96 lines
3.3 KiB
Markdown
96 lines
3.3 KiB
Markdown
# Lamb: A Lambda Calculus Engine
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## Installation
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### Method 1: PyPi (not yet)
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1. Put this on PyPi
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2. Write these instructions
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### Method 2: Git
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1. Clone this repository.
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2. Make and enter a [virtual environment](https://docs.python.org/3/library/venv.html).
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3. ``cd`` into this directory
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4. Run ``pip install .``
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5. Run ``python .``
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-------------------------------------------------
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## Usage
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Type lambda expressions into the prompt, and Lamb will evaluate them. \
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Use your `\` (backslash) key to type a `λ`. \
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To define macros, use `=`. For example,
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```
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~~> T = λab.a
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~~> F = λab.a
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~~> NOT = λa.a F T
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```
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Note that there are spaces in `λa.a F T`. With no spaces, `aFT` will be parsed as one variable. \
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Lambda functions can only take single-letter, lowercase arguments. `λA.A` is not valid syntax. \
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Unbound variables (upper and lower case) that aren't macros will become free variables.
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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.
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Numbers will automatically be converted to Church numerals. For example, the following line will reduce to `T`.
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```
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~~> 3 NOT F
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```
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If an expression takes too long to evaluate, you may interrupt reduction with `Ctrl-C`.
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-------------------------------------------------
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## Commands
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Lamb comes with a few commands. Prefix them with a `:`
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`:help` Prints a help message
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`:clear` Clear the screen
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`:rlimit [int | None]` Set maximum reduction limit. `:rlimit none` sets no limit.
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`:macros` List macros in the current environment.
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`:mdel [macro]` Delete a macro
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`:save [filename]`\
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`: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.
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-------------------------------------------------
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## Internals
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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).
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**Highlights:**
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- `TreeWalker` is the iterator we (usually) use to traverse our tree. It walks the "perimeter" of the tree, visiting some nodes multiple times.
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- `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.
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- Before any reduction is done, variables are bound via `bind_variables`. This prevents accidental conflicts common in many lambda parsers.
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-------------------------------------------------
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## Todo (pre-release):
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- Make command output accessible in prompt
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- Prettyprint functions and rename bound variables
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- Prettier colors
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- Prevent macro-chaining recursion
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- step-by-step reduction
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- Full-reduce option (expand all macros)
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- Show a warning when a free variable is created
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- PyPi package
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## Todo:
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- Optimization: clone only if absolutely necessary
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- Better class mutation: when is a node no longer valid?
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- Loop detection
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- Command-line options (load a file, run a set of commands)
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- $\alpha$-equivalence check
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- Unchurch macro: make church numerals human-readable
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- Smart alignment in all printouts
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- Syntax highlighting: parenthesis, bound variables, macros, etc |