Dependent Effects¶
In the programs we have seen so far, the available effects have remained constant. Sometimes, however, an operation can change the available effects. The simplest example occurs when we have a state with a dependent type—adding an element to a vector also changes its type, for example, since its length is explicit in the type. In this section, we will see how the library supports this. Firstly, we will see how states with dependent types can be implemented. Secondly, we will see how the effects can depend on the result of an effectful operation. Finally, we will see how this can be used to implement a type-safe and resource-safe protocol for file management.
Dependent States¶
Suppose we have a function which reads input from the console, converts
it to an integer, and adds it to a list which is stored in a STATE.
It might look something like the following:
readInt : Eff () [STATE (List Int), STDIO]
readInt = do let x = trim !getStr
put (cast x :: !get)
But what if, instead of a list of integers, we would like to store a
Vect, maintaining the length in the type?
readInt : Eff () [STATE (Vect n Int), STDIO]
readInt = do let x = trim !getStr
put (cast x :: !get)
This will not type check! Although the vector has length n on entry
to readInt, it has length S n on exit. The library allows us to
express this as follows:
readInt : Eff () [STATE (Vect n Int), STDIO]
[STATE (Vect (S n) Int), STDIO]
readInt = do let x = trim !getStr
putM (cast x :: !get)
The type Eff a xs xs' means that the operation
begins with effects xs available, and ends with effects xs’
available. We have used putM to update the state, where the M
suffix indicates that the type is being updated as well as the value.
It has the following type:
putM : y -> Eff () [STATE x] [STATE y]
Result-dependent Effects¶
Often, whether a state is updated could depend on the success or
otherwise of an operation. In our readInt example, we might wish to
update the vector only if the input is a valid integer (i.e. all
digits). As a first attempt, we could try the following, returning a
Bool which indicates success:
readInt : Eff Bool [STATE (Vect n Int), STDIO]
[STATE (Vect (S n) Int), STDIO]
readInt = do let x = trim !getStr
case all isDigit (unpack x) of
False => pure False
True => do putM (cast x :: !get)
pure True
Unfortunately, this will not type check because the vector does not get
extended in both branches of the case!
MutState.idr:18:19:When elaborating right hand side of Main.case
block in readInt:
Unifying n and S n would lead to infinite value
Clearly, the size of the resulting vector depends on whether or not the value read from the user was valid. We can express this in the type:
readInt : Eff Bool [STATE (Vect n Int), STDIO]
(\ok => if ok then [STATE (Vect (S n) Int), STDIO]
else [STATE (Vect n Int), STDIO])
readInt = do let x = trim !getStr
case all isDigit (unpack x) of
False => pureM False
True => do putM (cast x :: !get)
pureM True
Using pureM rather than pure allows the output effects to be
calculated from the value given. Its type is:
pureM : (val : a) -> EffM m a (xs val) xs
When using readInt, we will have to check its return
value in order to know what the new set of effects is. For example, to
read a set number of values into a vector, we could write the following:
readN : (n : Nat) ->
Eff () [STATE (Vect m Int), STDIO]
[STATE (Vect (n + m) Int), STDIO]
readN Z = pure ()
readN {m} (S k) = case !readInt of
True => rewrite plusSuccRightSucc k m in readN k
False => readN (S k)
The case analysis on the result of readInt means that we know in
each branch whether reading the integer succeeded, and therefore how
many values still need to be read into the vector. What this means in
practice is that the type system has verified that a necessary dynamic
check (i.e. whether reading a value succeeded) has indeed been done.
Note
Only case will work here. We cannot use if/then/else
because the then and else branches must have the same
type. The case construct, however, abstracts over the value
being inspected in the type of each branch.
File Management¶
A practical use for dependent effects is in specifying resource usage protocols and verifying that they are executed correctly. For example, file management follows a resource usage protocol with the following (informally specified) requirements:
- It is necessary to open a file for reading before reading it
- Opening may fail, so the programmer should check whether opening was successful
- A file which is open for reading must not be written to, and vice versa
- When finished, an open file handle should be closed
- When a file is closed, its handle should no longer be used
These requirements can be expressed formally by creating a
FILE_IO effect parameterised over a file handle state, which is
either empty, open for reading, or open for writing. The FILE_IO
effect’s definition is given below.
Note
This effect is mainly for illustrative purposes. Typically we would also like to support random access files and better reporting of error conditions.
Moreover, the FILE effect in the Effect.File module of
the effects library uses slightly more complicated types to
support erroneous behaviour of each function and to support more
compilcated modes of opening, like for reading and writing,
appending or truncating.
module Effect.File
import Effects
import Control.IOExcept
FILE_IO : Type -> EFFECT
data OpenFile : Mode -> Type
open : (fname : String)
-> (m : Mode)
-> Eff Bool [FILE_IO ()]
(\res => [FILE_IO (case res of
True => OpenFile m
False => ())])
close : Eff () [FILE_IO (OpenFile m)] [FILE_IO ()]
readLine : Eff String [FILE_IO (OpenFile Read)]
writeLine : String -> Eff () [FILE_IO (OpenFile Write)]
eof : Eff Bool [FILE_IO (OpenFile Read)]
Handler FileIO IO where { ... }
In particular, consider the type of open:
open : (fname : String)
-> (m : Mode)
-> Eff Bool [FILE_IO ()]
(\res => [FILE_IO (case res of
True => OpenFile m
False => ())])
This returns a Bool which indicates whether opening the file was
successful. The resulting state depends on whether the operation was
successful; if so, we have a file handle open for the stated purpose,
and if not, we have no file handle. By case analysis on the result,
we continue the protocol accordingly.
readFile : Eff (List String) [FILE_IO (OpenFile Read)]
readFile = readAcc [] where
readAcc : List String -> Eff (List String) [FILE_IO (OpenFile Read)]
readAcc acc = if (not !eof)
then readAcc (!readLine :: acc)
else pure (reverse acc)
Given a function readFile, above, which reads from
an open file until reaching the end, we can write a program which opens
a file, reads it, then displays the contents and closes it, as follows,
correctly following the protocol:
dumpFile : String -> Eff () [FILE_IO (), STDIO]
dumpFile name = case !(open name Read) of
True => do putStrLn (show !readFile)
close
False => putStrLn ("Error!")
The type of dumpFile, with FILE_IO () in its effect list,
indicates that any use of the file resource will follow the protocol
correctly (i.e. it both begins and ends with an empty resource). If we
fail to follow the protocol correctly (perhaps by forgetting to close
the file, failing to check that open succeeded, or opening the file
for writing) then we will get a compile-time error. For example,
changing open name Read to open name Write yields a compile-time
error of the following form:
FileTest.idr:16:18:When elaborating right hand side of Main.case
block in testFile:
Can't solve goal
SubList [(FILE_IO (OpenFile Read))]
[(FILE_IO (OpenFile Write)), STDIO]
In other words: when reading a file, we need a file which is open for
reading, but the effect list contains a FILE_IO effect carrying a
file open for writing.
Pattern-matching bind¶
It might seem that having to test each potentially failing operation
with a case clause could lead to ugly code, with lots of
nested case blocks. Many languages support exceptions to improve this,
but unfortunately exceptions may not allow completely clean resource
management—for example, guaranteeing that any open which did succeed
has a corresponding close.
Idris supports pattern-matching bindings, such as the following:
dumpFile : String -> Eff () [FILE_IO (), STDIO]
dumpFile name = do True <- open name Read
putStrLn (show !readFile)
close
This also has a problem: we are no longer dealing with the case where opening a file failed! The solution is to extend the pattern-matching binding syntax to give brief clauses for failing matches. Here, for example, we could write:
dumpFile : String -> Eff () [FILE_IO (), STDIO]
dumpFile name = do True <- open name Read | False => putStrLn "Error"
putStrLn (show !readFile)
close
This is exactly equivalent to the definition with the explicit case.
In general, in a do-block, the syntax:
do pat <- val | <alternatives>
p
is desugared to
do x <- val
case x of
pat => p
<alternatives>
There can be several alternatives, separated by a vertical bar
|. For example, there is a SYSTEM effect which supports
reading command line arguments, among other things (see Appendix
Effects Summary). To read command line arguments, we can use
getArgs:
getArgs : Eff (List String) [SYSTEM]
A main program can read command line arguments as follows, where in the
list which is returned, the first element prog is the executable
name and the second is an expected argument:
emain : Eff () [SYSTEM, STDIO]
emain = do [prog, arg] <- getArgs
putStrLn $ "Argument is " ++ arg
{- ... rest of function ... -}
Unfortunately, this will not fail gracefully if no argument is given, or if too many arguments are given. We can use pattern matching bind alternatives to give a better (more informative) error:
emain : Eff () [SYSTEM, STDIO]
emain = do [prog, arg] <- getArgs | [] => putStrLn "Can't happen!"
| [prog] => putStrLn "No arguments!"
| _ => putStrLn "Too many arguments!"
putStrLn $ "Argument is " ++ arg
{- ... rest of function ... -}
If getArgs does not return something of the form [prog, arg] the
alternative which does match is executed instead, and that value
returned.