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.
Unbound variables (upper and lower case) that aren't macros will become free variables.

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.

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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.

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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.

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). Nodes 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.

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Todo (pre-release):

• Make command output accessible in prompt
• Prettyprint functions and rename bound variables
• 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:

• Optimization: clone only if absolutely necessary
• 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
• Smart alignment in all printouts
• Syntax highlighting: parenthesis, bound variables, macros, etc