124 lines
4.2 KiB
Markdown
124 lines
4.2 KiB
Markdown
# 🐑 Lamb: A Lambda Calculus Engine
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- [Primary Repo](https://git.betalupi.com/Mark/lamb)
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- [Github Mirror](https://github.com/rm-dr/lamb)
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## :brain: What is lambda calculus?
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- [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)
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- [video 2](https://www.youtube.com/watch?v=pAnLQ9jwN-E): Continuation of video 1. Features combinators and numerals.
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- [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.
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- [handout](https://nc.betalupi.com/s/ormc-handouts/download?path=%2FAdvanced&files=Lambda%20Calculus.pdf): A handout I've written on lambda calculus. Solutions are available somewhere on `git.betalupi.com`. You'll have to find them yourself if you want them.
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## :package: Installation
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### Method 1: [PyPi](https://pypi.org/project/lamb-engine)
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1. *(Optional but recommended)* make and enter a [venv](https://docs.python.org/3/library/venv.html)
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- **On Windows, run the following in cmd or powershell:**
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- `cd Desktop`
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- `python -m venv lamb`
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- `.\Scripts\activate`
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2. `pip install lamb-engine`
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3. `lamb`
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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 ``lamb``
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-------------------------------------------------
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## 📖 Usage
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Type 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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Free variables will be shown with a `'`, like `a'`.
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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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Exit the prompt with `Ctrl-C` or `Ctrl-D`.
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There are many useful macros in [macros.lamb](./macros.lamb). Download the file, then load them with the `:load` command:
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```
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==> :load macros.lamb
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```
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You can also pass files to lamb directly to have them loaded at startup:
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```
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lamb file1 file2
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```
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Use your up/down arrows to recall history.
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Have fun!
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-------------------------------------------------
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## :card_file_box: Commands
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Lamb understands many commands. Prefix them with a `:` in the prompt.
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`:help` Print 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.
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`:mdel [macro]` Delete a macro
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`:delmac` Delete all macros
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`: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:
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- `M`: Macro expansion
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- `C`: Church expansion
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- `H`: History expansion
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- `F`: Function application
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`: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.
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`:save [filename]` \
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`:load [filename]` \
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Save or load macros from a file.
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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.
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-------------------------------------------------
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## Todo:
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- Prevent macro-chaining recursion
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- Cleanup warnings
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- Truncate long expressions in warnings
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- Loop detection
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- α-equivalence check
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- Unchurch command: make church numerals human-readable
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- Better syntax highlighting
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- Tab-complete file names and commands
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- Load default macros without manually downloading `macros.lamb` (via `requests`, maybe?)
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- Tests |