RE: What's so cool about Scheme?

["Bayley, Alistair" <address@hidden>]

> Semantic clarification: What are you referring to by "inclusional"
polymorphism?

I can think of three categories of polymorphism (I came across this
classification years ago, in a book on something object-oriented, but the
details escape me):

 - parametric (C++ templates, ML/Haskell lists)
 - inclusional (supertypes, subtypes, inheritance)
 - ad-hoc (overloaded functions where arguments do not share the same types
e.g. using '+' for addition and string concatenation)

I came to the conclusion inclusional polymorphism typifies the
object-oriented style of programming. Some languages support all 3 types
(C++), some just support parametric (ML), and some just inclusional (Java,
although they've recently added parametric).

Inclusional polymorphism is simply the case where when an object of a given
type is expected, an object that is a sub-type of the expected type may also
be used. Kinda obvious, but there you go...

I'm not sure what the relationship is between ad-hoc polymorphism and the
other types. For example, Haskell doesn't allow ad-hoc polymorphism in the
sense described above, but is does have a system for defining overloaded
operators. However, all instances of an overloaded function share a common
supertype (e.g. the arithmetic operators are defined over a variety of
concrete numeric types, all of which are subtypes of the Num class). 


> polymorphism is a necessary addition once you can create types and type
hierarchies

Type hierarchies tend to be found in languages that provide inheritance, and
use inheritance to create subtypes. Most OO-languages use inheritance to
create subtypes, and some people have trouble making the distinction between
inheritance and subtyping. As a counter-example, Emerald is a language that
supports inclusional polymorphism but does not have inheritance.


> I think of OO as being the ability to provide user-defined types with
invariants

I'm not sure what "invariants" are (but I do know that use-defined types
are). Is it possible to have "user-defined types with invariants" in a
language that would not be considered object-oriented (Modula, Pascal, C,
ML)?


-----Original Message-----
From: Mike Newhall [mailto:mike@newhall.net]
Sent: 03 June 2003 15:51
To: Bayley, Alistair
Cc: ll1-discuss@ai.mit.edu
Subject: RE: What's so cool about Scheme?


>procedural languages. That is, the thing that determines whether or not a
>language is object-oriented is: does it support inclusional polymorphism?

	Semantic clarification: What are you referring to by "inclusional"
polymorphism?

	I think of OO as being the ability to provide user-defined types
with invariants; polymorphism is a necessary addition once you can create
types and type hierarchies.


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