Polyglot Triple Graph Grammars (TGG)

ModelScript provides declarative, ahead-of-time (AOT) compiled Triple Graph Grammars (TGG) and Double-Pushout (DPO) algebraic graph rewriting via @modelscript/dsl/tgg.

TGG serves as the foundational synchronization mechanism across the computable digital thread, enabling bidirectional transformations between disparate engineering models (such as architectural SysML v2 specifications and 1D Modelica physical simulations).

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What is a Triple Graph Grammar?

A Triple Graph Grammar synchronizes three distinct graphs:

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• Source Graph ($G_S$): Represents domain concepts in the source language (e.g. SysML v2 Part Definitions, Ports, Requirements).
• Target Graph ($G_T$): Represents concepts in the target language (e.g. Modelica Models, Connectors, Equations).
• Correspondence Graph ($G_C$): Explicitly records semantic trace links between elements in the source and target models.

Rather than writing ad-hoc imperative glue code, engineers write declarative rules specifying how elements correspond.

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Declarative TGG Rules

A TGG rule specifies patterns in the source, correspondence, and target graphs simultaneously:

import { tggRule } from "@modelscript/dsl/tgg";

export const ComponentToModel = tggRule({
  name: "ComponentToModel",
  source: (s) => ({
    part: s.node("PartUsage", { name: s.var("compName") }),
    port: s.node("PortUsage", { parent: s.nodeRef("part") }),
  }),
  target: (t) => ({
    model: t.node("ModelDefinition", { name: t.var("compName") }),
    pin: t.node("PinConnector", { parent: t.nodeRef("model") }),
  }),
  correspondence: (c) => ({
    tracePart: c.link("part", "model"),
    tracePort: c.link("port", "pin"),
  }),
});

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AOT Compilation to WebAssembly

Unlike interpreted graph transformation engines, @modelscript/dsl/tgg compiles rules into deterministic AssemblyScript dispatch routines executing directly in WebAssembly:

• tgg_forward_dispatch: Incremental forward propagation from source changes to target models.
• tgg_backward_dispatch: Reverse propagation of parameter sizing or component changes back to architectural definitions.
• tgg_propagate_all_stale: High-throughput batch reconciliation across dirty workspace subgraphs.

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Critical Pair Analysis (CPA)

A notorious problem in graph transformation is rule conflict and non-determinism. ModelScript includes an automated Critical Pair Analysis (CPA) verification pass:

1. Confluence Verification: Analyzes whether overlapping rule applications could cause divergent target states.
2. Termination Guarantees: Proves that cyclic dependencies cannot cause infinite rewrite loops during synchronization.
3. Completeness Checking: Flags unmapped source elements that lack corresponding target constructors.