Lambda Calculus in F#
This is a fork of Brian Bern's Lambda Calculus implementation in F# with a few enhancements.
Enhancements
- I wanted to create a function that effectively maps each nutural number to a unique lambda function so that it creates a bijection between all natural numbers and all representable lambda functions. This is basically a form of ordered & compact serialization, nothing like this.
- This effectively would let you address lambda functions by their index.
- Added a DeBruijn expression model, which is used as an intermediate step to transform Natual numbers to Lambda functions.
Todo
- Fix lambdaToInt - This function converts a DeBruijn indexed function back to a nat
- Add lambdaToDeBruijn conversion
Motivation
In the Unison programming language, the big idea is:
Each Unison definition is identified by a hash of its syntax tree.
Put another way, Unison code is content-addressed.
What Unison does that's important is it does not include the names in the hash of the function. Actually, they go further, they separate names of the variables and functions from the function and inject it.
The Big Idea Here
Rather than identifying a function by the hash of its syntax tree, what if we identified a function by its unique natural number?
- Unlike a hash, using natural number to address is always reversable.
- Addresses are also continguous in a way that smaller addresses represent smaller functions.
- The addresses aren't just content addressable, the addresses are timeless addresses to a complete infinite database that requires no storage.
- Timeless addressing allows one to create a distributed global database where computers can prove things about functions.
- Timeless addressing allows one to create a distributed global database where computers can prove things about functions or their composition.
References
- Matthew P. Szudzik - The Rosenberg-Strong Pairing Function (2019)