A language for probability models.

How it works

Enumeration follows weighted outcomes

In enumeration mode, a world is a program state with a weight. Random choices split worlds, equivalent states merge, and reports summarize the remaining population. Boolean conditions follow the matching branch; probability conditions explore both.

1. 1 Random choices create worlds

   if 30% gives its two branches weights of 0.3 and 0.7. A discrete draw splits too: let r ~ 2d6 gives eleven possible totals, each with its probability.

   let weather = if 30% { "rain" } else { "sun" }report weather

   "rain"0.3

   "sun"0.7

2. 2 Equal worlds merge

   Worlds with the same state needed by later code combine, adding their weights. Here two paths reach 0 after two steps and combine into one world with weight ½.

   A thousand coin-flip steps have 2¹⁰⁰⁰ paths but only 1,001 final positions. Keeping only the current position lets those paths merge; storing the whole history would prevent that.

   var pos = 0repeat 3 { pos += if 50% { 1 } else { -1 } }report pos

3. 3 Reports summarize the results

   report collects values across worlds. It displays probabilities for events and summaries for numeric quantities. Ordinary expressions operate within each world; a report performs the aggregation.

   enumeratedweather    sun 70.00% · rain 30.00%

   sun

   rain

Forecasting

Forecast distributions over time

Select sampling for large state spaces or continuous calculations that enumeration does not support. Each run follows one random path, and reports include sampling uncertainty. Enumeration is the default; it does not automatically switch modes.

sample · 50,000 runs · seed 11MRR ≥ $100k after 18 months    33.3% ± 0.2%

let price = 49                 # $ per customer per monthlet churn ~ 3% to 7%           # share of customers who leave each month: uncertain, but fixedvar market ~ one_of([Boom: 20%, Steady: 60%, Slump: 20%])var signups ~ 60 to 150        # new customers per month at launchvar customers = 0for month in 1..18 {  let new ~ poisson(signups)  let lost ~ binomial(customers, churn)  customers += new - lost  report customers * price by month as "MRR ($)"  market = next_month(market)  let growth ~ match market {  # month-on-month growth in sign-ups    Boom   => 8% to 20%    Steady => 1% to 6%    Slump  => normal_range(-8%, 0%)   # growth can be negative: say which shape you mean  }  signups *= 1 + growth}report customers * price >= 100_000 as "MRR ≥ $100k after 18 months"

Continuous models

Analytic calculations where supported

Enumeration can keep a continuous draw as a distribution through affine calculations, thresholds, abs, min, max and clamp. Supported conjugate observations update its posterior without sampling individual values.

let arrival ~ uniform(0, 30)observe arrival > 10let wait = max(arrival - 15, 0)report wait as "wait (minutes)"report wait > 10 as "waiting more than 10 minutes"

enumerated · evidence 66.67%wait (minutes)                  mean 5.62 · sd 4.96 · 5% 0.00 · median 5.00 · 95% 14.00waiting more than 10 minutes    25.00%

let rate ~ beta(2, 2)observe 3 from binomial(5, rate)report ratereport rate > 50%

enumerated · evidence 21.43%rate          mean 0.56 · sd 0.16 · 5% 0.29 · median 0.56 · 95% 0.81rate > 50%    63.67%

Interpreting results

Results, methods and limits

enumerated · evidence 8.87%
sample · 50,000 runs · seed 11

let storm = bernoulli(30%)report storm and storm as "two independent storms"let happened ~ stormreport happened and happened as "the same storm twice"

enumeratedtwo independent storms    9.00%the same storm twice      30.00%

Get started

Run Probl

$ cargo install probl-cli --locked
$ probl run model.probl
$ probl run model.probl --runs 100000 --seed 3
$ probl check model.probl
$ probl repl

Examples

19 example models

Examples cover games, forecasting, calendars, decisions, monitoring and risk. Each includes assumptions and expected results, and opens in the playground.

• 01 A tour of Probl Every core idea on one page
• 02Game Craps, pass line bet Draws, a loop with no fixed end, fractions
• 03Game RPG duel Records, functions, distributions as fields, simulate, a balancing sweep
• 04Game Risk Dice pools; merging collapses a huge tree
• 05Game Snakes and ladders Maps, long games, independent copies of a distribution
• 06Game Blackjack Cards without replacement, tables with report … by
• 07Forecasting SaaS launch a to b estimates, regime switching, a fan chart over months
• 08Forecasting Sign-ups observe … from, learning a rate, then forecasting with it
• 09Forecasting An illustrative forecast of Probl's original plan, not a current release schedule Risks and dates: an illustrative forecast of the original plan, not a release schedule
• 10Physics Quantum key distribution (BB84) A classical BB84 intercept–resend model; measurement probabilities and Bayes' rule, without complex amplitudes
• 11Forecasting Delivery forecast Delivery uncertainty from today, weekends, explicit holidays and deadline probability
• 12Forecasting Invoice cash flow Recurring invoices anchored to a calendar day, payment delays and monthly cash-flow buckets
• 13Forecasting Contract renewal Leap-day renewals, notice periods and uncertain response dates
• 14Decisions Stock decisions Expected profit, choosing before uncertainty resolves, perfect information and regret
• 15Operations Staffing a help desk Continuous arrivals and service times, shared scenarios for staffing comparisons
• 16Model checking Model checking Replicate a dataset from a fitted rate and compare variation between days
• 17Monitoring Sensor tracking Noisy observations of a hidden state, incremental exact filtering and next-state prediction
• 18Risk Shared hazards Common hazards, equal marginal risks, different joint tails and reserve shortfalls
• 19Arrival times Analytic continuous outcomes — arrival times without sampling Analytic continuous reports, shared draws and threshold evidence