betlang

A ternary probabilistic programming language for modeling uncertainty

betlang is a Domain-Specific Language (DSL) for probabilistic programming built on Racket. Its core primitive is the ternary bet - a choice between three values with associated probabilities. This simple yet powerful concept enables elegant expression of complex probabilistic models.

Features

Core Language

• Ternary Bets: (bet A B C) - randomly select one of three values

• Weighted Probabilities: (bet/weighted '(A 5) '(B 3) '(C 2)) - non-uniform distributions

• Conditional Bets: Make decisions based on predicates

• Lazy Evaluation: Only compute the selected branch

• Composition Operators: Chain, compose, and combine bets

• Statistical Utilities: Probability estimation, entropy, expected values

Rich Standard Library

Statistics (lib/statistics.rkt)

• Descriptive statistics: mean, median, mode, variance, standard deviation

• Correlation and covariance analysis

• Statistical tests: chi-square, Kolmogorov-Smirnov

• Resampling methods: bootstrap, jackknife

• Time series: moving averages, exponential smoothing

• Monte Carlo simulation utilities

Probability Distributions (lib/distributions.rkt)

• Discrete: uniform, Bernoulli, binomial, geometric, Poisson, categorical, multinomial

• Continuous: normal, exponential, gamma, beta, chi-square, Student’s t

• Advanced: Weibull, Pareto, Cauchy, Laplace, Dirichlet

• Stochastic Processes: random walks, Brownian motion, Lévy flights

Bayesian Inference (lib/bayesian.rkt)

• Conjugate priors (Beta-Binomial, Normal-Normal)

• MCMC: Metropolis-Hastings, Gibbs sampling

• Importance sampling and rejection sampling

• Approximate Bayesian Computation (ABC)

• Credible intervals and Bayes factors

• Posterior predictive distributions

Optimization (lib/optimization.rkt)

• Simulated annealing

• Genetic algorithms

• Particle swarm optimization

• Evolutionary strategies

• Cross-entropy method

• Hill climbing and random search

• Ternary search

Advanced Sampling (lib/sampling.rkt)

• Stratified sampling

• Latin hypercube sampling

• Quasi-random sequences (Sobol, Halton)

• Sequential Monte Carlo (particle filters)

• Hamiltonian Monte Carlo

• Slice sampling

• Variance reduction techniques

Markov Chains (lib/markov.rkt)

• Discrete-time Markov chains

• Transition matrix learning

• Stationary distribution estimation

• Hidden Markov Models (Viterbi)

• Text generation with Markov chains

Combinators (lib/combinators.rkt)

• Monadic operations: pure, bind, join

• Error handling: try, retry, fallback

• Performance: memoization, caching, throttling

• Logical operations: and, or, xor

• Advanced composition patterns

Ternary Logic (lib/ternary.rkt)

• Kleene’s three-valued logic

• Ternary operations: AND, OR, NOT, XOR

• Majority voting and consensus

• Higher-order functions for ternary values

• Truth table generation

Tools

Interactive REPL (repl/shell.rkt)

• Comprehensive help system (:help)

• Session statistics tracking (:stats)

• Command history (:history)

• Built-in examples (:examples)

• Error handling and pretty-printing

• Persistent logging

Analysis Tools (tools/analyzer.rkt)

• Comprehensive bet analysis

• Strategy comparison

• Convergence analysis

• Text-based histograms

• Probability reports

• Entropy analysis over time

Benchmarks (benchmarks/performance.rkt)

• 15 comprehensive performance tests

• Core operations benchmarking

• Distribution sampling performance

• Statistical function benchmarks

Examples

Financial Modeling (examples/finance.rkt)

• Stock price simulation (GBM)

• Option pricing (Black-Scholes Monte Carlo)

• Value at Risk (VaR) calculation

• Credit risk modeling

• Interest rate simulation

• Portfolio optimization

• Bond pricing

• Market crash scenarios

• 10+ complete examples

Monte Carlo Simulations (examples/monte-carlo.rkt)

• Pi estimation

• Buffon’s needle

• Monte Carlo integration

• European option pricing

• Random walk analysis

• Percolation simulation

• Variance reduction techniques

Game Theory (examples/game-theory.rkt)

• Rock-paper-scissors tournaments

• Prisoner’s dilemma

• Matching pennies

• Battle of the sexes

• Hawk-dove evolutionary dynamics

• All-pay auctions

Probabilistic Data Structures (examples/probabilistic-structures.rkt)

• Skip lists

• Bloom filters

• HyperLogLog cardinality estimation

• Count-Min sketch

• Reservoir sampling

• Cuckoo hashing

• Treaps

Basic Tutorial (examples/basic-tutorial.rkt)

• Step-by-step introduction

• Real-world examples

• Customer service simulation

Quick Start

Installation

git clone https://github.com/hyperpolymath/betlang.git
cd betlang

Your First Bet

Start the REPL:

racket repl/shell.rkt

Try some bets:

betlang> (bet 1 2 3)
2

betlang> (bet 'heads 'tails 'edge)
heads

betlang> (bet/weighted '(common 7) '(uncommon 2) '(rare 1))
common

betlang> (bet-parallel 10 'win 'draw 'lose)
(win lose win draw win win lose draw win win)

Run Examples

= Financial modeling

racket examples/finance.rkt

= Monte Carlo simulations

racket examples/monte-carlo.rkt

= Game theory

racket examples/game-theory.rkt

= Tutorial

racket examples/basic-tutorial.rkt

Run Tests

racket tests/basics.rkt

Performance Benchmarks

racket benchmarks/performance.rkt

Documentation

• [Tutorial](docs/tutorial.md) - Comprehensive tutorial from basics to advanced

• [Semantics](docs/semantics.md) - Formal language semantics

• [API Reference](docs/api-reference.md) - Complete API documentation

• [Architecture](docs/architecture.md) - Project structure

• [CLAUDE.md](CLAUDE.md) - AI assistant context

Language Philosophy

betlang embraces the ternary principle - fundamental operations involve three choices. This design:

• Models three-way decisions naturally (win/draw/lose, yes/no/maybe)

• Provides richer expressiveness than binary choices

• Creates interesting emergent probabilistic properties

• Inspired by musical ternary form (A-B-A)

Use Cases

• Quantitative Finance: Option pricing, risk analysis, portfolio optimization

• Statistical Modeling: Bayesian inference, hypothesis testing

• Machine Learning: Probabilistic classification, sampling methods

• Simulation: Monte Carlo methods, agent-based modeling

• Game Theory: Strategic decision-making, evolutionary dynamics

• Data Science: Resampling, bootstrapping, statistical analysis

• Research: Probabilistic programming, stochastic processes

Project Statistics

• Lines of Code: 6,000+

• Libraries: 10+

• Functions: 180+

• Examples: 8 comprehensive example files

• Documentation: 2,000+ lines

• Test Cases: 25+

Requirements

• Racket 7.0 or later

Contributing

Contributions are welcome! Please ensure: - Code follows Racket conventions - New features align with ternary philosophy - Tests are included - Documentation is updated

License

See LICENSE file for details.

Citation

If you use betlang in research, please cite:

@software{betlang2025,
  title={betlang: A Ternary Probabilistic Programming Language},
  author={betlang Contributors},
  year={2025},
  url={https://github.com/hyperpolymath/betlang}
}

Acknowledgments

Inspired by: - Musical ternary form (A-B-A) - Probabilistic programming languages - Racket’s expressiveness - Three-valued logic systems

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Happy betting! 🎲

For questions, issues, or discussions, please open an issue on GitHub.