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Putting Constraints on PatternsFlat and Orderless Functions

2.3.6 Patterns Involving Alternatives

Specifying patterns that involve alternatives.

This defines h to give p when its argument is either a or b.

In[1]:= h[a | b] := p

The first two cases give p.

In[2]:= {h[a], h[b], h[c], h[d]}

Out[2]=

You can also use alternatives in transformation rules.

In[3]:= {a, b, c, d} /. (a | b) -> p

Out[3]=

Here is another example, in which one of the alternatives is itself a pattern.

In[4]:= {1, x, x^2, x^3, y^2} /. (x | x^_) -> q

Out[4]=

When you use alternatives in patterns, you should make sure that the same set of names appear in each alternative. When a pattern like (a[x_] | b[x_]) matches an expression, there will always be a definite expression that corresponds to the object x. On the other hand, if you try to match a pattern like (a[x_] | b[y_]), then there will be a definite expression corresponding either to x, or to y, but not to both. As a result, you cannot use x and y to refer to definite expressions, for example on the right-hand side of a transformation rule.

Here f is used to name the head, which can be either a or b.

In[5]:= {a[2], b[3], c[4], a[5]} /. (f:(a|b))[x_] -> r[f, x]

Out[5]=

Putting Constraints on PatternsFlat and Orderless Functions