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Orderless

Status: Partial

implemented with documented limitations or caveats; some argument forms fall through to symbolic/unevaluated output.

Description

Orderless is an attribute that can be assigned to a symbol f to indicate that the elements e_i in expressions of the form f[e_1, e_2, ...] should automatically be sorted into canonical order. This property is accounted for in pattern matching.

Examples

No verified examples yet for this function.

Implementation notes

Orderless is an attribute marker symbol, not a function. attr.c maps the name to the ATTR_ORDERLESS bitflag. A head carrying this bit makes the evaluator's ordering step (eval_sort_args in eval.c) sort the arguments into canonical order (expr_compare), giving commutative behaviour. The pattern matcher also accounts for ATTR_ORDERLESS so a pattern can match commuted arguments. Plus and Times set this bit. The symbol appears only as an argument to Attributes/SetAttributes, or inside a Function[..., Orderless] attribute spec (purefunc.c maps SYM_Orderless → ATTR_ORDERLESS).

Attributes: none registered.

Implementation status

Partial — implemented with documented limitations or caveats; some argument forms fall through to symbolic/unevaluated output.

References

Notes & additional examples

Worked examples

In[1]:= SetAttributes[g, Orderless]
Out[1]= Null

In[2]:= g[3, 1, 2]
Out[2]= g[1, 2, 3]

In[3]:= g[c, a, b]
Out[3]= g[a, b, c]

Notes

Orderless marks a head as commutative, so its arguments are automatically sorted into canonical order. Plus and Times carry this attribute by default; canonical ordering is also used when matching patterns against Orderless heads.