In Scheme and some other Lisp dialects, a numerical tower is the set of data types that represent numbers in a given programming language.
Each type in the tower conceptually "sits on" a more fundamental type, so an integer is a rational number and a number, but the inverse is not necessarily true, i.e. not every number is an integer; this asymmetry implies that a language can allow implicit coercions of numerical types—without creating semantic problems—in only one direction: coercing an integer to a rational loses no information and does not affect the results of a function, but to coerce most reals to an integer could well result in a problem (for example, the real 1/3 does not equal any integer).
Scheme programming language, and also other Lisp dialects, defines all its arithmetic within this model. Some given implementations may extend or adapt the tower. Kawa, for example, extends it with a Quantity type that is even more generic than Number. Smalltalk is another programming language that follows this model, but it has a Magnitude as superclass of Number. Another popular variant is having both exact and inexact versions of the tower or parts of it. Most languages and language implementations do not support a Scheme-like numerical tower. Some languages support it only in a limited way.
Famous quotes containing the words numerical and/or tower:
“The moment a mere numerical superiority by either states or voters in this country proceeds to ignore the needs and desires of the minority, and for their own selfish purpose or advancement, hamper or oppress that minority, or debar them in any way from equal privileges and equal rights—that moment will mark the failure of our constitutional system.”
—Franklin D. Roosevelt (1882–1945)
“Shall I still be love’s house on the widdershin earth,
Woe to the windy masons at my shelter?
Love’s house, they answer, and the tower death
Lie all unknowing of the grave sin-eater.”
—Dylan Thomas (1914–1953)