About: Numerical tower

In Scheme and in Lisp dialects inspired by it, the numerical tower is a set of data types that represent numbers and a logic for their hierarchical organisation. Each type in the tower conceptually "sits on" a more fundamental type, so an integer is a rational number and a number, but the converse is not necessarily true, i.e. not every number is an integer. This asymmetry implies that a language can safely allow implicit coercions of numerical types—without creating semantic problems—in only one direction: coercing an integer to a rational loses no information and will never influence the value returned by a function, but to coerce most reals to an integer would alter any relevant computation (e.g., the real 1/3 does not equal any integer) and is thus impermissible.