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From: norvell@csri.toronto.edu (Theodore Stevens Norvell)
Subject: Re: Polymorphism
Message-ID: <8904222245.AA05210@ellesmere.csri.toronto.edu>
Summary: Definition of Polymorphism
Organization: University of Toronto, CSRI
References: <5957@pdn.paradyne.com> <2841@crete.cs.glasgow.ac.uk>
Date: Sat, 22 Apr 89 18:45:15 EDT

In article <2841@crete.cs.glasgow.ac.uk> jack@cs.glasgow.ac.uk (Jack Campin)
makes some good points, but wrote:
>
>alan@rnms1.paradyne.com (Alan Lovejoy) wrote:
>> To say the same thing more concretely:  numbers, characters, data types,
>> procedures, variables, addresses, blocks, execution contexts, name bindings, 
>> scopes, processes and the number of bits in an integer must all be "first 
>> class objects."
>
>You and Harland may mean that by "polymorphic", but the rest of the world
>certainly doesn't.  The mathematically understood senses of polymorphism are
>(1) the Hindley type system, as implemented in Milner's ML and most functional
>languages since, and (2) Girard's more powerful type system F, reinvented by
>Reynolds and not fully implemented in any language I can think of [...]
>
Perhaps this is a quibble, but surely you are confusing "polymorphism" with
"polymorphic type inference".  Consider the following quotation describing
polymorphic programming:
	A widely employed style of programming, particularly in structure-
	processing languages which impose no discipline of types (LISP is
	a perfect example), entails defining procedures which work well on
	objects of a wide variety (e.g, on lists of atoms, integers, or
	lists).
Surely Harland's Poly is another perfect example.  In Poly can one not
define procedures which work well on objects of a very wide variety?

The quotation, by the way, is from Milner's seminal paper `A Theory
of Type Polymorphism in Programming', (J. Comp. & Sys. Sci., 17, 1978)
in which he used Hindley's system (without knowing it was Hindley's)
to do strong type checking in a lisp-like language (ML).  The introduction
of this approach did not suddenly make LISP, Prolog, or Smalltalk (or
Poly, had it existed at the time) less polymorphic.  Nor did it make
languages that use other approaches to strong type checking of polymorphic
programs (e.g., C++ and Modula-3) less polymorphic.

Milner also credits the term "polymorphism" to Strachey in 1967 which
predates even Hindley's work (1969).

The term "polymorphic type inference", on the other hand describes
perfectly the work of Hindley, Milner, Girard, Reynolds, McCracken,
Cardelli, Wand, etc.

Theo Norvell
U of Toronto

On the other hand, language is living.  Perhaps I'm just out of date.