pure project 🧫

🧫 implement all by nothing but only lexical closure . 🧬

Docs

• ☄️ Lambda Calculus 101
• 🦠 Fixed Point Things
• 🧊 Pure Lexical Equivalents

Intro

This is a theoretical verification in Functional Programming studies.

The only one necessary thing of a language for this pure project is a lexical closure feature, means it bind its free variables by the lexical scoping, not the dynamic scoping, and this also called closure or function closure. That means there is a first-classed function means all function is valve and it will pick all the symbol where it be defined which is needed by it-self. With out such thing, all of this projec shall not works.

And with such feature, we can make these things:

• Laziness -- without lexical closure feature, then we'll must get the laziness just from a language design and implementation.
• Currying -- if we don't have the closure feature, then we cannot do any currying things that means no (elegant) pipe then I shall give up this pure project at its begin.
• Tuple -- we can get numbers of values and let them applies one by one onto a picker, and then we just give a specific picker to get the specific value we've just given in.
• Iterator -- we have the tuple now and an iterator (or List or Sequence) is just a special 2 length tuple whith a value as the head and a closure as the tail which can just get the next such tuple. (and you can do almost everything with it such as you can just simply take a Iterator <Tuple <...>> as a Table <...> ...)
• Pipeline -- a simple pipe is just a λxf.fx while we're all in currying style and a Y(λgxf.g(fx)) could be a yard that always can give a closure to its next parameter, and with such thing we can just play pure functional programming with out any OO Method grammar to make the nesting callings be listing callings (like pipeline (x) (f) (f) (f) ... (sys.out)).

And, with these things, we can do almost (maybe full) things about the compute works, and just with clear, clean, and declarative code expressions.

Thanks for

• CS3110 from Cornell University
• ISMISM courses by Liu Si Mo also called Wei Ming Zi
• Lacanian Psychoanalysis theory from the Lacanianists
• Dialectic or Logic method from Georg Wilhelm Friedrich Hegel, Karl Marx and the Leninists
• Lambda Calculate from Alonzo Church and Currying theory
• Lexical Closure feature that provide this project almost
• The Functional Programming For The Rest of Us | defmacro which told me the CPS Programming
• Rain World game which give me some idea for the names

Implementations

• TypeScript
• Rust
• Java
• ...

Further Reading

• Combinatory logic ^{wiki.en wiki.zh}
• Kolmogorov complexity ^{wiki.en wiki.zh intro.paulv}
• Condensed matter physics ^{wiki.en wiki.zh}
• Lotka–Volterra equations ^{wiki.en wiki.zh}
• Андрей Никола́евич Колмогоров (Andrey Nikolaevich Kolmogorov) ^{wiki.ru wiki.zh wiki.en}
• Intuitive statistics (folk statistics) ^wiki.en
• Lazy K ^site.trompcl
• Lambda Diagrams ^{site.trompcl src.git.polux show.prime.youtube}
• Lambda Calculus ^{intro.raul.pdf intro.trompcl.pdf cl.tromp tromp.homepage.git dsc.ml.stackoverflow}
• De Bruijn ^{wiki.en wiki.en.indices}
• Binary Lambda Calculus ^{intro.trompcl intro.tromp.gist wiki.en wiki.en.logic tromp.lispnyc ait.tromp machine.blc.ioccc machine.blc.src.ioccc}
• De Bruijn ^{OEIS wiki.en.notation wiki.en.sequence generator.jgeisler0303 intro.http (NAN) intro.chessprogramming (NAN)}
• Kolmogorov axioms (Probability axioms) ^{wiki.en wiki.zh}
• John Tromp Things ^{John Tromp homepage.ghio orimaze pearls legalgo}
• Unlambda Lang ^{unl.site esoteric.oerjan}
• Combinatorics (Math) ^{wiki.en wiki.zh}
• Typed lambda calculus ^{wiki.en wiki.zh}
• Kappa calculus ^wiki.en
• Fixed-Point Combinator ^{wiki.en wiki.zh}
• Fixed-Point Iteration ^wiki.en
• Point-free style ^{wiki.haskell wiki.en wiki.apl qa qa}