Unique¶

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description¶

Unique[]

generates a new symbol; Unique["x"] or Unique[x] uses a name prefix; Unique[{x, ...}] gives a list of fresh symbols. Each is Temporary and never previously used.

Examples (5)¶

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

Basic examples (1)¶

In[1]:= {Unique[], Unique["x"], Unique[{a, b}]}
Out[1]= {$1, x2, {a3, b3}}

Applications (4)¶

In[2]:= Unique[]
Out[2]= $1

In[3]:= Unique[x]
Out[3]= x2

In[4]:= Unique["c"]
Out[4]= c3

In[5]:= Unique[{p, q}]
Out[5]= {p4, q4}

Implementation notes¶

Algorithm. builtin_unique (src/modular.c) generates fresh, never-before-used symbols. Unique[] uses the prefix "$"; Unique[x] or Unique["x"] uses the symbol's name or the string as prefix (unique_prefix_of); Unique[{a, b, ...}] returns a list of fresh symbols, one per element, all sharing one numeric suffix (the Wolfram behaviour). The suffix is drawn from the module counter module_number, the same monotone source Module uses for its x$n temporaries.

unique_make_batch guarantees freshness by scanning: it advances module_number until prefix<n> names no existing symbol for every prefix in the batch, then takes that value and post-increments. Each generated symbol is created with expr_new_symbol and tagged ATTR_TEMPORARY, and the user-visible $ModuleNumber OwnValue is re-synced from the counter (unique_sync_module_number), so Unique and Module share one numbering. An unusable prefix (not a symbol or string) makes the batch fail and the head returns NULL.

Attributes & limits. Unique has no special attributes — its single argument is evaluated normally. It accepts zero or one argument; the list form yields one suffix-sharing symbol per element.

Protected.
The numeric suffix is drawn from the shared $ModuleNumber counter (the same source Module uses), advanced until the generated name is unused, so every result is genuinely fresh and distinct.
Created symbols have the Temporary attribute.

Attributes: Protected.

References¶

See also: Module

Source: src/modular.c
Specification: docs/spec/builtins/scoping-constructs.md
Tests: tests/test_series.c

Notes & additional examples¶

Notes¶

Unique[] generates a brand-new symbol, Unique[x] or Unique["x"] uses the given name as a prefix, and Unique[{a, b, ...}] returns a list of fresh symbols sharing one numeric suffix. Each name is formed from a prefix and a number drawn from the $ModuleNumber counter — the same counter Module uses for its locals.

Freshness is guaranteed by construction: the counter is advanced until the candidate name is unused for every prefix in the batch, so a returned symbol has never named anything before. Each generated symbol is Temporary.