# 馃悜 Lamb: A Lambda Calculus Engine ![Lamb Demo](https://github.com/rm-dr/lamb/assets/96270320/d518e344-e7c8-47ed-89c4-7ce273bf4e2d) ## :brain: What is lambda calculus? - [video 1](https://www.youtube.com/watch?v=3VQ382QG-y4): Introduction and boolean logic. The first few minutes are a bit confusing, but it starts to make sense at about [`6:50`](https://youtu.be/3VQ382QG-y4?t=400) - [video 2](https://www.youtube.com/watch?v=pAnLQ9jwN-E): Continuation of video 1. Features combinators and numerals. - [blog](https://www.driverlesscrocodile.com/technology/lambda-calculus-for-people-a-step-behind-me-1): Another introduction. Moves slower than the two videos above and doesn't assume CS knowledge. Four-part series. - [handout](https://static.betalupi.com/ormc/Advanced/Lambda%20Calculus.pdf): A handout I've written on lambda calculus. ## :package: Installation ### Method 1: [PyPi](https://pypi.org/project/lamb-engine) 1. *(Optional but recommended)* make and enter a [venv](https://docs.python.org/3/library/venv.html) - **On Windows, run the following in cmd or powershell:** - `cd Desktop` - `python -m venv lamb` - `.\Scripts\activate` 2. `pip install lamb-engine` 3. `lamb` ### Method 2: Git 1. Clone this repository. 2. Make and enter a [virtual environment](https://docs.python.org/3/library/venv.html). 3. ``cd`` into this directory 4. Run ``pip install .`` 5. Run ``lamb`` ------------------------------------------------- ## 馃摉 Usage Type expressions into the prompt, and Lamb will evaluate them. \ Use your `\` (backslash) key to type a `位`. \ To define macros, use `=`. For example, ``` ==> T = 位ab.a ==> F = 位ab.a ==> NOT = 位a.a F T ``` Note that there are spaces in `位a.a F T`. With no spaces, `aFT` will be parsed as one variable. \ Lambda functions can only take single-letter, lowercase arguments. `位A.A` is not valid syntax. \ Free variables will be shown with a `'`, like `a'`. Macros are case-sensitive. If you define a macro `MAC` and accidentally write `mac` in the prompt, `mac` will become a free variable. Numbers will automatically be converted to Church numerals. For example, the following line will reduce to `T`. ``` ==> 3 NOT F ``` If an expression takes too long to evaluate, you may interrupt reduction with `Ctrl-C`. \ Exit the prompt with `Ctrl-C` or `Ctrl-D`. There are many useful macros in [macros.lamb](./macros.lamb). Download the file, then load them with the `:load` command: ``` ==> :load macros.lamb ``` You can also pass files to lamb directly to have them loaded at startup: ``` lamb file1 file2 ``` Use your up/down arrows to recall history. Have fun! ------------------------------------------------- ## :card_file_box: Commands Lamb understands many commands. Prefix them with a `:` in the prompt. `:help` Print a help message `:clear` Clear the screen `:rlimit [int | None]` Set maximum reduction limit. `:rlimit none` sets no limit. `:macros` List macros. `:mdel [macro]` Delete a macro `:delmac` Delete all macros `:step [yes | no]` Enable or disable step-by-step reduction. Toggle if no argument is given. When reducing by steps, the prompt tells you what kind of reduction was done last: - `M`: Macro expansion - `C`: Church expansion - `H`: History expansion - `F`: Function application `:expand [yes | no]` Enable or disable full expansion. Toggle if no argument is given. If full expansion is enabled, ALL macros will be expanded when printing output. `:save [filename]` \ `:load [filename]` \ Save or load macros from a file. The lines in a file look exactly the same as regular entries in the prompt, but can only contain macro definitions. See [macros.lamb](./macros.lamb) for an example. ------------------------------------------------- ## Todo: - Prevent macro-chaining recursion - Cleanup warnings - Truncate long expressions in warnings - Loop detection - Unchurch command: make church numerals human-readable - Better syntax highlighting - Tab-complete file names and commands - Load default macros without manually downloading `macros.lamb` (via `requests`, maybe?)