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Default

Status: Experimental

present and registered, but lightly documented and not yet covered by dedicated tests.

Description

Default[f]
    gives the default value supplied for a missing optional argument of
    f when the pattern _. (Optional[Blank[]]) appears in a rule.
Default[f, i]
    gives the default value for the i-th argument position of f.

Examples

No verified examples yet for this function.

Implementation notes

Default is not a builtin handler — it is a symbol whose DownValues the user assigns (Default[f] = v) and which the pattern matcher consumes when filling an Optional pattern (x_., i.e. Optional[x_, Default[f]]). get_default_value(pat_head, pos, total_pats) in src/default_helper.c looks up the default for a function head: if no user Default DownValues exist it short-circuits to the built-in fallbacks (Plus -> 0, Times/Power -> 1, else none); otherwise it evaluates Default[f, pos, total_pats], then Default[f, pos], then Default[f], returning the first that the user has defined (detected by the result differing from the constructed expression), before falling back to the same Plus/Times/Power defaults. The matcher calls this once per Optional-pattern attempt, hence the no-rule fast path.

Attributes: none registered.

Implementation status

Experimental — present and registered, but lightly documented and not yet covered by dedicated tests.

References

Notes & additional examples

Worked examples

In[1]:= Default[h] = 1
Out[1]= 1

In[2]:= h[x_, y_.] := {x, y}
Out[2]= Null

In[3]:= h[5]
Out[3]= {5, 1}

In[4]:= h[5, 9]
Out[4]= {5, 9}

In[1]:= Default[q] = 0
Out[1]= 0

In[2]:= q[a_, b_.] := {a, b}
Out[2]= Null

In[3]:= q[7]
Out[3]= {7, 0}

Notes

Default[f] = v sets the value used for a missing optional argument matched by _. (Optional[Blank[]]). When the optional argument is supplied it is used directly, otherwise the stored default is substituted before the rule fires. This is the mechanism that lets Plus- and Times-style patterns absorb absent terms; for an ad hoc head you register the default yourself, as the two examples (additive default 0, multiplicative-style default 1) show. To attach a per-position default use the Default[f, i] form.