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syntax and informal semantics This chapter presents a concise definition of the abstract syntax and informal semantics of the elements of the χ formalism. The syntax definition is incomplete in the sense that the syntax of predicates, expressions, etc. is defined at a high level of abstraction. This is done because different implementations of χ , such as tools for simulation, verification, or real-time control, may impose different syntactical restrictions. The intention of this chapter is to define the χ formalism that encompasses a variety of (future) tools without posing unnecessary syntactical restrictions. 2.1 Syntax of processes A χ process is a triple 〈p, σ, E〉, where p ∈ P denotes a process term as defined in Section 2.5, σ ∈6⊥ denotes a variable valuation as defined in Section 3.1, and E denotes an environment. A variable valuation is a partial function (see Section 3.2) from variables to values. Syntactically, a variable valuation is denoted by a set of pairs {x0 7→ c0, . . . , xn 7→ cn}, where xi denotes a variable and ci its value. A variable valuation is also referred to simply as a valuation. An environment E is a tuple (D,U, J, R), where D : V 7→D is a partial function from variables to dynamic types, hereafter referred to as a dynamic type mapping, U : (Lbasic ∪ τ } ∪H) 7→ B is an urgency mapping in the form of a partial function from basic action labels, the internal action label τ (see Section 2.5), and channels, to boolean values indicating whether an action label or a channel is urgent or not, J ⊆ V denotes the set of jumping variables, and R ⊆ R denotes a recursion definition. Here, V , Lbasic, H, and R denote the sets of all variables, basic action labels, channels, and all recursion definitions, respectively, and the set of dynamic types D is defined asD = {disc, cont,alg}. Syntactically, an urgency mapping for actions or channels