Add comprehensive academic proofs and formal verification#2
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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.
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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
Type Theory
Domain Mathematics
Verification
Proofs
White Papers
Each document includes theorems, proofs (or proof sketches), definitions, and clearly marked TODO sections for areas requiring further development.