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### 2562. Consistent total ordering of pointers by comparison functors

Section: 22.10.8 [comparisons] Status: C++17 Submitter: Casey Carter Opened: 2015-11-18 Last modified: 2017-07-30

Priority: 3

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Discussion:

N4567 22.10.8 [comparisons]/14 specifies that the comparison functors provide a total ordering for pointer types:

> For templates `greater`, `less`, `greater_equal`, and `less_equal`, the specializations for any pointer type yield a total order, even if the built-in operators `<`, `>`, `<=`, `>=` do not.

It notably does not specify:

- whether the specializations of all of the named templates for a given pointer type yield the same total order

- whether the total order imposed respects the partial order imposed by the built-in operators

- whether the total order imposed is consistent with the partition induced by `==`

All of which are important for sane semantics and provided by common implementations, since the built-in operators provide a total order and the comparison functors yield that same order.

It would be extremely confusing — if not outright insane — for e.g.:

- `less<int*>` and `greater<int*>` to yield different orders

- `less<int*>` to disagree with `<` on the relative order of two pointers for which `<` is defined

- `less<int*>` to order `a` before `b` when `a == b`, i.e., not preserve equality.

Consistent semantics for the various comparison functors and the built-in operators is so intuitive as to be assumed by most programmers.

Related issues: 2450, 2547.

Previous resolution [SUPERSEDED]:

> This wording is relative to N4567.

> 1. Alter 22.10.8 [comparisons]/14 to read:

>    > For templates `greater`, `less`, `greater_equal`, and `less_equal`, the specializations for any pointer type yield a the same total order, even if the built-in operators `<`, `>`, `<=`, `>=` do not. The total order shall respect the partial order imposed by the built-in operators.

[2016-05-20, Casey Carter comments and suggests revised wording]

The new proposed wording is attempting to address the issue raised in the 2016-02-04 telecon.

The real issue I'm trying to address here is ensure that "weird" implementations provide the same kind of consistency for pointer orderings as "normal" implementations that use a flat address spaces and have totally ordered `<`. If `a < b` is true for `int` pointers `a` and `b`, then `less<int*>(a, b)`, `less_equal<int*>(a, b)`, `less<char*>(a, b)`, `less<void*>(a, b)`, and `greater<int*>(b, a)` should all hold. I think this wording is sufficient to provide that.

Previous resolution [SUPERSEDED]:

> This wording is relative to N4582.

> 1. Alter 22.10.8 [comparisons] to read:

>    > -14- For templates `greater`, `less`, `greater_equal`, and `less_equal`, the specializations for any pointer type yield a the same total order. That total order is consistent with the partial order imposed by, even if the built-in operators `<`, `>`, `≤`, and `>` do not. [Note: When `a < b` is well-defined for pointers `a` and `b` of type `P`, this implies `(a < b) == less<P>(a, b)`, `(a > b) == greater<P>(a, b)`, and so forth. — end note] For template specializations `greater<void>`, `less<void>`, `greater_equal<void>`, and `less_equal<void>`, if the call operator calls a built-in operator comparing pointers, the call operator yields a total order.

[2016-08-04 Chicago LWG]

LWG discusses and concludes that we are trying to accomplish the following:

1. >     T* a = /* ... */;
   >     T* b = /* ... */;

   if `a < b` is valid, `a < b == less<T*>(a, b)`, and analogously for `>`, `<=`, `>=`.

2. >     less<void>(a, b) == less<T*>(a, b);
   >     less<T*>(a, b) == greater<T*>(b, a);

   etc.

3. `less<T*>` produces a strict total ordering with which the other three function objects are consistent

4. `less<void>` when applied to pointers produces a strict total ordering with which the other three are consistent

5. `less<void>` when applied to pointers of the same type produces the same strict total ordering as `less<T*>`, and analogously for the other three

6. we are not addressing `less<void>` (and the other three) when applied to pointers of differing types

Walter and Nevin revise Proposed Wording accordingly.

[2016-08 - Chicago]

Thurs PM: Moved to Tentatively Ready

Proposed resolution:

This wording is relative to N4606.

1. Change 22.10.8 [comparisons] p14 as indicated:

   > -14- For templates `greater`, `less`, `greater_equal`, and `less_equal` `less`, `greater`, `less_equal`, and `greater_equal`, the specializations for any pointer type yield a strict total order that is consistent among those specializations and is also consistent with the partial order imposed by , even if the built-in operators `<`, `>`, `<=`, `>=` do not. [Note: When `a < b` is well-defined for pointers `a` and `b` of type `P`, this implies `(a < b) == less<P>(a, b)`, `(a > b) == greater<P>(a, b)`, and so forth. — end note] For template specializations `greater<void>`, `less<void>`, `greater_equal<void>`, and `less_equal<void>``less<void>`, `greater<void>`, `less_equal<void>`, and `greater_equal<void>`, if the call operator calls a built-in operator comparing pointers, the call operator yields a strict total order that is consistent among those specializations and is also consistent with the partial order imposed by those built-in operators.