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HoldAll

Status: Stable

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

Description

HoldAll

is an attribute that specifies that all arguments to a function are to be maintained in an unevaluated form.

Notes You can use Evaluate to evaluate the arguments of a HoldAll function in a controlled way. Even when a function has attribute HoldAll, Sequence objects that appear in its arguments are still by default flattened; Unevaluated wrappers on a held argument are, however, left intact (use HoldComplete/HoldAllComplete to also suppress Sequence flattening).

Examples (9)

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

Basic examples (4)

In[1]:= Hold[1+1, 2+2]
Out[1]= Hold[1 + 1, 2 + 2]

In[2]:= Hold[Sequence[a, b], c]
Out[2]= Hold[a, b, c]

In[3]:= Hold[Unevaluated[1+2]]
Out[3]= Hold[Unevaluated[1 + 2]]

In[4]:= Hold[Evaluate[1+2], 3+4]
Out[4]= Hold[3, 3 + 4]

Applications (5)

Give f the HoldAll attribute

In[5]:= SetAttributes[f, HoldAll]

In[6]:= Attributes[f]
Out[6]= {HoldAll}

The argument is held, so the sum is not computed

In[7]:= f[2 + 3]
Out[7]= f[2 + 3]

An ordinary head evaluates its argument first

In[8]:= g[2 + 3]
Out[8]= g[5]

:= is defined to hold all of its arguments

In[9]:= Attributes[SetDelayed]
Out[9]= {HoldAll, Protected, SequenceHold}

Implementation notes

What it is. HoldAll is an attribute symbol, not a function ā€” one of the tokens the attribute system (src/attr.c) maps to and from bitflags. In attr.h the flag is ATTR_HOLDALL, defined as the pair ATTR_HOLDFIRST | ATTR_HOLDREST. get_attribute_flag("HoldAll") returns that combined flag, and when attributes_to_list finds both bits set it emits the single symbol HoldAll (otherwise HoldFirst / HoldRest individually).

Effect. When a head carries ATTR_HOLDALL the evaluator suppresses evaluation of every argument before calling the head (step 3 of the evaluation loop), so the arguments reach the head unevaluated. Hold, SetDelayed, Function, Attributes, OwnValues/DownValues and many control-flow heads carry it. Unlike HoldAllComplete (ATTR_HOLDALLCOMPLETE) it does not also suppress upvalue lookup or the Sequence/Unevaluated-stripping machinery.

Usage. HoldAll has no C handler and no standalone meaning; it appears only inside Attributes[...], SetAttributes[sym, HoldAll] and ClearAttributes[sym, HoldAll]. Setting it on a head f is what makes f[2 + 3] stay f[2 + 3] rather than reducing to f[5].

Attributes: none registered.

References

See also: SequenceHold, HoldFirst, HoldRest, Hold, HoldForm, HoldPattern, Function

Notes & additional examples

Notes

HoldAll is an attribute symbol, not a function. A head carrying it has all of its arguments held unevaluated before the head runs ā€” the mechanism behind Hold, SetDelayed (:=), Function and the control-flow heads. It appears only inside Attributes[...], SetAttributes[sym, HoldAll] and ClearAttributes[sym, HoldAll].

Internally HoldAll is the pair HoldFirst | HoldRest; Attributes reports that pair as the single token HoldAll. Unlike HoldAllComplete it still allows upvalue lookup and Sequence/Unevaluated processing on the held arguments.