https://github.com/aartaka/stdlambda
Standard library for Lambda Calculus, finally making LC a practical programming language.
https://github.com/aartaka/stdlambda
arithmetic boolean-logic cons lambda-calculus list recursion set stdlib
Last synced: 17 days ago
JSON representation
Standard library for Lambda Calculus, finally making LC a practical programming language.
- Host: GitHub
- URL: https://github.com/aartaka/stdlambda
- Owner: aartaka
- License: bsd-2-clause
- Created: 2024-01-04T19:17:47.000Z (over 1 year ago)
- Default Branch: master
- Last Pushed: 2025-01-20T17:18:29.000Z (3 months ago)
- Last Synced: 2025-02-11T17:16:58.220Z (2 months ago)
- Topics: arithmetic, boolean-logic, cons, lambda-calculus, list, recursion, set, stdlib
- Homepage:
- Size: 56.6 KB
- Stars: 14
- Watchers: 2
- Forks: 0
- Open Issues: 7
-
Metadata Files:
- Readme: README.org
- License: LICENSE
Awesome Lists containing this project
README
#+TITLE:stdlambda—Standard Library for Lamdba Calculus
Lambda Calculus is an inspiring idea, but most of the resources about
it list just a couple of utilities and ways to encode data, without
getting deep enough into building a _practical_ set of
primitives. ~stdlambda~ tries to do just that: provide a more or less
practical set of primitives for programming in Lambda
Calculus. Included are:
- Frequent combinators like ~S~, ~K~, ~I~, and ~Y~.
- Church Booleans and all the possible logical operations on them.
- Church Numerals and arithmetics on them.
- List-encoded numerals might be provided in the future.
- Church Pairs (with an opinionated ~nil = false~) and Haskell/Lisp-inspired utilities on them.
- nil = ~λx.true~ pairs might be provided in the future.
Sources of inspiration and code:
- [[http://www.golfscript.com/lam/][Universal Lambda page]].
- Justine Tunney's [[https://justine.lol/lambda/][SectorLambda page]].
- Hikaru Ikuta's [[https://github.com/woodrush/lambdacraft][Lambdacraft]]
* Getting Started
- Feed the definitions from provided files into your Lambda Calculus
interpreter. The files (and their interdependencies) are:
- ~combinators.lambda~ :: Logical/stack combinators, no deps.
- ~bool.lambda~ :: Boolean ops, no deps.
- ~numbers.lambda~ :: Numeric, arithmetics. Depends on ~combinators.lambda~ and ~bool.lambda~.
- ~cons.lambda~ :: Conses. Depends on ~bool.lambda~.
- ~list.lambda~ :: Linked lists and utils for them. Mostly fold operations. Depends on ~cons.lambda~, ~numbers.lambda~, ~combinators.lambda~, ~bool.lambda~.
- ~set.lambda~ :: Operations on lists-as-sets. Depends on ~list.lambda~ and its transitive dependencies.
- ~alist.lambda~ :: Associative (key-value) lists. Depends on ~cons.lambda~ and ~combinators.lambda~.
- ~alias.lambda~ :: Aliases for all of the above.
- Run the code using these primitives. Say
#+begin_src lisp
fac = Y λr.λn.(if (=0 n) 1 (× n (r (1- n))))
(fac 5)
#+end_src
* Format
The format is the single-letter single-argument lambdas. The approximate regex would be:
#+begin_src
.* = (λ[a-z]\.)*.*
#+end_src
Not all function applications are enclosed into parentheses and not all applications are single-argument. Example:
#+begin_src
first = compose car (0 cdr)
#+end_src
and not
#+begin_src
first = ((compose car) (0 cdr))
#+end_src
It's too much work to maintain such a code.
I might reconsider that in the future, though.
* Acknowledgements
- Many logical combinators come from [[https://wiki.xxiivv.com/site/logic][Devine Lu Linvega logic page]].
- Lists (and ~foldr~ especially) come from the [[http://www.golfscript.com/lam/][Golfscript Universal Lambda page]].
- Many list primitives and names for things come from Common Lisp and Scheme.
- Things like ~conjoin~ and ~compose~ especially come from Alexandria library.