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lamb/README.md

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# 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. \
Unbound variables (upper and lower case) that aren't macros will become free variables. Free variables will be shown with a `'`, like `a'`.
Be careful, 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`.
-------------------------------------------------
## Commands
Lamb comes with a few commands. Prefix them with a `:`
`: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
`:save [filename]`\
`:load [filename]` Save or load the current environment to a file. The lines in a file look exactly the same as regular entries in the prompt, but must only contain macro definitions.
-------------------------------------------------
## 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):
- Make command output accessible in prompt
- Prettier colors
- Prevent macro-chaining recursion
- step-by-step reduction
- Full-reduce option (expand all macros)
- Show a warning when a free variable is created
- PyPi package
## Todo:
- Better class mutation: when is a node no longer valid?
- Loop detection
- Command-line options (load a file, run a set of commands)
- $\alpha$-equivalence check
- Unchurch macro: make church numerals human-readable
- Syntax highlighting: parenthesis, bound variables, macros, etc