V2EX fixpoint

Fixpoint

Definition / 定义

fixpoint(名词):通常指不动点对某个函数或变换 \(f\) 而言,满足 \(f(x)=x\) 的点 \(x\)。在计算机科学中也常指通过迭代求解方程/递归定义时达到的稳定结果(不再变化的值)。
(更常见的写法是 fixed point,但在某些学术与工程语境中也会写作 fixpoint。)

Pronunciation / 发音

/fkspnt/

Examples / 例句

A fixpoint is a value that doesn’t change under a function.
不动点是在函数作用下不会改变的值。

In denotational semantics, recursive definitions are interpreted as the least fixpoint of a suitable operator.
在指称语义学中,递归定义通常被解释为某个合适算子的最小不动点。

Etymology / 词源

fixpointfix(固定)+ point(点)构成,字面意思是“固定的点”。在数学中“不动点(fixed point)”概念很早就存在;在计算机科学里,随着递归、迭代求解与语义学的发展,“不动点/最小不动点”等表述被广泛用于描述“反复应用规则后最终稳定下来的结果”。

Related Words / 相关词

Literary Works / 文学作品举例

  • Structure and Interpretation of Computer Programs(SICP,讨论递归与求值过程时涉及 fixed point 思想)
  • Gdel, Escher, Bach: an Eternal Golden Braid(常以“自指/不动点”相关思想展开讨论)
  • Introduction to the Theory of Computation(计算理论教材中常出现 fixed point 定理/相关概念)
  • Types and Programming Languages(类型系统与语义章节中涉及不动点与递归的形式化)
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