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RuleDelayed

Status: Stable

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

Description

lhs :> rhs or RuleDelayed[lhs, rhs] represents a delayed rewrite rule: rhs is held and evaluated only each time the rule fires, after the pattern bindings on lhs are substituted into rhs.

Examples (4)

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

Applications (4)

In[1]:= {1, 2, 3} /. n_ :> n^2
Out[1]= {1, 4, 9}

In[2]:= FullForm[a :> b]
Out[2]= RuleDelayed[a, b]

In[3]:= x^4 + 3 x^2 + 1 /. x^n_ :> x^(n+1)/(n+1)
Out[3]= 1 + x^3 + 1/5 x^5

In[4]:= {f[1], f[2], f[3]} /. f[n_] :> n!
Out[4]= {1, 2, 6}

Implementation notes

RuleDelayed[lhs, rhs] (:>) is a passive delayed-rewrite object with no builtin handler. Its ATTR_HOLDREST | ATTR_SEQUENCEHOLD | ATTR_PROTECTED attributes hold rhs unevaluated at construction; the rule engine (is_rule in src/replace.c) detects the RuleDelayed head and, each time the rule fires, substitutes the fresh pattern bindings into the held rhs and only then evaluates it (see the delayed flag threaded through ReplaceRule/ReplaceListState). This is the difference from Rule, whose RHS is evaluated once up front.

Attributes: HoldRest, Protected, SequenceHold.

References

Notes & additional examples

Notes

a :> b is shorthand for RuleDelayed[a, b]. The right-hand side is held and evaluated separately for each match, after the pattern bindings are substituted in.