| 词条 | Numerical tower |
| 释义 |
In Scheme and Lisp dialects inspired by it, 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 converse 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). The Scheme programming language defines all its arithmetic within this model, as do most other Lisp dialects.[1] Some implementations may extend or adapt the tower. Kawa, a Scheme implementation for JVM, 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; R7RS Scheme recommends but does not strictly require this of implementations. Most programming languages and language implementations do not support a Scheme-like numerical tower, though some languages provide limited or inconsistent support if implementation simplicity permits. References1. ^http://www.schemers.org/Documents/Standards/R5RS/HTML/r5rs-Z-H-9.html#%_sec_6.2.1 {{DEFAULTSORT:Numerical Tower}}{{compu-prog-stub}} 1 : Data types |
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