Equation 5 · Part 1 · What Claude Code's Permission Model Actually Allows, in Plain Terms

Symbol c

\text{decision}(c) = \begin{cases} \text{deny}, & c \in D \\ \text{ask}, & c \notin D \text{ and } c \in A \\ \text{allow}, & c \notin D \cup A \text{ and } c \in W \\ \text{ask (default)}, & \text{otherwise} \end{cases}

c

What this part means

c is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Its job in the formula

c is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Full expressionSymbol cArticle meaning

The passage around this formula

The precedence is simple enough to state directly. For a tool call c checked against the deny set D , the ask set A , and the allow set W : $\text{decision}(c) = \begin{cases} \text{deny}, & c \in D \\ \text{ask}, & c \notin D \text{ and } c \in A \\ \text{allow}, & c \notin D \cup A \text{ and } c \in W \\ \text{ask (default)}, & \text{otherwise} \end{cases}$ . An unmatched command does not fail open into silent execution. It falls through to a prompt — what the documentation calls fail-closed matching [ 2 ] .

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

[2] Security ↗

These citations provide research context; check each source for the exact claim it supports.