1  = BetLang Playground
  2  :toc: macro
  3  :icons: font
  4  
  5  // SPDX-License-Identifier: AGPL-3.0-or-later
  6  
  7  image:https://img.shields.io/badge/Language-BetLang-red[BetLang]
  8  image:https://img.shields.io/badge/Logic-Ternary-purple[Ternary Logic]
  9  image:https://img.shields.io/badge/Programming-Probabilistic-orange[Probabilistic]
 10  image:https://img.shields.io/badge/License-AGPL--3.0-blue[License]
 11  
 12  *Playground for BetLang - Ternary Logic & Probabilistic Programming*
 13  
 14  toc::[]
 15  
 16  == Overview
 17  
 18  BetLang explores ternary logic and probabilistic programming, providing tools for reasoning under uncertainty.
 19  
 20  === Key Features
 21  
 22  * **Ternary Logic**: True, False, and Unknown values
 23  * **Probabilistic Programming**: Distributions, sampling, inference
 24  * **Uncertainty Modeling**: Combine logic with probability
 25  * **Bayesian Inference**: Bayes' theorem and belief updating
 26  
 27  == Ternary Logic
 28  
 29  === Three-Valued Logic
 30  
 31  BetLang extends boolean logic with an "Unknown" value:
 32  
 33  |===
 34  | Value | Symbol | Meaning
 35  
 36  | True | T | Definitely true
 37  | False | F | Definitely false
 38  | Unknown | U | Uncertain/undefined
 39  |===
 40  
 41  === Truth Tables
 42  
 43  [source]
 44  ----
 45  AND | T | U | F |        OR | T | U | F |
 46  ----+---+---+---+       ----+---+---+---+
 47    T | T | U | F |         T | T | T | T |
 48    U | U | U | F |         U | T | U | U |
 49    F | F | F | F |         F | T | U | F |
 50  ----
 51  
 52  === Example
 53  
 54  [source,betlang]
 55  ----
 56  -- Sensor readings with uncertainty
 57  let sensor_a: Ternary = T   -- Known true
 58  let sensor_b: Ternary = U   -- Faulty sensor (unknown)
 59  let sensor_c: Ternary = F   -- Known false
 60  
 61  -- Ternary operations
 62  let result = sensor_a AND sensor_b  -- U (unknown propagates)
 63  let any_true = sensor_a OR sensor_b -- T (true dominates in OR)
 64  ----
 65  
 66  == Probabilistic Programming
 67  
 68  === Probability Types
 69  
 70  [source,betlang]
 71  ----
 72  -- Probability values (0 to 1)
 73  let coin_flip: Probability = 0.5
 74  let biased_coin: Probability = 0.7
 75  
 76  -- Sampling
 77  let heads = bernoulli(coin_flip)  -- true or false
 78  let value = uniform(0, 10)        -- float in [0, 10)
 79  let sample = normal(0, 1)         -- standard normal
 80  ----
 81  
 82  === Bayesian Inference
 83  
 84  [source,betlang]
 85  ----
 86  -- Bayes' theorem: P(A|B) = P(B|A) * P(A) / P(B)
 87  let prior = 0.01           -- P(disease)
 88  let sensitivity = 0.99     -- P(positive|disease)
 89  let evidence = 0.0594      -- P(positive)
 90  
 91  let posterior = bayes(sensitivity, prior, evidence)
 92  -- P(disease|positive) = 0.1667
 93  ----
 94  
 95  == Uncertainty Modeling
 96  
 97  Combine ternary logic with probability:
 98  
 99  [source,betlang]
100  ----
101  -- Convert probability to ternary based on confidence
102  fn probability_to_ternary(p: Probability) -> Ternary:
103      if p > 0.9:
104          T  -- High confidence true
105      else if p < 0.1:
106          F  -- High confidence false
107      else:
108          U  -- Uncertain
109  ----
110  
111  == Project Structure
112  
113  [source]
114  ----
115  betlang-playground/
116  ├── src/
117  │   ├── main.ts        # Main entry point
118  │   ├── ternary.ts     # Ternary logic implementation
119  │   └── probability.ts # Probabilistic programming
120  ├── examples/          # Example programs
121  ├── test/             # Test suite
122  ├── docs/             # Documentation
123  ├── deno.json         # Deno configuration
124  ├── rescript.json     # ReScript configuration
125  ├── justfile          # Build commands
126  └── Mustfile          # Mandatory checks
127  ----
128  
129  == Getting Started
130  
131  [source,bash]
132  ----
133  # Clone the repository
134  git clone https://github.com/hyperpolymath/betlang-playground.git
135  cd betlang-playground
136  
137  # Run the demo
138  just dev
139  
140  # Run tests
141  just test
142  
143  # Run ternary logic demo
144  just ternary-demo
145  
146  # Run probability demo
147  just probability
148  ----
149  
150  == Examples
151  
152  * `src/ternary.ts` - Ternary logic operations and truth tables
153  * `src/probability.ts` - Probability distributions and inference
154  * `test/` - Comprehensive test suite
155  
156  == License
157  
158  SPDX-License-Identifier: AGPL-3.0-or-later