🐑 Lamb: A Lambda Calculus Engine

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🧠 What is lambda calculus?

• video 1: Introduction and boolean logic. The first few minutes are a bit confusing, but it starts to make sense at about 6:50

• video 2: Continuation of video 1. Features combinators and numerals.

• blog: Another introduction. Moves slower than the two videos above and doesn't assume CS knowledge. Four-part series.

• handout: 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.

📦 Installation

Method 1: PyPi

1. (Optional but recommended) make and enter a venv
   • 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.
3. cd into this directory
4. Run pip install .
5. Run lamb

📖 Usage

Type 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. 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!

🗃️ 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 for an example.

Todo:

• Prevent macro-chaining recursion
• Cleanup warnings
• Truncate long expressions in warnings
• Loop detection
• α-equivalence check
• 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?)
• Tests