In compiler theory, a reaching definition for a given instruction is an earlier instruction whose target variable can reach (be assigned to) the given one without an intervening assignment. For example, in the following code:
d1 : y := 3 d2 : x := y
<code>d1</code> is a reaching definition for <code>d2</code>. In the following, example, however:
d1 : y := 3 d2 : y := 4 d3 : x := y
<code>d1</code> is no longer a reaching definition for <code>d3</code>, because <code>d2</code> kills its reach: the value defined in <code>d1</code> is no longer available and cannot reach <code>d3</code>.
The similarly named reaching definitions is a data-flow analysis which statically determines which definitions may reach a given point in the code. Because of its simplicity, it is often used as the canonical example of a data-flow analysis in textbooks. The data-flow confluence operator used is set union, and the analysis is forward flow. Reaching definitions are used to compute use-def chains.
The data-flow equations used for a given basic block in reaching definitions are:
In other words, the set of reaching definitions going into are all of the reaching definitions from 's predecessors, . consists of all of the basic blocks that come before in the control-flow graph. The reaching definitions coming out of are all reaching definitions of its predecessors minus those reaching definitions whose variable is killed by plus any new definitions generated within .
For a generic instruction, we define the and sets as follows:
where is the set of all definitions that assign to the variable . Here is a unique label attached to the assigning instruction; thus, the domain of values in reaching definitions are these instruction labels.
Reaching definition is usually calculated using an iterative worklist algorithm.
Input: control-flow graph CFG = (Nodes, Edges, Entry, Exit)