2.3.4 Specifying Types of Expression in PatternsYou can tell a lot about what "type" of expression something is by looking at its head. Thus, for example, an integer has head Integer, while a list has head List. In a pattern, _h and x_h represent expressions that are constrained to have head h. Thus, for example, _Integer represents any integer, while _List represents any list.
| x_h | an expression with head h | | x_Integer | an integer | | x_Real | an approximate real number | | x_Complex | a complex number | | x_List | a list | | x_Symbol | a symbol |
Patterns for objects with specified heads. | This replaces just those elements that are integers. | |
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{a, 4, 5, b} /. x_Integer -> p[x]
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You can think of making an assignment for f[x_Integer] as like defining a function f that must take an argument of "type" Integer. | This defines a value for the function gamma when its argument is an integer. | |
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gamma[n_Integer] := (n - 1)!
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| The definition applies only when the argument of gamma is an integer. | |
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gamma[4] + gamma[x]
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| The object 4. has head Real, so the definition does not apply. | |
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| This defines values for expressions with integer exponents. | |
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d[x_^n_Integer] := n x^(n-1)
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| The definition is used only when the exponent is an integer. | |
In[6]:=
d[x^4] + d[(a+b)^3] + d[x^(1/2)]
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