# Lamb: A Lambda Calculus Engine

![Lamb screenshot](./misc/screenshot.png)

## Installation

### Method 1: PyPi (not yet)
1. Put this on PyPi
2. Write these instructions

### 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 ``python .``

-------------------------------------------------

## Usage


Type lambda expressions into the prompt, and Lamb will evaluate them. \
Use your `\` (backslash) key to type a `λ`. \
To define macros, use `=`. For example,
```
==> T = λab.a
==> F = λab.a
==> NOT = λa.a F T
```

Note that there are spaces in `λa.a F T`. With no spaces, `aFT` will be parsed as one variable. \
Lambda functions can only take single-letter, lowercase arguments. `λA.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). Load them with the `:load` command:
```
==> :load macros.lamb
```

Have fun!

-------------------------------------------------

## Commands

Lamb understands many commands. Prefix them with a `:` in the prompt.

`:help` Prints a help message

`:clear` Clear the screen

`:rlimit [int | None]` Set maximum reduction limit. `:rlimit none` sets no limit.

`:macros` List macros in the current environment.

`:mdel [macro]` Delete a macro

`:clearmacros` Delete all macros

`: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.

-------------------------------------------------

## Internals

Lamb treats each λ expression as a binary tree. Variable binding and reduction are all simple operations on that tree. All this magic happens in [`nodes.py`](./lamb/nodes.py).

**Highlights:**
 - `TreeWalker` is the iterator we (usually) use to traverse our tree. It walks the "perimeter" of the tree, visiting some nodes multiple times.
 - `Node` is the base class for all nodes. Any node has `.left` and `.right` elements, which may be `None` (empty). `Node`s also reference their parent and their direction relative to their parent, to make tree traversal easy.
 - Before any reduction is done, variables are bound via `bind_variables`. This prevents accidental conflicts common in many lambda parsers.

-------------------------------------------------


## Todo (pre-release, in this order):
 - Cleanup warnings
 - Truncate long expressions in warnings
 - Prevent macro-chaining recursion
 - Full-reduce option (expand all macros)
 - step-by-step reduction
 - Cleanup files
 - Update screenshot
 - Update documentation & "internals" section.
 - PyPi package


## Todo:
 - History queue + command indexing
 - Show history command
 - Better class mutation: when is a node no longer valid?
 - Loop detection
 - $\alpha$-equivalence check
 - Command-line options (load a file, run a set of commands)
 - Unchurch macro: make church numerals human-readable
 - Syntax highlighting: parenthesis, bound variables, macros, etc
 - Tests