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An inductively defined recursive data definition is one that specifies how to construct instances of the data. For example, linked lists can be defined inductively (here, using Haskell syntax):
An inductively defined recursive data definition is one that specifies how to construct instances of the data. For example, linked lists can be defined inductively (here, using Haskell syntax):
归纳定义是指定如何构造数据实例的定义。例如，字符串列表可以被归纳定义为（这里使用Haskell语法）：
<syntaxhighlight lang="haskell">data ListOfStrings = EmptyList | Cons String ListOfStrings</syntaxhighlight>
<syntaxhighlight lang="haskell">data ListOfStrings = EmptyList | Cons String ListOfStrings</syntaxhighlight>
归纳定义的另一个例子是'''<font color="#ff8000">自然数 natural numbers</font>'''（或正整数）：
归纳定义的另一个例子是'''<font color="#ff8000">自然数 natural numbers</font>'''（或正整数）：
<pre>A natural number is either 1 or n+1, where n is a natural number.</pre>
<pre>A natural number is either 1 or n+1, where n is a natural number.</pre>
This says that an expression is either a number, a product of two expressions, or a sum of two expressions. By recursively referring to expressions in the second and third lines, the grammar permits arbitrarily complex arithmetic expressions such as <code>(5 * ((3 * 6) + 8))</code>, with more than one product or sum operation in a single expression.
This says that an expression is either a number, a product of two expressions, or a sum of two expressions. By recursively referring to expressions in the second and third lines, the grammar permits arbitrarily complex arithmetic expressions such as <code>(5 * ((3 * 6) + 8))</code>, with more than one product or sum operation in a single expression.
这意味着一个表达式要么是一个数字，要么是两个表达式的乘积，要么是两个表达式的和。通过在第二行和第三行中递归引用表达式，该语法允许任意复杂的算术表达式，如 < code > (5 * ((3 * 6) + 8)) </code > ，在一个表达式中有多个乘积或和运算。
这意味着一个表达式要么是一个数字，要么是两个表达式的乘积，要么是两个表达式的和。通过在第二行和第三行中递归引用表达式，该语法允许任意复杂的算术表达式，如 <code> (5 * ((3 * 6) + 8)) </code> ，在一个表达式中有多个乘积或和运算。
===协归纳定义的数据和共递归===
{{main|Coinduction|Corecursion}}
{{main|Coinduction|Corecursion}}
A coinductive data definition is one that specifies the operations that may be performed on a piece of data; typically, self-referential coinductive definitions are used for data structures of infinite size.
A coinductive data definition is one that specifies the operations that may be performed on a piece of data; typically, self-referential coinductive definitions are used for data structures of infinite size.
A coinductive data definition is one that specifies the operations that may be performed on a piece of data; typically, self-referential coinductive definitions are used for data structures of infinite size.
A coinductive data definition is one that specifies the operations that may be performed on a piece of data; typically, self-referential coinductive definitions are used for data structures of infinite size.
协归纳数据定义是一种规定了可以对一段数据进行操作的定义；;通常，自引用的协归纳定义用于无限大小的数据结构。
A coinductive definition of infinite [[stream (computer science)|streams]] of strings, given informally, might look like this:
A coinductive definition of infinite [[stream (computer science)|streams]] of strings, given informally, might look like this: