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 |
| Exogenous Signal (z) | An external signal entering the system from outside | BoundaryAction outputs flowing through Ports. Paper uses u for the selected action; codebase uses z for exogenous signals to avoid conflation. |
| Decision (d) | The output of the policy mapping d = g(x, z) | Policy forward_out ports. Corresponds to the paper's selected action u ∈ U_x. |
| Admissible Input Space (U_x) | The set of inputs available given the current state x (paper Def 2.5) | Structural skeleton via AdmissibleInputConstraint; behavioral constraint requires runtime |
| Input Map (g) | Maps state and exogenous signals to a decision: g(x, z) → d | Policy blocks (endogenous decision logic) |
| State Update Map (f) | Takes current state and decision, produces the next state: f(x, d) → 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 | A sequence of states under repeated application of h | Structural recurrence 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