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DownValues

Status: Stable

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

Description

DownValues[s]

gives a list of down-value rules for s.

Examples (5)

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

Basic examples (2)

In[1]:= f[x_] := x^2; DownValues[f]
Out[1]= {HoldPattern[f[x_]] :> x^2}

In[2]:= a = 5; OwnValues[a]
Out[2]= {HoldPattern[a] :> 5}

Applications (3)

In[3]:= square[n_] := n*n

In[4]:= DownValues[square]
Out[4]= {HoldPattern[square[n_]] :> n n}

In[5]:= square[7]
Out[5]= 49

Implementation notes

builtin_down_values (1-arg, symbol only) calls symtab_get_down_values(sym) to fetch the raw Rule* linked list held on the SymbolDef, then rules_to_list walks it, wrapping each node's pattern/replacement pair (deep-copied) in a Rule[lhs, rhs] and collecting them into a List. The rules are returned unevaluated ā€” they are emitted as literal RuleDelayed-style Rule heads without re-evaluating the stored patterns. DownValues are stored newest-first, which is the traversal order here.

  • Each rule is returned as HoldPattern[lhs] :> rhs (a RuleDelayed whose left-hand side is wrapped in HoldPattern), matching Mathematica. The HoldPattern keeps the stored pattern from re-matching its own definition, and the RuleDelayed keeps the right-hand side unevaluated, so the returned list is inert: querying DownValues[f] for a recursive f does not re-trigger the recursion, and a right-hand side such as RandomInteger[...] is shown held rather than evaluated afresh on each query.
  • Returns {} for a symbol that carries no rules of the requested kind.

Attributes: HoldAll, Protected.

References

See also: OwnValues, RuleDelayed, HoldPattern

Notes & additional examples

Notes

DownValues[s] returns the pattern rules defined on s via f[args] := .... Each entry is the stored lhs -> rhs rule the evaluator tries when s is called.