IO Monad - SML

1. Introduction
2. Using Modules
3. References

1. Introduction

We can construct the IO Monad in Standard ML, which has been done in Gordon's PhD thesis. There the construction uses an abstract type:

infix 1 >> >>=
abstype 'a Job = JOB of unit -> 'a
with
    (* exec : 'a Job -> 'a *)
    fun exec (JOB f)  = f ()
    (* return : 'a -> 'a Job *)
    fun return x      = JOB (fn _ => x)
    (* (>>=) : 'a Job * ('a -> 'b Job) -> 'b Job *)
    fun (JOB f) >>= q = JOB (fn _ => exec (q (f ())))
    (* getStr : int -> TextIO.vector Job *)
    fun getStr n      = JOB (fn _ => TextIO.inputN(TextIO.stdIn, n))
    (* putStr : string -> unit Job *)
    fun putStr s      = JOB (fn _ => print s)
end

(* (>>) : 'a Job * 'b Job -> 'b Job *)
fun p >> q  =  p >>= (fn _ => q);

(* gettingLine : string -> string Job *)
fun gettingLine s =
    getStr 1 >>= (fn c => if c = "\n"
                          then return(s)
                          else gettingLine (s^c));

(* getLine : string Job *)
val getLine = gettingLine "";

val main : unit Job =
    putStr "First name: " >> getLine >>= (fn first =>
    putStr "Second name: " >> getLine >>= (fn second =>
    putStr ("Hello "^first^" "^second^"\n")));
(* exec main; *)

2. Using Modules

We can encode the IO Monad using SML's Module system. The signature for a Monad would be:

signature MONAD = sig
    type 'a m;
    val return : 'a -> 'a m;
    val bind : 'a m -> ('a -> 'b m) -> 'b m;
end;

The IO Monad requires a few more public-facing methods.

signature IO_MONAD =
sig
    include MONAD;
    val exec : 'a m -> 'a;
    val getStr : int -> TextIO.vector m;
    val putStr : string -> unit m;
end;

Observe we just switched the Job constructor to m. The implementation details are straightforward.

3. References

Andrew Gordon,
"Functional Programming and Input/Output".
Ph.D. Thesis, Cambridge, 1994; Eprint.
Simon Peyton Jones,
"Tackling the awkward squad: monadic input/output, concurrency, exceptions, and foreign-language calls in Haskell".
in Engineering theories of software construction, IOS Press, 2001; Eprint and pdf.
- Discusses the IO monad using a "two tier" semantics, with process semantics for the IO part and some denotational semantics for a lazy lambda calculus.

IO Monad - SML

Table of Contents

1. Introduction

2. Using Modules

3. References