Formal Semantics of the Kconfig Language

The Kconfig language defines a set of symbols that are assigned a value in a configuration. We describe the semantics of the Kconfig language according to the behaviour exhibited in the xconfig configurator. We assume an abstract syntax representation for concepts in the Kconfig language and delegate the details of the translation from concrete to abstract syntaxes to a later document. 1 Abstract syntax Identifiers and expressions. We start be defining the preliminary concepts available in the Kconfig language. Let Id be a finite set of names identifying a symbol—more precisely, Id ∈ P(String). Let Const = Tri ∪ String ∪ Hex ∪ Int be the set of values assignable to each feature and available as constants in expressions, where Tri = {0t, 1t, 2t}. Tri is ordered such that 0t < 1t < 2t. The Tri, String, Hex, and Int domains are disjoint (i.e. mutually exclusive). We can now define an expression in the Kconfig language. KExpr(Id) is a set of expressions over Id generated by the following grammar, where e ∈ KExpr(Id), iv ∈ Id ∪ Const, ⊗ ∈ {or, and}, ⊖ ∈ {=, 6=}: e ::= e⊗ e | not e | iv ⊖ iv | iv (1) Evaluating a KExpr returns a tristate value (i.e. v ∈ Tri). We will define the semantics of an eval function in Section 2.2. Kconfig model. Kconfig denotes the set of all possible models in the Kconfig language. Thus a single Kconfig model m ∈ Kconfig is a tuple consisting of a set of configs and a set of choices. Kconfig is defined as: Kconfig = P(Configs)× P(Choices) (2) Given a Kconfig model m ∈ Kconfig, we define the shorthand mconfig to refer to its set of configs and mchoice to refer to its set of choices. The semantics defined in this document directly reflect the behavior of the Linux make xconfig tool, which could  in some specific cases  act differently from what the Kconfig language developers originally had in mind. At least in case of the reverse dependency the documentation explicitly states the following gap: "Select should be used with care. Select will force a symbol to a value without visiting the dependencies. By abusing select you are able to select a symbol foo even if foo depends on bar that is not set."