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Flat

Status: Partial

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

Description

Flat is an attribute that can be assigned to a symbol f to indicate that all expressions involving nested functions f should be flattened out. This property is accounted for in pattern matching.

Examples (3)

Every input below was run against the current Mathilda build and its output recorded.

Applications (3)

In[1]:= SetAttributes[f, Flat]
Out[1]= Null

In[2]:= f[f[a, b], c]
Out[2]= f[a, b, c]

In[3]:= f[a, f[b, f[c, d]]]
Out[3]= f[a, b, c, d]

Implementation notes

Flat is an attribute marker symbol, not a function. attr.c maps the name to the ATTR_FLAT bitflag (via SetAttributes/the attribute name table). When a head carries ATTR_FLAT, the evaluator's flattening step (eval_flatten_args in eval.c) splices nested same-head calls into the parent argument list, giving associative behaviour (f[a, f[b, c]] → f[a, b, c]). The pattern matcher (match.c) also consults ATTR_FLAT when matching sequence patterns against such heads. Plus and Times set this bit. The symbol Flat itself only ever appears as an argument to Attributes/SetAttributes or inside a Function[..., Flat] attribute spec (pure_function_attributes in purefunc.c maps SYM_Flat → ATTR_FLAT).

Attributes: none registered.

References

Notes & additional examples

Notes

Flat marks a head as associative, so nested calls with the same head are flattened into a single argument sequence. Plus and Times carry this attribute by default; the flattening is also accounted for during pattern matching.