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Add comprehensive academic proofs and formal verification#2

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claude/add-academic-proofs-G3zZU
Dec 31, 2025
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Add comprehensive academic proofs and formal verification#2
hyperpolymath merged 1 commit into
mainfrom
claude/add-academic-proofs-G3zZU

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This commit adds exhaustive academic documentation covering the theoretical foundations of the Anvomidav DSL for figure skating choreography notation.

Formal Specification

  • grammar.adoc: Complete EBNF grammar, lexical specification, parsing complexity
  • semantics.adoc: Operational, denotational, and axiomatic semantics
  • automata-theory.adoc: DFAs, PDAs, timed automata, tree automata

Type Theory

  • type-system.adoc: Dependent types, refinement types, effect system, linear types
  • category-theory-foundations.adoc: CCCs, monads, adjunctions, fibred categories

Domain Mathematics

  • rink-geometry.adoc: Coordinate systems, paths, collision detection, topology
  • temporal-specification.adoc: LTL, MTL, duration calculus, timed CSP
  • skating-physics.adoc: Mechanics, dynamics, biomechanics
  • numerical-analysis.adoc: Integration, error analysis, constraint handling

Verification

  • rules-specification.adoc: Formal ISU rule encoding
  • verification-methodology.adoc: Theorem proving, model checking, runtime verification
  • abstract-interpretation.adoc: Abstract domains, Galois connections, static analysis
  • computational-complexity.adoc: Time/space bounds, decision problems, FPT

Proofs

  • soundness-completeness.adoc: Type soundness, semantic correctness, compiler correctness

White Papers

  • anvomidav-overview.adoc: Technical white paper summarizing the language

Each document includes theorems, proofs (or proof sketches), definitions, and clearly marked TODO sections for areas requiring further development.

This commit adds exhaustive academic documentation covering the theoretical
foundations of the Anvomidav DSL for figure skating choreography notation.

## Formal Specification
- grammar.adoc: Complete EBNF grammar, lexical specification, parsing complexity
- semantics.adoc: Operational, denotational, and axiomatic semantics
- automata-theory.adoc: DFAs, PDAs, timed automata, tree automata

## Type Theory
- type-system.adoc: Dependent types, refinement types, effect system, linear types
- category-theory-foundations.adoc: CCCs, monads, adjunctions, fibred categories

## Domain Mathematics
- rink-geometry.adoc: Coordinate systems, paths, collision detection, topology
- temporal-specification.adoc: LTL, MTL, duration calculus, timed CSP
- skating-physics.adoc: Mechanics, dynamics, biomechanics
- numerical-analysis.adoc: Integration, error analysis, constraint handling

## Verification
- rules-specification.adoc: Formal ISU rule encoding
- verification-methodology.adoc: Theorem proving, model checking, runtime verification
- abstract-interpretation.adoc: Abstract domains, Galois connections, static analysis
- computational-complexity.adoc: Time/space bounds, decision problems, FPT

## Proofs
- soundness-completeness.adoc: Type soundness, semantic correctness, compiler correctness

## White Papers
- anvomidav-overview.adoc: Technical white paper summarizing the language

Each document includes theorems, proofs (or proof sketches), definitions,
and clearly marked TODO sections for areas requiring further development.
@hyperpolymath
hyperpolymath merged commit 445d4c7 into main Dec 31, 2025
1 of 2 checks passed
@hyperpolymath
hyperpolymath deleted the claude/add-academic-proofs-G3zZU branch December 31, 2025 13:15
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2 participants