each effect, therefore, we must explain how it is executed in a particular computation context for run to work in that context. This is achieved with the following interface:

interface Handler (e : Effect) (m : Type -> Type) where
      handle : resource -> (eff : e t resource resource') ->
               ((x : t) -> resource' x -> m a) -> m a

We have already seen some implementation declarations in the effect summaries in Section Simple Effects. An implementation of Handler e m means that the effect declared with signature e can be run in computation context m. The handle function takes:

• The resource on input (so, the current value of the state for State)
• The effectful operation (either Get or Put x for State)
• A continuation, which we conventionally call k, and should be passed the result value of the operation, and an updated resource.

There are two reasons for taking a continuation here: firstly, this is neater because there are multiple return values (a new resource and the result of the operation); secondly, and more importantly, the continuation can be called zero or more times.

A Handler for State simply passes on the value of the state, in the case of Get, or passes on a new state, in the case of Put. It is defined the same way for all computation contexts:

Handler State m where
     handle st Get     k = k st st
     handle st (Put n) k = k () n

This gives enough information for Get and Put to be used directly in Eff programs. It is tidy, however, to define top level functions in Eff, as follows:

get : Eff x [STATE x]
get = call Get

put : x -> Eff () [STATE x]
put val = call (Put val)

putM : y -> Eff () [STATE x] [STATE y]
putM val = call (Put val)

An implementation detail (aside): The call function converts an Effect to a function in Eff, given a proof that the effect is available. This proof can be constructed automatically by , since it is essentially an index into a statically known list of effects:

call : {e : Effect} ->
       (eff : e t a b) -> {auto prf : EffElem e a xs} ->
       Eff t xs (\v => updateResTy v xs prf eff)

This is the reason for the Can’t solve goal error when an effect is not available: the implicit proof prf has not been solved automatically because the required effect is not in the list of effects xs.

Such details are not important for using the library, or even writing new effects, however.

Summary

The following listing summarises what is required to define the STATE effect:

data State : Effect where
     Get :      sig State a  a
     Put : b -> sig State () a b

STATE : Type -> EFFECT
STATE t = MkEff t State

Handler State m where
     handle st Get     k = k st st
     handle st (Put n) k = k () n

get : Eff x [STATE x]
get = call Get

put : x -> Eff () [STATE x]
put val = call (Put val)

putM : y -> Eff () [STATE x] [STATE y]
putM val = call (Put val)

Console I/O

Then listing below gives the definition of the STDIO effect, including handlers for IO and IOExcept. We omit the definition of the top level Eff functions, as this merely invoke the effects PutStr, GetStr, PutCh and GetCh directly.

Note that in this case, the resource is the unit type in every case, since the handlers merely apply the IO equivalents of the effects directly.

data StdIO : Effect where
     PutStr : String -> sig StdIO ()
     GetStr : sig StdIO String
     PutCh : Char -> sig StdIO ()
     GetCh : sig StdIO Char

Handler StdIO IO where
    handle () (PutStr s) k = do putStr s; k () ()
    handle () GetStr     k = do x <- getLine; k x ()
    handle () (PutCh c)  k = do putChar c; k () ()
    handle () GetCh      k = do x <- getChar; k x ()

Handler StdIO (IOExcept a) where
    handle () (PutStr s) k = do ioe_lift $ putStr s; k () ()
    handle () GetStr     k = do x <- ioe_lift $ getLine; k x ()
    handle () (PutCh c)  k = do ioe_lift $ putChar c; k () ()
    handle () GetCh      k = do x <- ioe_lift $ getChar; k x ()

STDIO : EFFECT
STDIO = MkEff () StdIO

Exceptions

The listing below gives the definition of the Exception effect, including two of its handlers for Maybe and List. The only operation provided is Raise. The key point to note in the definitions of these handlers is that the continuation k is not used. Running Raise therefore means that computation stops with an error.

data Exception : Type -> Effect where
     Raise : a -> sig (Exception a) b

Handler (Exception a) Maybe where
     handle _ (Raise e) k = Nothing

Handler (Exception a) List where
     handle _ (Raise e) k = []

EXCEPTION : Type -> EFFECT
EXCEPTION t = MkEff () (Exception t)

Non-determinism

The following listing gives the definition of the Select effect for writing non-deterministic programs, including a handler for List context which returns all possible successful values, and a handler for Maybe context which returns the first successful value.

data Selection : Effect where
     Select : List a -> sig Selection a

Handler Selection Maybe where
     handle _ (Select xs) k = tryAll xs where
         tryAll [] = Nothing
         tryAll (x :: xs) = case k x () of
                                 Nothing => tryAll xs
                                 Just v => Just v

Handler Selection List where
     handle r (Select xs) k = concatMap (\x => k x r) xs

SELECT : EFFECT
SELECT = MkEff () Selection

Here, the continuation is called multiple times in each handler, for each value in the list of possible values. In the List handler, we accumulate all successful results, and in the Maybe handler we try the first value in the list, and try later values only if that fails.

File Management

Result-dependent effects are no different from non-dependent effects in the way they are implemented. The listing below illustrates this for the FILE_IO effect. The syntax for state transitions { x ==> {res} x’ }, where the result state x’ is computed from the result of the operation res, follows that for the equivalent Eff programs.

data FileIO : Effect where
     Open : (fname: String)
            -> (m : Mode)
            -> sig FileIO Bool () (\res => case res of
                                                True => OpenFile m
                                                False => ())
     Close : sig FileIO () (OpenFile m)

     ReadLine  :           sig FileIO String (OpenFile Read)
     WriteLine : String -> sig FileIO ()     (OpenFile Write)
     EOF       :           sig FileIO Bool   (OpenFile Read)

Handler FileIO IO where
    handle () (Open fname m) k = do h <- openFile fname m
                                    if !(validFile h)
                                             then k True (FH h)
                                             else k False ()
    handle (FH h) Close      k = do closeFile h
                                    k () ()

    handle (FH h) ReadLine        k = do str <- fread h
                                         k str (FH h)
    handle (FH h) (WriteLine str) k = do fwrite h str
                                         k () (FH h)
    handle (FH h) EOF             k = do e <- feof h
                                         k e (FH h)

FILE_IO : Type -> EFFECT
FILE_IO t = MkEff t FileIO

Note that in the handler for Open, the types passed to the continuation k are different depending on whether the result is True (opening succeeded) or False (opening failed). This uses validFile, defined in the Prelude, to test whether a file handler refers to an open file or not.