A chain with integer arithmetic: a discrete total order, locally finite (every bounded interval is finite), so a distributive lattice under min and max, with the NNO's step and the arithmetic operators as a shape. Finite on a machine word, unbounded for a bignum. Not a ring: int's overflow is undefined and a cardinal may saturate at \(\aleph_0\); the ring is IsRing's to claim. More...

Concept definition

template<typename T>
concept dedekind::category::IsIntegerChain = 
    HasNNOStep<std::remove_cvref_t<T>> &&
    std::totally_ordered<std::remove_cvref_t<T>> &&
    requires(const std::remove_cvref_t<T> a, const std::remove_cvref_t<T> b) {
      a + b;
      a - b;
      a * b;
      a / b;
      a % b;
    } && is_integer_chain<std::remove_cvref_t<T>>::value

Detailed Description

A chain with integer arithmetic: a discrete total order, locally finite (every bounded interval is finite), so a distributive lattice under min and max, with the NNO's step and the arithmetic operators as a shape. Finite on a machine word, unbounded for a bignum. Not a ring: int's overflow is undefined and a cardinal may saturate at \(\aleph_0\); the ring is IsRing's to claim.

Template Parameters

T	the carrier.