TauLib · API Book VI

TauLib.BookVI.Consumer.Evolution

TauLib.BookVI.Consumer.Evolution

Evolution as PPAS optimization on fitness landscapes.

Registry Cross-References

  • [VI.D50] PPAS Algorithm on Fitness Landscapes — PPASFitness

  • [VI.T27] Evolution as Optimization (NP-hard → polynomial) — evolution_is_ppas

  • [VI.R20] Fitness Landscape Topology — FitnessLandscapeTopology

Cross-Book Authority

  • Book III, Part IX: III.T33 Admissibility Collapse / PPAS (Prover–Proof–Admissibility–Specifier)

  • Book III, Part I: P vs NP force (NP-hard optimization in polynomial time)

Ground Truth Sources

  • Book VI Chapter 37 (2nd Edition): Evolution as PPAS

  • Book VI Chapter 38 (2nd Edition): Speciation and Fitness Landscapes

Tau.BookVI.Evolution.PPASFitness

source structure Tau.BookVI.Evolution.PPASFitness :Type

[VI.D50] PPAS Algorithm on Fitness Landscapes. Population = Prover, Selection = Verifier (Book III, Part IX). The NP-hard fitness landscape optimization (Book III, Part I) is solved in polynomial generations by the PPAS protocol: mutation proposes, selection verifies, population converges.

  • landscape_np_hard : Bool Fitness landscape is NP-hard.

  • prover : String Population acts as prover.

  • verifier : String Selection acts as verifier.

  • polynomial_converge : Bool PPAS achieves polynomial convergence.

Instances For

Tau.BookVI.Evolution.instReprPPASFitness.repr

source def Tau.BookVI.Evolution.instReprPPASFitness.repr :PPASFitness → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookVI.Evolution.instReprPPASFitness

source instance Tau.BookVI.Evolution.instReprPPASFitness :Repr PPASFitness

Equations

  • Tau.BookVI.Evolution.instReprPPASFitness = { reprPrec := Tau.BookVI.Evolution.instReprPPASFitness.repr }

Tau.BookVI.Evolution.ppas_fit

source def Tau.BookVI.Evolution.ppas_fit :PPASFitness

Equations

  • Tau.BookVI.Evolution.ppas_fit = { } Instances For

Tau.BookVI.Evolution.EvolutionOptimization

source structure Tau.BookVI.Evolution.EvolutionOptimization :Type

[VI.T27] Evolution as Optimization: NP-hard → polynomial. Four evolutionary forces: mutation, selection, drift, migration. Together they implement the PPAS protocol (Book III, Part IX, III.T33) that reduces NP-hard search to polynomial convergence.

  • force_count : ℕ Number of evolutionary forces.

  • count_eq : self.force_count = 4 Exactly 4 forces.

  • mutation : Bool Force 1: mutation (variation generator).

  • selection : Bool Force 2: selection (fitness filter).

  • drift : Bool Force 3: genetic drift (stochastic sampling).

  • migration : Bool Force 4: migration (gene flow).

  • convergence : Bool Convergence in polynomial generations.

Instances For

Tau.BookVI.Evolution.instReprEvolutionOptimization.repr

source def Tau.BookVI.Evolution.instReprEvolutionOptimization.repr :EvolutionOptimization → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookVI.Evolution.instReprEvolutionOptimization

source instance Tau.BookVI.Evolution.instReprEvolutionOptimization :Repr EvolutionOptimization

Equations

  • Tau.BookVI.Evolution.instReprEvolutionOptimization = { reprPrec := Tau.BookVI.Evolution.instReprEvolutionOptimization.repr }

Tau.BookVI.Evolution.evo_opt

source def Tau.BookVI.Evolution.evo_opt :EvolutionOptimization

Equations

  • Tau.BookVI.Evolution.evo_opt = { force_count := 4, count_eq := Tau.BookVI.Evolution.evo_opt._proof_1 } Instances For

Tau.BookVI.Evolution.evolution_is_ppas

source theorem Tau.BookVI.Evolution.evolution_is_ppas :evo_opt.force_count = 4 ∧ evo_opt.convergence = true ∧ ppas_fit.polynomial_converge = true

Tau.BookVI.Evolution.ppas_polynomial_convergence

source theorem Tau.BookVI.Evolution.ppas_polynomial_convergence :ppas_fit.landscape_np_hard = true ∧ ppas_fit.polynomial_converge = true

Tau.BookVI.Evolution.FitnessLandscapeTopology

source structure Tau.BookVI.Evolution.FitnessLandscapeTopology :Type

[VI.R20] Fitness Landscape Topology. Rugged landscapes with epistatic interactions, NK-model structure, and multiple attractor basins. Speciation occurs at saddle points between basins.

  • epistatic : Bool Epistatic interactions present.

  • nk_model : Bool NK-model structure.

  • attractor_basins : Bool Attractor basins present.

Instances For

Tau.BookVI.Evolution.instReprFitnessLandscapeTopology

source instance Tau.BookVI.Evolution.instReprFitnessLandscapeTopology :Repr FitnessLandscapeTopology

Equations

  • Tau.BookVI.Evolution.instReprFitnessLandscapeTopology = { reprPrec := Tau.BookVI.Evolution.instReprFitnessLandscapeTopology.repr }

Tau.BookVI.Evolution.instReprFitnessLandscapeTopology.repr

source def Tau.BookVI.Evolution.instReprFitnessLandscapeTopology.repr :FitnessLandscapeTopology → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookVI.Evolution.fitness_topo

source def Tau.BookVI.Evolution.fitness_topo :FitnessLandscapeTopology

Equations

  • Tau.BookVI.Evolution.fitness_topo = { } Instances For

Tau.BookVI.Evolution.fitness_landscape_rugged

source theorem Tau.BookVI.Evolution.fitness_landscape_rugged :fitness_topo.epistatic = true ∧ fitness_topo.nk_model = true ∧ fitness_topo.attractor_basins = true