IO Semantics: Difference between revisions

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The idea is to define <hask>IO</hask> as
The idea is to define <hask>IO</hask> as
<haskell>
<haskell>
newtype IO a = IO {runIO :: (a -> IOTree) -> IOTree}
data IO a = Done a
          | PutChar Char (IO a)
          | GetChar (Char -> IO a)
</haskell>
</haskell>
This is equivalent to defining <hask>IO</hask> as <hask>Cont IOTree</hask> from the [[monad template library]].  The monad functions for <hask>IO</hask> are derived from the monad functions for <hask>Cont</hask>.
<haskell>
return x = IO (\k -> k x)
x >>= f = IO (\k -> runIO x (\a -> runIO (f a) k))
</haskell>
<hask>IOTree</hask> is the ultimate result of a program.  For simplicity we will give an example of <hask>IOTree</hask> that gives semantics for teletype IO.
<haskell>
data IOTree = Done
            | PutChar Char IOTree
            | GetChar (Char -> IOTree)
</haskell>
(This is a tree because the <hask>GetChar</hask> node has one subtree for every character)


<hask>IOTree</hask> contains all the information needed to execute teletype interactions.
For simplicity this an example of <hask>IO</hask> that only gives semantics for teletype IO.
One interprets (or executes) an <hask>IOTree</hask> by tracing a route from root of the tree to a leaf.
 
Think of <hask>IO a</hask> as a tree whose leaves are <hask>Done a</hask> that holds the result of the program.  <hask>PutChar</hask> is a node that has one child tree and the node holds one character of data. <hask>GetChar</hask> is a node that has many children; it has one child for every <hask>Char</hask>, but <hask>GetChar</hask> holds no data itself.
 
This tree contains all the information needed to execute teletype interactions.
One interprets (or executes) an <hask>IO a</hask> by tracing a route from root of the tree to a leaf.
 
If a <hask>PutChar</hask> node is encountered, the character data contained at that node is output to the terminal and then its subtree is executed.  It is at this point that Haskell code evaluated in order to determine what character should be displayed before continuing.  If a <hask>GetChar</hask> node is encountered, a character is read from the terminal (blocking if necessary) and the subtree corresponding to the character received is executed.  If <hask>Done</hask> is encountered the program ends.  <hask>Done</hask> holds the result of the computation, but in the case of <hask>main :: IO ()</hask> the data is of type <hask>()</hask> and thus contains no information and is ignored.


If a <hask>PutChar</hask> node is encountered, the character data contained at that node is output to the terminal and then its subtree is executed.  It is only at this point that Haskell code is ever necessarily evaluated in order to determine what character should be displayed before continuing.  If a <hask>GetChar</hask> node is encountered, a character is read from the terminal (blocking if necessary) and the subtree corresponding to the character received is executed. If <hask>Done</hask> is encountered the program ends.
This execution is not done anywhere in a haskell program, rather it is done by the run-time system.
The primitive IO commands are defined using these constructors.
<haskell>
putChar :: Char -> IO ()
putChar x = IO (\k -> PutChar x (k ()))


getChar :: IO Char
The monadic operations are defined as follows:
getChar = IO (\k -> GetChar (\x -> k x))
</haskell>


If the <hask>PutChar</hask> constructor was defined (isomorphically) as
<haskell>
<haskell>
| PutChar Char (() -> IOTree)
return :: a -> IO a
return x = Done x
 
(>>=) :: IO a -> (a -> IO b) -> IO b
Done x >>= f = f x
PutChar c x >>= f = PutChar c (x >>= f)
GetChar g >>= f = GetChar (\c -> g c >>= f)
</haskell>
</haskell>


Then the primitive IO commands could be defined directly in terms of these constructors:
As you can see <hask>return</hask> is just another name for <hask>Done</hask>.  The bind operation takes a tree <hask>x</hask> and a function <hask>f</hask> and replaces the <hask>Done</hask> nodes (the leaves) of <hask>x</hask> by a new tree produce by applying <hask>f</hask> to the data held in the <hask>Done</hask> nodes.


The primitive IO commands are defined using these constructors.
<haskell>
<haskell>
putChar :: Char -> IO ()
putChar :: Char -> IO ()
putChar = IO . PutChar
putChar x = PutChar x (Done ())


getChar :: IO Char
getChar :: IO Char
getChar = IO GetChar
getChar = GetChar (\c -> Done c)
</haskell>
</haskell>


The function <hask>putChar</hask> builds a small <hask>IO ()</hask> tree that contains one <hask>PutChar</hask> node holding the character data followed by <hask>Done</hask>.
The function <hask>getChar</hask> builds a short <hask>IO Char</hask> tree that begins with a <hask>GetChar</hask> that holds one <hask>Done</hask> node holding every character.


Other teletype commands can be defined in terms of these primitives
Other teletype commands can be defined in terms of these primitives
Line 55: Line 54:
putStr = mapM_ putChar
putStr = mapM_ putChar
</haskell>
</haskell>
More generally speaking, <hask>IOTree</hask> will represent the desired interaction with the operating system.  For every system call there will be a corresponding constructor in <hask>IOTree</hask> of the form
 
More generally speaking, <hask>IO a</hask> will represent the desired interaction with the operating system.  For every system call there will be a corresponding constructor in <hask>IOTree</hask> of the form
<haskell>
<haskell>
| SysCallName p1 p2 ... pn (r -> IOTree)
| SysCallName p1 p2 ... pn (r -> IO a)
</haskell>
</haskell>
where <hask>p1</hask> ... <hask>pn</hask> are the parameters for the system call, and <hask>r</hask> is the result of the system call.  (Thus <hask>PutChar</hask> and <hask>GetChar</hask> will not occur as constructors of <hask>IOTree</hask> if they don't correspond to system calls)
where <hask>p1</hask> ... <hask>pn</hask> are the parameters for the system call, and <hask>r</hask> is the result of the system call.  (Thus <hask>PutChar</hask> and <hask>GetChar</hask> will not occur as constructors of <hask>IOTree</hask> if they don't correspond to system calls)
We said that the ultimate result of a program is an <hask>IOTree</hask>, however the main function has type <hask>IO ()</hask>.  This is isomorphic to <hask>(() -> IOTree) -> IOTree</hask>, or equivalently <hask>IOTree -> IOTree</hask> which is not right.
The simple solution to this is that the runtime system produces an <hask>IOTree</hask> from main by evaluating <hask>runIO main (\() -> Done) :: IOTree</hask>.  Here <hask>\() -> Done</hask> represents the "rest of the program", which in this case is nothing.
The sophisticated solution to this problem is that <hask>main</hask> is passed to the operating system which will bind the next program (perhaps a shell) to <hask>main</hask>.  Thus the semantics of our Haskell program becomes embedded into the semantics of the entire operating system run.
The type for <hask>IO a</hask> that we have given contains invalid programs such as
<haskell>
IO (\k -> filterTree (not . isPutChar) (k ())) :: IO ()
</haskell>
which would remove the output of any future <hask>putChar</hask> commands.  However, none of these illegal programs can be generated from the monadic interface and the primitive operations provided.

Revision as of 21:49, 8 May 2010

Semantics of IO: A Continuation Approach

The following is inspired by Luke Palmer's post. This only describes one possible semantics of IO a; your actually implementation may vary.

The idea is to define IO as 

data IO a = Done a
          | PutChar Char (IO a)
          | GetChar (Char -> IO a)

For simplicity this an example of IO that only gives semantics for teletype IO.

Think of IO a as a tree whose leaves are Done a that holds the result of the program. PutChar is a node that has one child tree and the node holds one character of data. GetChar is a node that has many children; it has one child for every Char, but GetChar holds no data itself.

This tree contains all the information needed to execute teletype interactions. One interprets (or executes) an IO a by tracing a route from root of the tree to a leaf.

If a PutChar node is encountered, the character data contained at that node is output to the terminal and then its subtree is executed. It is at this point that Haskell code evaluated in order to determine what character should be displayed before continuing. If a GetChar node is encountered, a character is read from the terminal (blocking if necessary) and the subtree corresponding to the character received is executed. If Done is encountered the program ends. Done holds the result of the computation, but in the case of main :: IO () the data is of type () and thus contains no information and is ignored.

This execution is not done anywhere in a haskell program, rather it is done by the run-time system.

The monadic operations are defined as follows: 

return :: a -> IO a
return x = Done x

(>>=) :: IO a -> (a -> IO b) -> IO b
Done x >>= f = f x
PutChar c x >>= f = PutChar c (x >>= f)
GetChar g >>= f = GetChar (\c -> g c >>= f)

As you can see return is just another name for Done. The bind operation takes a tree x and a function f and replaces the Done nodes (the leaves) of x by a new tree produce by applying f to the data held in the Done nodes.

The primitive IO commands are defined using these constructors. 

putChar :: Char -> IO ()
putChar x = PutChar x (Done ())

getChar :: IO Char
getChar = GetChar (\c -> Done c)

The function putChar builds a small IO () tree that contains one PutChar node holding the character data followed by Done.

The function getChar builds a short IO Char tree that begins with a GetChar that holds one Done node holding every character.

Other teletype commands can be defined in terms of these primitives 

putStr :: String -> IO ()
putStr = mapM_ putChar

More generally speaking, IO a will represent the desired interaction with the operating system. For every system call there will be a corresponding constructor in IOTree of the form 

	| SysCallName p1 p2 ... pn (r -> IO a)

where p1 ... pn are the parameters for the system call, and r is the result of the system call. (Thus PutChar and GetChar will not occur as constructors of IOTree if they don't correspond to system calls)

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