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Subject: Re: [boost] Boost.Algorithm design question
From: Andrew Sutton (asutton.list_at_[hidden])
Date: 2011-11-01 10:43:56

>>> Realistically though, when is == not (at least) an equivalence
>>> relation?
>> Realistically, and in this context, when the two sides are not of the same
>> type.
> In most of the cases that I care about, there is some underlying type like
> "string" or "integer", on which an equivalence relation exists in some
> formal sense.  Then there are some concrete C++ types like
> std::basic_string<char,allocator_1> or std::basic_string<char,allocator_2>
> or int32_t or int64_t.  operator== is defined on pairs of these concrete
> types in some way that approximates to the equivalence relation on the
> underlying formal type, but with some inevitable flakiness at the edges,
> such as comparison between two char*s or comparison between integers with
> different numbers of bits.

Sure, but these types are inherently related. It should be reasonable
to write the semantics of comparisons on related types in terms of the
underlying type (or more abstract type, I guess). I can convince
myself that those operations on those types have precise semantics:
they define an equivalence relation.

We attach meaning to symbols. I doubt that many people on this list
would read the expression "a == b" as "a and b are operated on by some
function with the name == that has some result". I tend to read it as
"a is equal to b". If I read it that way, I happen to know something
extra about the operator; it's an equivalence relation. I also happen
to know something about the values: an expression involving a will
yield the same result as the same expression involving b (with some
notable exceptions). This additional knowledge seems like a good

I don't see how attaching specific meaning to operations impacts
implementation flexibility. It certainly impacts design choices and
choices about algorithm usage, but I hope in a positive way.

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