Glossary¶
GDS terminology mapped to framework concepts.
| Term | Definition | In the framework |
|---|---|---|
| State (x) | The current configuration of the system — a point in the state space | A value held by StateVariables inside an Entity |
| State Space (X) | All possible configurations; can be any data structure, not just ℝⁿ | Product of all Entity variables, each typed by TypeDef |
| Input (u) | An external or agent-chosen action that influences the next state | A signal flowing through Ports on a block's Interface |
| Admissible Input Space (U_x) | The set of inputs available given the current state x | Constraints encoded in ControlAction blocks |
| Input Map (g) | Selects an input u from the admissible set — may be a decision-maker or stochastic process | BoundaryAction (exogenous) or Policy (endogenous) |
| State Update Map (f) | Takes current state and chosen input, produces the next state: f(x, u) → x⁺ | Mechanism blocks — the only blocks that write to state |
| State Transition Map (h) | The composed pipeline h = f|_x ∘ g — one full step of the system | The wiring produced by >> composition |
| Trajectory (x₀, x₁, ...) | A sequence of states produced by repeatedly applying h | Temporal iteration via .loop() |
| Reachability | Can the system reach state y from state x through some sequence of inputs? | check_reachability() in the verification engine |
| Controllability | Can the system be steered to a target state from any nearby initial condition? | Formal property checked at the spec level |
| Configuration Space | The subset of X where every point is reachable from some initial condition | Characterized by transitive closure over the wiring graph |
Intellectual Lineage¶
- GDS formalism (Roxin 1960s; Zargham & Shorish 2022) — state transitions composed over arbitrary data structures
- MSML (BlockScience) — block roles, parameter tracking, typed transmission channels
- BDP-lib (Block Diagram Protocol) — abstract/concrete separation, structural validation
- Categorical cybernetics (Ghani, Hedges et al.) — bidirectional composition with contravariant feedback