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If

Status: Stable

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

Description

If[cond, t]
    gives t if cond evaluates to True; gives Null otherwise.
If[cond, t, f]
    gives t if cond is True, f if False, and is left unevaluated
    if cond is neither.
If[cond, t, f, u]
    also supplies u as the result when cond is neither True nor False.
If has attribute HoldRest: only the branch chosen by cond is evaluated.

Examples

All examples below are verified against the current Mathilda build.

In[1]:= If[True, x, y]
Out[1]= x

In[2]:= If[a < b, 1, 0, Indeterminate]
Out[2]= Indeterminate

Implementation notes

Algorithm. builtin_if accepts 2–4 arguments and is registered with ATTR_HOLDREST, so only the condition (arg 0) is evaluated by the standard evaluator before the builtin runs; the branches stay held. The handler inspects the evaluated condition: if it is the interned symbol True it returns a copy of arg 1; if it is False it returns a copy of arg 2 (the else branch), or Null when no else branch was supplied. The returned branch is still "held" data that the outer fixed-point evaluator then reduces. If the condition is neither True nor False, a 4-argument call returns a copy of the fourth argument (the "neither" / indeterminate branch), and otherwise the call returns NULL, leaving If[...] unevaluated so a symbolic condition flows through unchanged. Truth testing is pointer equality against SYM_True/SYM_False, never a string compare.

  • HoldRest, evaluating only the chosen branch.
  • Remains unevaluated if the condition is undetermined and u is not provided.
  • If[condition, t] returns Null if condition evaluates to False.

Attributes: HoldRest, Protected.

Implementation status

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

References

Notes & additional examples

Worked examples

In[1]:= If[3 > 2, yes, no]
Out[1]= yes

In[1]:= If[x > 0, pos, neg]
Out[1]= If[x > 0, pos, neg]

In[1]:= If[1 == 2, a, b, c]
Out[1]= b

In[1]:= If[PrimeQ[7], prime, composite]
Out[1]= prime

Notes

If[cond, t, f] evaluates t when cond is True and f when it is False. If has the HoldRest attribute, so only the selected branch is evaluated — the other is never run. When the condition is neither True nor False (e.g. the symbolic x > 0), If returns unevaluated rather than guessing. The optional fourth argument u is returned for that indeterminate case in the four-argument form If[cond, t, f, u].