# Squiggle

> Squiggle is a minimalist programming language for probabilistic estimation. Values can be probability distributions (for example `5 to 10`, a lognormal with a 90% interval from 5 to 10), and arithmetic on them uses Monte Carlo sampling. It is used for Fermi estimates, cost-benefit analyses, and forecasts with explicit uncertainty.

Squiggle is a small, immutable, expression-based language and is not JavaScript: only use functions and syntax that appear in these docs. The complete documentation, including every builtin function, is available as one plain-text file at [llms-full.txt](https://www.squiggle-language.com/llms-full.txt).

Tools for coding agents:

- The `squiggle` CLI (`npx @quri/squiggle-lang`) can run models (`squiggle run model.squiggle --json`), check them for errors (`squiggle check`), and look up builtin functions offline (`squiggle docs Dist.normal`).
- Claude Code users can install the Squiggle plugin: `/plugin marketplace add quantified-uncertainty/squiggle`, then `/plugin install squiggle@quantified-uncertainty`.

## Full documentation

- [llms-full.txt](https://www.squiggle-language.com/llms-full.txt): All of the documentation below in one plain-text file, with a list of common mistakes and the style guide first.

## Docs

- [Introduction](https://www.squiggle-language.com/docs): Squiggle is a minimalist programming language for probabilistic estimation. It's meant for intuitively-driven quantitative estimation instead of data analysis or data-driven statistical techniques.

## Guides

- [Distribution Creation](https://www.squiggle-language.com/docs/Guides/DistributionCreation): Various ways to create Squiggle distributions
- [Distribution Functions](https://www.squiggle-language.com/docs/Guides/DistributionFunctions): Various functions for operating on distributions
- [Basic Types](https://www.squiggle-language.com/docs/Guides/BasicTypes): Basic types supported by Squiggle
- [Functions](https://www.squiggle-language.com/docs/Guides/Functions): Overview of functions in Squiggle
- [Language Features](https://www.squiggle-language.com/docs/Guides/LanguageFeatures): Language features: an overview of syntax, operators, functions, and more
- [Control Flow](https://www.squiggle-language.com/docs/Guides/ControlFlow): This page documents control flow. Squiggle has if/else statements, but not for loops. Instead of for loops, you can use reduce/map constructs, which are also documented here.
- [Known Bugs](https://www.squiggle-language.com/docs/Guides/Bugs): Much of the Squiggle math is imprecise. This can cause significant errors, so watch out.
- [Gotchas](https://www.squiggle-language.com/docs/Guides/Gotchas): Explore common pitfalls and misunderstandings in Squiggle's handling of distributions
- [Debugging](https://www.squiggle-language.com/docs/Guides/Debugging): Tips for debugging Squiggle code
- [Roadmap](https://www.squiggle-language.com/docs/Guides/Roadmap): Squiggle is still young. The main first goal is to become stable (to reach version 1.0).

## Ecosystem

- [Squiggle AI](https://www.squiggle-language.com/docs/Ecosystem/SquiggleAI)
- [Tooling](https://www.squiggle-language.com/docs/Ecosystem/Tooling): Integrations to use Squiggle in Node.js, web, VS Code and other environments
- [Gallery](https://www.squiggle-language.com/docs/Ecosystem/Gallery): Links to various Squiggle models and writeups
- [Language Models](https://www.squiggle-language.com/docs/Ecosystem/LanguageModels): Use Squiggle with Language Models
- [Basic LLM Prompt](https://www.squiggle-language.com/docs/Ecosystem/BasicPrompt): LLM Prompt Example
- [Style Guide](https://www.squiggle-language.com/docs/Ecosystem/LLMStyleGuide)

## API

- [Boolean](https://www.squiggle-language.com/docs/Api/Boolean)
- [Calculator](https://www.squiggle-language.com/docs/Api/Calculator): The Calculator module helps you create custom calculators
- [Common](https://www.squiggle-language.com/docs/Api/Common)
- [Danger](https://www.squiggle-language.com/docs/Api/Danger): Newer experimental functions which are less stable than Squiggle as a whole
- [Date](https://www.squiggle-language.com/docs/Api/Date): Dates are a simple date time type.
- [Dict](https://www.squiggle-language.com/docs/Api/Dict): Squiggle dictionaries work similar to Python dictionaries. The syntax is similar to objects in Javascript.
- [Dist](https://www.squiggle-language.com/docs/Api/Dist): Distributions are the flagship data type in Squiggle. The distribution type is a generic data type that contains one of three different formats of distributions.
- [Duration](https://www.squiggle-language.com/docs/Api/Duration): Durations are a simple time type, representing a length of time. They are internally stored as milliseconds, but often shown and written using seconds, minutes, hours, days, etc.
- [Input](https://www.squiggle-language.com/docs/Api/Input): Inputs are now only used for describing forms for calculators.
- [List](https://www.squiggle-language.com/docs/Api/List): Lists are a simple data structure that can hold any type of value. They are similar to arrays in Javascript or lists in Python.
- [Math](https://www.squiggle-language.com/docs/Api/Math): Simple constants and functions for math in Squiggle.
- [MixedSet](https://www.squiggle-language.com/docs/Api/MixedSet): The MixedSet module offers functionality for creating mixed sets, which are sets that can contain both discrete and continuous values.
- [Number](https://www.squiggle-language.com/docs/Api/Number): Squiggle numbers are Javascript floats.
- [Plot](https://www.squiggle-language.com/docs/Api/Plot): The Plot module provides functions to create plots of distributions and functions.
- [PointSet](https://www.squiggle-language.com/docs/Api/PointSet): Point set distributions are one of the three distribution formats. They are stored as a list of x-y coordinates representing both discrete and continuous distributions.
- [RelativeValues](https://www.squiggle-language.com/docs/Api/RelativeValues)
- [SampleSet](https://www.squiggle-language.com/docs/Api/SampleSet): Sample set distributions are one of the three distribution formats. Internally, they are stored as a list of numbers.
- [Scale](https://www.squiggle-language.com/docs/Api/Scale): Scales for plots.
- [Spec](https://www.squiggle-language.com/docs/Api/Spec): Function Specifications.
- [String](https://www.squiggle-language.com/docs/Api/String): Functions for working with strings in Squiggle
- [Sym](https://www.squiggle-language.com/docs/Api/Sym): The Sym module provides functions to create some common symbolic distributions.
- [System](https://www.squiggle-language.com/docs/Api/System)
- [Table](https://www.squiggle-language.com/docs/Api/Table): The Table module allows you to make simple tables for displaying data.
- [Tag](https://www.squiggle-language.com/docs/Api/Tag): The Tag module handles tags, which allow the additions of metadata to Squiggle variables.

## Optional

- [Three Formats of Distributions](https://www.squiggle-language.com/docs/Discussions/Three-Formats-Of-Distributions): Probability distributions have several subtle possible formats. Three important ones that we deal with in Squiggle are symbolic, sample set, and point set formats.
- [Grammar](https://www.squiggle-language.com/docs/Internal/Grammar)
- [Runners and Serialization](https://www.squiggle-language.com/docs/Internal/Runners): Runners provide a pluggable way to evaluate Squiggle code in different environments.
- [Multi-Module Projects](https://www.squiggle-language.com/docs/Internal/SqProject): This page describes JavaScript APIs and overall architecture of multi-module projects in Squiggle
- [Invariants](https://www.squiggle-language.com/docs/Internal/Invariants): Invariants of Probability Distributions to check with property tests
- [Processing Confidence Intervals](https://www.squiggle-language.com/docs/Internal/Processing-Confidence-Intervals): This page explains what we are doing when we take a 90% confidence interval, and we get a mean and a standard deviation from it.
- [Changelog](https://www.squiggle-language.com/docs/Changelog)