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IO Semantics

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(Rewritten to remove continuations.)
Current revision (21:57, 8 May 2010) (edit) (undo)
 
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[[Category:Theoretical_foundations]]
[[Category:Theoretical_foundations]]
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== Semantics of IO: A Continuation Approach ==
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== Semantics of IO: A Free Approach ==
The following is inspired by [http://luqui.org/blog/archives/2008/03/29/io-monad-the-continuation-presentation/ Luke Palmer's post]. This only describes one possible semantics of <hask>IO a</hask>; your actually implementation may vary.
The following is inspired by [http://luqui.org/blog/archives/2008/03/29/io-monad-the-continuation-presentation/ Luke Palmer's post]. This only describes one possible semantics of <hask>IO a</hask>; your actually implementation may vary.

Current revision

Semantics of IO: A Free 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)
Retrieved from "http://www.haskell.org/haskellwiki/IO_Semantics"

Category: Theoretical foundations