Lamb: A Lambda Calculus Engine

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.
3. cd into this directory
4. Run pip install .
5. Run python .

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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. Load them with the :load command:

==> :load macros.lamb

You may use up/down arrows to recall history.

Have fun!

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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

: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.

:delmac 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 for an example.

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Todo (pre-release, in this order):

• Write "how it works"
• PyPi package

Todo:

• Prevent macro-chaining recursion
• Cleanup warnings
• Truncate long expressions in warnings
• History indexing
• Show history command
• Loop detection
• \alpha-equivalence check
• Command-line options (load a file)
• Unchurch command: make church numerals human-readable
• Better Syntax highlighting
• Complete file names and commands
• Tests