Explain why the following guarded commands in SR are not...

Explain why the following guarded commands in SR are not equivalent: $\begin{array}{ll}\text { if } a\langle b \rightarrow c:=a & \text { if } a\langle b \rightarrow c:=a \\ \text { [] } b\langle c \rightarrow c:=b & {[] b\langle c \rightarrow c:: b} \\ \text { [] else } \rightarrow c:=d & {[] \text { true } \rightarrow c:=d} \\ \text { fi } & \text { fi }\end{array}$ if $\mathrm{a}\langle\mathrm{b} \rightarrow \mathrm{c}:=\mathrm{a} \quad$ if $\mathrm{a}\langle\mathrm{b} \rightarrow \mathrm{c}:=\mathrm{a}$ [] $\mathrm{b}<\mathrm{c} \rightarrow \mathrm{c}:=\mathrm{b} \quad$ [] $\mathrm{b}\langle\mathrm{c} \rightarrow \mathrm{c}:=\mathrm{b}$ [] else $\rightarrow c:=d$ [] true $\rightarrow c:=d$ fi fi

Explain why the following guarded commands in SR are not equivalent:
$\begin{array}{ll}\text { if } a\langle b \rightarrow c:=a & \text { if } a\langle b \rightarrow c:=a \\ \text { [] } b\langle c \rightarrow c:=b & {[] b\langle c \rightarrow c:: b} \\ \text { [] else } \rightarrow c:=d & {[] \text { true } \rightarrow c:=d} \\ \text { fi } & \text { fi }\end{array}$
if $\mathrm{a}\langle\mathrm{b} \rightarrow \mathrm{c}:=\mathrm{a} \quad$ if $\mathrm{a}\langle\mathrm{b} \rightarrow \mathrm{c}:=\mathrm{a}$
[] $\mathrm{b}<\mathrm{c} \rightarrow \mathrm{c}:=\mathrm{b} \quad$ [] $\mathrm{b}\langle\mathrm{c} \rightarrow \mathrm{c}:=\mathrm{b}$
[] else $\rightarrow c:=d$ [] true $\rightarrow c:=d$
fi
fi

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Key Concepts

Nondeterministic Choice in Conditional Statements

The semantics of guarded commands rely on nondeterministic choice among enabled guards when there is more than one possibility. Altering the guards—such as by introducing a 'true' guard that is always enabled—can disrupt the expected nondeterminism and may marshal control flow in a manner that diverges from the intended mutual exclusivity of the options.

Guarded Commands

Guarded commands are a programming construct where actions are associated with boolean conditions called guards. In such constructions, one of the actions whose guard evaluates to true is chosen for execution, typically in a nondeterministic way. Understanding the basic structure of guarded commands is crucial to assessing how different guard formulations affect program behavior.

Guard Evaluation and the ELSE Clause

A specific aspect of guarded commands is the use of an 'else' clause, which is only activated when none of the preceding guards evaluate to true. This provides a default case that is only executed in the absence of any other enabled guard. In contrast, replacing the 'else' with a guard that has the value 'true' creates a branch that is always enabled, thereby altering the intended conditional behavior.

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