# Monadic Typing and Overloading for ML-style Polymorphic References,
Koji Kagawa

## abstract

It is well-known that the ML-style {\sf ref} operator
interferes badly with the Damas/Milner polymorphic type inference
system. There have been a lot of proposals for the typing of
references of ML as an extension of the Damas/Milner type inference
system. Some of them are too complex for programmers to
understand. Among them, Wright's proposal is simple but not too
restrictive. His solution it to limit polymorphism to let-bindings
whose right-hand-side is a value (an expression which can not
syntactically involve computation).
On the other hand, in the pure functional language community, monads
are used more and more widely in writing programs with side-effect.
In some Haskell implementations, a monad for stateful computations and
a (monadic) operator which corresponds roughly to ML's {\sf ref}
operator is offered. In such systems, since the result of the {\sf
ref}-like operator is bound by $\lambda$ rather than by {\tt let}, we
can basically get the same effect as Wright's proposal.
However, this restriction is explained only syntactically. It relies
on the fact that the monad of state transformers is an abstract
type. But the primary reason to make state transformers abstract is to
guarantee in-place updating. If we knew the implementation of state
transformers, we could inline state transformers which contain {\sf
ref}-like operators and make results of the {\sf ref} operator {\sf
let}-bound. Then there would be no essential account why the result of
the {\sf ref}-like operator should be given monomorphic types.
In this paper, the implementation of the {\sf ref}-like operator in
the monadic form is investigated and the need for $\lambda$-binding is
explained using the notion of type classes (overloading) with multiple
arguments.