TagSet

TagSet(f, expr, value)

f /: expr = value

assigns the evaluated value to expr and associates the corresponding rule with the symbol f.

Create an upvalue without using UpSet:

>> x /: f(x) = 2
2

>> f(x)
2

>> DownValues(f)
{}

>> UpValues(x)
{HoldPattern(f(x)):>2}

The symbol f must appear as the ultimate head of lhs or as the head of a leaf in lhs:

>> x /: f(g(x)) = 3
 : Tag x not found or too deep for an assigned rule.

>> g /: f(g(x)) = 3;

>> f(g(x))
3