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polymorphic equality and overloading
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Date: 2000-07-07 (14:31)
From: Eijiro Sumii <sumii@s...>
Subject: Re: polymorphic equality and overloading
Dear Dr. Pierre Weis,

> No. As you know (and as I wrote in the Caml FAQ) the polymorphic
> equality in Caml is the "equality in mathematics" for many (or most?)
> datatypes. A few exceptions are (as in maths)
> -- functions, for which mathematical equality needs complex demonstrations
> -- quotient types using complex equivalence relations, such as
> rational numbers or even reals or complex numbers.

Are the exceptions really "a few"?  For example---apart from (some
representations of) mathematical entities such as rational numbers,
complex numbers, polynomials, etc.---simple database entries like
"type student = { id : int; name : string; address : string }" would
have an equality different from the polymorphic equality (in the Set
and Map modules, for instance).

> Note also that polymorphic equality is just pratical and useful,

That is exactly what I asked in my second message ("Is that just
because it is often useful?"), and if the answer is yes, that's ok for

> and not confusing at all if you know something about mathematical
> entities involved in the values manipulated by Caml programs.

Unfortunately, the different treatments of equality and addition (for
example) *did* confuse a friend of mine.  (He has a master's degree in
computer science in the University of Tokyo---as I also do---and
definitely knows much about mathematics and computer science.)

> Choosing Haskell for the treatment of equality in the language is just
> All the best for your experiments with modern programming languages

Oh, I *love* OCaml.:-) As I wrote in a previous message, I'm not a
Haskell advocator.  (By the way, I've been programming in "modern"
languages---such as Scheme, Standard ML, Caml and Haskell---for 5
years, or 15 years if you admit LOGO as a modern language.)

Best wishes,

// Eijiro Sumii <sumii@saul.cis.upenn.edu>
// currently visiting: Department of Computer and Information Science,
// School of Engineering and Applied Science, University of Pennsylvania