# C++ named requirements: LessThanComparable

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< cpp‎ | named req

The type must work with `<` operator and the result should have standard semantics.

### Requirements

The type `T` satisfies LessThanComparable if

Given

- a, b, and c, expressions of type `T` or const T.

The following expressions must be valid and have their specified effects.

Expression | Return type | Requirements
--- | --- | ---
a < b | implicitly convertible to bool | Establishes strict weak ordering relation with the following properties: For all `a`, !(a < a). If a < b then !(b < a). If a < b and b < c then a < c. Defining equiv(a, b) as !(a < b) && !(b < a), if equiv(a, b) and equiv(b, c), then equiv(a, c).

### Notes

To satisfy this requirement, types that do not have built-in comparison operators have to provide a user-defined `operator<`.

For the types that are both EqualityComparable and LessThanComparable, the C++ standard library makes a distinction between

- Equality, which is the value of the expression a == b and
- Equivalence, which is the value of the expression !(a < b) && !(b < a).

### See also

Compare | a BinaryPredicate that establishes an ordering relation (named requirement)
strict_weak_order (C++20) | specifies that a `relation` imposes a strict weak ordering (concept)

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