We have now seen several side-effecting operations provided by the Effects
library, and examples of their use in Section sect-simpleff
. We have also seen how operations may modify the available effects by changing state in Section sect-depeff
. 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.
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 typea
, which is not updated, and running theGet
operation returns something of typea
.Put
takes ab
as an argument. It has a resource of typea
on input, which is updated to a resource of typeb
. Running thePut
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 sect-simpleff
. 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 forState
) - The effectful operation (either
Get
orPut x
forState
) - 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.
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)
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
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)
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.
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.