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Volume 13 — φ-Type System and Structure Typing

Type Theory for Golden-Base Computation​

This volume develops a complete type system for φ-constrained programming. Types themselves must respect the no-11 constraint, leading to a unique type theory where types are trace structures.

Chapter Index​

Chapter 208: TypePhi​

φ-Trace Based Collapse Typing System

Foundation of trace-based types.

Chapter 209: TensorType​

Hierarchy of Collapse Tensor Types

Type hierarchies in tensor space.

Chapter 210: CollapseFuncType​

Structural Function Type Classifications

Function types preserving constraints.

Chapter 211: TypeInfer​

Inference Rules over Collapse Paths

Type inference algorithms.

Chapter 212: ObsTypeFilter​

Observer-Specific Type Filters

Types relative to observer perspective.

Chapter 213: TypeConstraint​

Safety and Compatibility Rules on Collapse Types

Constraint satisfaction in types.

Chapter 214: TypeMorph​

Collapse Type Morphisms in Structural Categories

Category theory of types.

Chapter 215: GenericTraceType​

Parametric φ-Type Traces

Generic and parametric types.

Chapter 216: TypeUnify​

Unification Rules for Trace Type Resolution

Type unification algorithms.

Chapter 217: TypeError​

Collapse-Type Conflict and Diagnostics

Type error detection and reporting.

Chapter 218: DepType​

Dependent Type System from Trace-Derived Quantities

Dependent types in trace space.

Chapter 219: InterfaceTrace​

Collapsible Trait Structures for Trace Composition

Interface and trait systems.

Chapter 220: ObsViewType​

Observer-Dependent View of Trace Types

Type perspectives per observer.

Chapter 221: ZetaTyped​

ζ-Weighted Types for Spectrum-Specific Collapse

Spectral type classifications.

Chapter 222: TypeLattice​

Lattice Ordering of Trace Type Subsumption

Type ordering and subtyping.

Chapter 223: TypeCollapseOp​

Collapse-Type Specific Operator Interfaces

Type-directed operations.

Key Concepts Introduced​

  1. Trace Types: Types as trace structures
  2. Type Inference: Constraint-based inference
  3. Observer Types: Perspective-dependent typing
  4. Dependent Types: Value-dependent types
  5. Type Safety: φ-constraint preservation
  6. Generic Types: Parametric polymorphism

Dependencies​

  • Volume 12: Language syntax
  • Volume 11: Computational model
  • Volume 15: Category theory

Next Steps​

  • Volume 14: Module systems
  • Volume 19: Type checking in compiler
  • Volume 21: Types for AGI

"Types trace the golden paths of safety."