Set¶

Status: Stable

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

Description¶

lhs = rhs or Set[lhs, rhs] evaluates rhs once and assigns the result to lhs. When lhs is a symbol, the assignment is stored as an OwnValue; when lhs has the form f[args...] it is stored as a DownValue on f. Set has attribute HoldFirst so lhs is not evaluated before the assignment.

Examples (2)¶

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

Applications (2)¶

In[1]:= x = 5
Out[1]= 5

In[2]:= x + 1
Out[2]= 6

Implementation notes¶

Algorithm. Set (=) is not a registered builtin; it is a special primitive handled directly inside evaluate_step in src/eval.c (step 6, guarded by head_name == SYM_Set). The head carries ATTR_HOLDFIRST (src/attr.c), so the RHS is evaluated by the generic evaluator before the primitive runs but the LHS is held. The primitive then partially evaluates the LHS to find the assignment target: for f[args] = rhs it evaluates only the arguments (not the head f), so f[x] = 1 with x = c installs a rule keyed on the evaluated f[c]. Arguments are held when they are pattern-bearing (lhs_arg_contains_pattern — to stop existing DownValues from rewriting the pattern being defined), when the LHS head has Hold attributes, for the first arg of Part, and for symbol/nested-List elements of a List LHS (destructuring targets must not be value-substituted). The shaped target is passed to apply_assignment(lhs, rhs, is_delayed=false), and Set returns the (already-evaluated) RHS.

Data structures. apply_assignment dispatches on the LHS shape: a bare EXPR_SYMBOL installs an OwnValue via symtab_add_own_value; a function head installs a DownValue via symtab_add_down_value keyed on the head symbol (the whole LHS becomes the stored pattern); a List LHS recurses element-wise for destructuring ({x,y} = {1,2}); a Part LHS routes to expr_part_assign. Writes to ATTR_PROTECTED targets (resolved through Condition/HoldPattern/Part wrappers by assignment_target_symbol) are refused with a Set::wrsym message but still return the RHS. $RecursionLimit assignments additionally mirror the value into the C-side limit.

Attributes: HoldFirst, Protected, SequenceHold.

References¶

See also: SetDelayed

Source: src/eval.c
Specification: docs/spec/builtins/assignment-and-rules.md
Tests: tests/test_eval.c
Tests: tests/test_intrat.c
Tests: tests/test_linalg.c
Tests: tests/test_linearsolve.c

Notes & additional examples¶

Notes¶

= (Set) evaluates the right-hand side once and stores the result. For a bare symbol the assignment is an OwnValue, so later uses of x substitute the stored value.