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Navigation Algebra for MAP Core

(Human-First DAHN Navigation → Cypher-Ready Foundation)

This document defines a deliberately constrained, imperative execution algebra designed to power interactive, gesture-driven navigation of MAP property graphs before introducing declarative Cypher compilation. It establishes a minimal operand model (Value, Row, RowSet), a lightweight execution tree structure, and a transaction-scoped interpreter that cleanly separates ontology, resolved structural projection, and instance state.

The algebra is intentionally limited to navigation-oriented operations (Seed, Expand, Filter, Project, Distinct, OrderBy, Skip, Limit) while remaining forward-compatible with future declarative OpenCypher compilation and optimization. It serves as the foundational execution layer upon which the full query planner algebra will later be built.

This plan defines the smallest execution algebra that can subsume:

  • Current MAP imperative operations
  • A powerful subset of Cypher
  • Future extensibility toward declarative query compilation

It incorporates:

  • Transaction-scoped execution
  • Flattened ResolvedType runtime projection
  • Strict separation of structure vs state
  • Semantic newtypes for descriptor references
  • No query optimization (yet)

Step 1 — Stabilize the Three-Layer Architecture

Before introducing algebra, explicitly formalize three runtime layers:

1. Ontology Layer (Persistent, Holonic)

  • TypeDescriptor
  • Extends
  • InstanceProperties
  • InstanceRelationships
  • All schema semantics remain declarative

2. Runtime Structural Layer (Ephemeral Projection)

Introduce immutable: