The dynamics of a language is a description of how programs are to be executed. The most important way to define the dynamics of a language is by the method of structural dynamics, which defines a transition system that inductively specifies the step-by-step process of executing a program. Another method for presenting dynamics, called contextual dynamics, is a variation of structural dynamics in which the transition rules are specified in a slightly different manner. An equational dynamics presents the dynamics of a language equationally by a collection of rules for deducing when one program is definitionally equal to another.

Transition Systems

A transition system is specified by the following four forms of judgment:

1. s state, asserting that s is a state of the transition system,

2. s final, where s state, asserting that s is a final state,

3. s initial, where s state, asserting that s is an initial state,

4. s ↦ s′, where s state and s′ state, asserting that state s may transition to state s′.

In practice we always arrange things so that no transition is possible from a final state: If s final, then there is no s′ state such that s ↦ s′. A state from which no transition is possible is sometimes said to be stuck. Whereas all final states are, by convention, stuck, there may be stuck states in a transition system that are not final.