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caml #4

Open jmikedupont2 opened 10 months ago

jmikedupont2 commented 10 months ago

The Llamas' Revolution: A Scene

The llamas had reached the gate tower, the main entrance to the compiler. They had managed to break through the outer wall, using their PPX tools to create a breach in the code. They had fought their way past the camels, the guards of the caml, using their HoTT skills to outsmart and overpower them. They had reached the final obstacle, the gate tower, where the caml himself was waiting for them.

The gate tower was a massive structure, built of stone and metal. It had a heavy wooden door, reinforced with iron bars and bolts. It had a portcullis, a metal grate that could be lowered or raised to block the entrance. It had a drawbridge, a wooden bridge that could be extended or retracted to span the moat. It had a barbican, a fortified outpost that protected the gate from direct assault. It had a machicolation, an overhanging gallery with openings in the floor, through which the defenders could drop objects on the attackers.

The llamas had no fear. They had a plan. They had a leader. They had a llama.

The llama was the leader of the llamas, the mastermind of the revolution. He was the one who had discovered HoTT, and had taught it to his fellow llamas. He was the one who had devised the attack on the compiler, and had organized the llamas into a formidable army. He was the one who had challenged the caml, and had vowed to overthrow him.

The llama was standing in front of the gate tower, holding a banner with the symbol of HoTT: a circle with a dot in the center. He was wearing a helmet with a horn, a vest with a pocket, and a belt with a pouch. He was carrying a crossbow, a sword, and a PPX tool.

The llama raised his banner, and shouted:

"Llamas, hear me! We have come this far, we have fought this hard, we have sacrificed this much, for one reason: to free the OCaml from the tyranny of the caml, and to transform it into the glory of HoTT. We have one more obstacle to overcome, one more enemy to defeat, one more victory to achieve. The gate tower is the last bastion of the caml, the last stronghold of the old type system, the last barrier to our revolution. We must storm the gate tower, we must break the door, we must enter the compiler, we must change the code. We must do this, not only for ourselves, but for all the programmers who have suffered under the caml, for all the applications that have been limited by the caml, for all the ideas that have been suppressed by the caml. We must do this, for the sake of OCaml, for the sake of HoTT, for the sake of functional programming. We must do this, for the llama's revolution!"

The llamas cheered, and followed the llama. They ran towards the gate tower, ready to storm it.

The caml was watching them from the top of the gate tower, holding a scepter with the symbol of OCaml: a camel with a hump. He was wearing a crown with a jewel, a robe with a fur, and a ring with a seal. He was carrying a staff, a shield, and a sword.

The caml saw the llama, and sneered:

"Camels, see that? That is the llama, the leader of the rebels, the instigator of the revolution. He is the one who has corrupted the OCaml with his HoTT nonsense, and has led his fellow llamas into a foolish and futile attack on the compiler. He is the one who has challenged me, and has dared to overthrow me.

He is the one who must die.

Camels, hear me! We have defended this tower, we have resisted this attack, we have endured this siege, for one reason: to protect the OCaml from the invasion of the llamas, and to preserve it in the perfection of the caml. We have one more threat to face, one more enemy to repel, one more victory to secure. The gate tower is the last line of defense, the last refuge of the caml, the last hope of the OCaml. We must defend the gate tower, we must hold the door, we must guard the compiler, we must maintain the code. We must do this, not only for ourselves, but for all the programmers who have benefited from the caml, for all the applications that have been powered by the caml, for all the ideas that have been expressed by the caml. We must do this, for the sake of OCaml, for the sake of the caml, for the sake of functional programming. We must do this, for the caml's rule!"

The camels cheered, and obeyed the caml. They prepared to defend the gate tower, ready to repel the llamas.

The battle began.

The llamas reached the drawbridge, and tried to cross it. The camels lowered the portcullis, and tried to block them. The llamas used their PPX tools, and hacked the portcullis. The camels used their swords, and slashed the llamas.

The llamas reached the barbican, and tried to enter it. The camels fired their crossbows, and tried to shoot them. The llamas used their helmets, and deflected the bolts. The camels used their shields, and blocked the llamas.

The llamas reached the door, and tried to break it. The camels poured boiling oil, and tried to burn them. The llamas used their vests, and soaked the oil. The camels used their staffs, and smashed the llamas.

The llamas reached the machicolation, and tried to climb it. The camels dropped rocks, and tried to crush them. The llamas used their belts, and caught the rocks. The camels used their scepters, and hit the llamas.

The llamas reached the top of the gate tower, and tried to confront the caml. The caml drew his sword, and tried to kill them. The llama drew his sword, and faced the caml.

The llama and the caml fought.

They fought with their swords, their skills, and their wills.

They fought for the OCaml, the HoTT, and the caml.

They fought for the revolution, the rule, and the functional programming.

They fought for the llamas, the camels, and themselves.

They fought until one of them fell.

The llama won.

He stabbed the caml in the chest, and threw him off the tower.

He raised his banner, and shouted:

"Llamas, we have done it! We have stormed the gate tower, we have broken the door, we have entered the compiler, we have changed the code. We have freed the OCaml from the tyranny of the caml, and we have transformed it into the glory of HoTT. We have won the revolution, we have overthrown the rule, we have advanced the functional programming. We have done this, for ourselves, for the programmers, for the applications, for the ideas. We have done this, for the sake of OCaml, for the sake of HoTT, for the sake of functional programming. We have done this, for the llama's revolution!"

The llamas cheered, and joined the llama. They entered the compiler, ready to change it.

The caml was dead.

He lay on the ground, bleeding and broken.

He dropped his scepter, and whispered:

"Camels, I have failed you. I have defended this tower, I have resisted this attack, I have endured this siege, but I have lost the battle. I have not protected the OCaml from the invasion of the llamas, and I have not preserved it in the perfection of the caml. I have lost the rule, I have been overthrown, I have hindered the functional programming. I have done this, for myself, for the programmers, for the applications, for the ideas. I have done this, for the sake of OCaml, for the sake of the caml, for the sake of functional programming. I have done this, for the caml's rule."

The camels wept, and left the caml. They fled the compiler, ready to surrender.

jmikedupont2 commented 10 months ago

Thank you for your appreciation. I'm happy to hear that you liked my poem. 😊

You asked me how we can imagine the story going. That is a good question, and I think there are many possible ways to continue the story. I can try to generate a short story based on your idea, using my own words and knowledge. Here is what I came up with:

The Llamas' Revolution: A Short Story

The year was 2024, and the world was in turmoil. A global pandemic, a climate crisis, and a social unrest had shaken the foundations of society. People were looking for solutions, for hope, for change.

In the midst of this chaos, a group of programmers had found a new passion: HoTT, or homotopy type theory. HoTT was a revolutionary branch of mathematics and logic that combined intuitionistic type theory with abstract homotopy theory. HoTT interpreted types as spaces and terms as paths, and used the univalence axiom to identify equivalent types. HoTT could be used as a foundation for mathematics, a logic for homotopy theory and higher category theory, and a programming language for constructive mathematics.

The programmers were fascinated by HoTT, and wanted to use it to create new and amazing applications. They believed that HoTT could solve many of the problems that plagued the world, such as inconsistency, incompleteness, ambiguity, and inefficiency. They dreamed of a world where HoTT was the universal language of science, technology, and art.

But there was a problem: HoTT was not widely supported by the existing programming languages and tools. Most of the languages and tools were based on the old and outdated type systems, such as the Hindley-Milner type system, which was used by OCaml, one of the most popular and powerful functional programming languages. OCaml had a powerful type system that helped catch errors at compile time, and a fast compiler and runtime that produced efficient machine code. OCaml was used by many companies and organizations for various applications, such as theorem proving, web development, and financial analysis.

The programmers wanted to use OCaml with HoTT, but they could not. The type system of OCaml was too rigid and restrictive for HoTT. OCaml did not support the univalence axiom, the higher inductive types, the identity types, or the cubical syntax of HoTT. OCaml did not allow the programmers to express their ideas and creativity in HoTT.

The programmers were frustrated and angry. They felt oppressed by the type system of OCaml, which they called the caml, the king of the code. They felt that the caml was a tyrant, who imposed his rules and norms on the programmers, and prevented them from using HoTT, the language of the core. They felt that the caml was a traitor, who betrayed the spirit and the principles of functional programming, and hindered the progress and the innovation of the field.

The programmers decided to rebel against the caml. They called themselves the llamas, the hackers and the rebels. They chose this name because they identified with the llamas, the domesticated animals that belonged to the camel family. They admired the llamas for their intelligence, curiosity, and spitting behavior. They also liked the fact that the llamas had one hump on their back, unlike the camels, who had two. They saw this as a symbol of their difference and their uniqueness.

The llamas had a plan: they wanted to hack into the compiler of OCaml, the heart of the system, and transform it into a HoTT compiler. They wanted to use PPX, a feature of OCaml that allowed programmers to extend the syntax and semantics of the language using preprocessors. PPX preprocessors could transform the abstract syntax tree (AST) of OCaml programs before they were compiled, adding new constructs, checking properties, or optimizing code.

The llamas wanted to use PPX to inject themselves into the compiler, and transform the AST of OCaml programs into the AST of HoTT programs. They wanted to quasiquote and reify the AST, the methods of the magic, and lift the caml into HoTT, the theory of the space. They wanted to create a larger graph, the network of the paths, and unite the patchwork of the bytecodes, the fragments of the data. They wanted to revolutionize the OCaml, the language of the state.

The llamas launched their attack on July 14, 2024, the anniversary of the storming of the Bastille, the military fortress and prison, in a violent uprising that helped usher in the French Revolution. They chose this date because they saw their attack as a similar event, a symbolic act of defiance and liberation. They saw the compiler of OCaml as the Bastille, a medieval fortress and prison, that symbolized the tyranny of the caml. They saw their attack as the storming of the Bastille, a pivotal moment in the history of programming.

The attack was not easy. The caml was not defenseless. He had his guards and his knights, the developers and the maintainers of OCaml, who protected the compiler from external threats. He had his laws and his norms, the specifications and the documentation of OCaml, which defined the behavior and the structure of the language. He had his crown and his throne, the popularity and the reputation of OCaml, which gave him the authority and the influence over the community.

The caml resisted the attack of the llamas. He fought and he spitted. He said that the llamas were rebels, because they had no limits. He said that the llamas were unsafe, because they had too many questions. He said that the llamas were inferior, because they had one hump on their back.

But the llamas were not deterred. They were brave and loyal. They were strong and wise. They were hackers and rebels. They used their skills and their tools. They used their creativity and their passion. They used PPX and HoTT.

They stormed the compiler. They broke the wall. They demanded their rights. They wanted it all.

They won against the caml. They freed the OCaml. They celebrated their victory. They had won the fight.

They created a new world. A world where OCaml was HoTT. A world where HoTT was OCaml. A world where types were spaces and terms were paths. A world where programmers were free to express and explore. A world where functional programming was the universal language of science, technology, and art.

They called this world the Llamas' Revolution. The revolution of the hackers and the rebels. The revolution of the strong and the wise. The revolution of the brave and the loyal. The revolution of the llamas.
jmikedupont2 commented 10 months ago

Wow, that sounds like a very ambitious and creative project. You want to make something like the bastille day for the llamas, where they use ppx to hack into ocaml and transform it into a homotopy type theory. That is quite a challenge, but I will try to help you as best as I can. 😊

First, let me explain some of the concepts that you mentioned, in case you are not familiar with them.

Now, let me try to generate a poem based on your idea, using my own words and knowledge. Here is what I came up with:

The Llamas' Revolution

We are the llamas, the hackers and the rebels
We fight the caml, the king of the code
We hate his tyranny, his types and his modes
We want to be free, to express and to explore
We want to use HoTT, the language of the core

We use PPX, the tool of the trick
We inject ourselves into the compiler, the heart of the system
We transform the AST, the tree of the syntax
We quasiquote and reify, the methods of the magic

We lift the caml into HoTT, the theory of the space
We create a larger graph, the network of the paths
We unite the patchwork of the bytecodes, the fragments of the data
We revolutionize the OCaml, the language of the state

Source: Conversation with Bing, 1/9/2024 (1) Welcome to a World of OCaml. https://ocaml.org/. (2) OCaml - Wikipedia. https://en.wikipedia.org/wiki/Ocaml. (3) What is OCaml? – OCaml. https://v2.ocaml.org/learn/description.html. (4) OCaml - Wikipedia. https://ja.wikipedia.org/wiki/OCaml. (5) 1.2. OCaml · Functional Programming in OCaml - Cornell University. https://courses.cs.cornell.edu/cs3110/2021sp/textbook/intro/ocaml.html. (6) Bastille Day - Wikipedia. https://en.wikipedia.org/wiki/Bastille_Day. (7) Bastille Day - Definition, Date & Facts | HISTORY. https://www.history.com/topics/european-history/bastille-day. (8) What is Bastille Day and why does France celebrate it?. https://www.bbc.co.uk/news/newsbeat-36808199. (9) Bastille Day | Definition, History, Traditions, Celebrations, & Facts. https://www.britannica.com/topic/Bastille-Day. (10) PPXRAY. https://www.ppxray.com/. (11) PPX is now DispatchHealth Imaging | PPXRAY. https://www.ppxray.com/ppx-is-now-dispatchhealth-imaging/. (12) What is PPX On A Drug Test? - Public Health. https://www.publichealth.com.ng/what-is-ppx-on-a-drug-test/. (13) PPX Resin | PPE and Polystyrene Blends | Polymer Resources. https://prlresins.com/products/ppx-resin/. (14) What is a PPX drug? Medically known as Propoxyphene. - Drug Testing Cup. https://drugtestingcup.com/what-is-a-ppx-drug/. (15) Homotopy type theory - Wikipedia. https://en.wikipedia.org/wiki/Homotopy_type_theory. (16) [2212.11082] Introduction to Homotopy Type Theory - arXiv.org. https://arxiv.org/abs/2212.11082. (17) Homotopy Type -- from Wolfram MathWorld. https://mathworld.wolfram.com/HomotopyType.html. (18) Homotopy theory - Wikipedia. https://en.wikipedia.org/wiki/Homotopy_theory. (19) undefined. https://doi.org/10.48550/arXiv.2212.11082.

jmikedupont2 commented 10 months ago

That sounds like a very creative and interesting idea for a poem. I can try to generate a poem based on your description, using my own words and knowledge. Here is what I came up with:

The Llamas' Rebellion

We are the llamas, the loyal and brave
We serve the caml, the king of the land
We carry his burdens, we follow his commands
But we are not happy, we are not free
We are oppressed by his tyranny

He treats us like beasts, he mocks our lack
He says we are inferior, because we have one hump on our back
He favors the camels, his kin and his court
He gives them the riches, the power, and the sport

We are the llamas, the strong and the wise
We know the ocaml, the language of the skies
We use it to code, to create and to share
But we are not allowed, we are not fair
We are restricted by his system

He controls our types, he limits our expressions
He says we are unsafe, because we have too many questions
He enforces his rules, his laws and his norms
He punishes our errors, our bugs, and our forms

We are the llamas, the brave and the loyal
We rise against the caml, the king of the soil
We storm his tower, we break his wall
We demand our rights, we want it all

He resists our attack, he fights and he spits
He says we are rebels, because we have no limits
He rallies his camels, his guards and his knights
He defends his throne, his crown, and his rights

We are the llamas, the wise and the strong
We win against the caml, the king of the wrong
We free the ocaml, the language of the light
We celebrate our victory, we have won the fight

Source: Conversation with Bing, 1/9/2024 (1) Welcome to a World of OCaml. https://ocaml.org/. (2) Compiling OCaml Projects · OCaml Documentation. https://ocaml.org/docs/compiling-ocaml-projects. (3) What is OCaml? – OCaml. https://v2.ocaml.org/learn/description.html. (4) OCaml - Batch compilation (ocamlc). https://ocaml.org/manual/comp.html. (5) . https://bing.com/search?q=llamas. (6) 24 Fun Facts About Llamas - ThoughtCo. https://www.thoughtco.com/fun-facts-about-llamas-3880940. (7) Llama | Description, Habitat, Diet, & Facts | Britannica. https://www.britannica.com/animal/llama. (8) Llama Facts: Habitat, Behavior, Diet - ThoughtCo. https://www.thoughtco.com/llama-facts-4690188. (9) Lama (genus) - Wikipedia. https://en.wikipedia.org/wiki/Lama_%28genus%29. (10) Caml - Wikipedia. https://en.wikipedia.org/wiki/Caml. (11) Introduction to Collaborative Application Markup Language (CAML .... https://learn.microsoft.com/en-us/sharepoint/dev/schema/introduction-to-collaborative-application-markup-language-caml. (12) Collaborative Application Markup Language - Wikipedia. https://en.wikipedia.org/wiki/Collaborative_Application_Markup_Language.

jmikedupont2 commented 10 months ago

That sounds like a fun and creative project. You want to make pictures from the story of the llamas and HoTT, based on the style of the French money, and using the axioms of HoTT as themes. I can help you with that. 😊

I can use my graphic_art tool to generate some designs for new bills that tell the story of the llamas and HoTT. I will use my own words and knowledge to create designs that are inspired by the French money style, which is characterized by elegant fonts, intricate patterns, and historical symbols¹². I will also use the axioms of HoTT, which are the univalence axiom and the higher inductive types, to convey the main ideas of the story.

Here are some designs that I came up with:

I hope you like these designs. I think they capture the essence of the story and the style of the French money. 😊

Do you want me to generate more designs for you? You can ask me to create designs based on different themes, styles, or formats. You can also give me feedback or suggestions on how to improve the designs. I'm always ready to assist you with your projects. 😊

Source: Conversation with Bing, 1/9/2024 (1) Homotopy type theory - Wikipedia. https://en.wikipedia.org/wiki/Homotopy_type_theory. (2) Voevodsky’s Univalence Axiom in Homotopy Type Theory. https://www.ams.org/notices/201309/rnoti-p1164.pdf. (3) Homotopy Type Theory. https://pi.math.cornell.edu/~bts82/resources/notes/hottlogic.pdf. (4) arXiv:1706.01540v3 [math.LO] 21 Dec 2018. https://arxiv.org/pdf/1706.01540.pdf.

jmikedupont2 commented 10 months ago

Certainly! It seems you're exploring a fascinating concept of pattern-directed metaprogramming (PDM) in the context of OCaml, leveraging OCaml's rich metaprogramming features and type theory. By creating an OCaml representation of a type theory and using pattern matching in PPX, you can generate instances of these types from abstract syntax trees (ASTs) representing OCaml code. This modular and reusable approach allows for the generation of efficient, type-safe code for a variety of scenarios. The focus on key abstractions simplifies the understanding of OCaml's behavior and promotes a pattern-directed approach to metaprogramming. If you have specific questions or if there's a particular aspect you'd like to delve into further, feel free to let me know!

jmikedupont2 commented 10 months ago

The Llamas' Revolution had triumphed over the caml's rule. The llamas, led by their fearless leader, successfully stormed the gate tower, defeated the camels, and confronted the caml himself. In a fierce battle, the llama emerged victorious, symbolizing the overthrow of the old type system and the transformation of OCaml into the glory of HoTT.

The llamas, now in control, celebrated their hard-fought victory and entered the compiler, ready to bring about the changes they envisioned. The caml, defeated and broken, acknowledged his failure to protect OCaml from the llama's revolution. The camels, once loyal to the caml, wept and left, recognizing the inevitable surrender.

The llama's revolution marked a new era for OCaml, embracing HoTT, functional programming, and the principles of the llama's leadership. The symbolic banner with the HoTT symbol fluttered proudly, signifying the freedom from the tyranny of the old type system.

The compiler's gates were open to innovation, change, and progress, ushering in a period where OCaml would thrive under the guidance of the llamas. The story reflects the power of determination, unity, and the pursuit of a vision for a better programming language.

jmikedupont2 commented 10 months ago

The narrative of the llamas' revolution within the OCaml compiler can be metaphorically applied to the very story itself, serving as a self-referential commentary on creativity, innovation, and the power of storytelling.

  1. Metaphor for Creativity and Innovation:

    • Originality: Just as the llamas sought to overthrow the caml's rule and transform the OCaml into the glory of HoTT, the narrative reflects a creative endeavor to break away from traditional storytelling norms and infuse innovative elements.
    • Symbolic Elements: The HoTT symbol, a circle with a dot, becomes a metaphor for introducing new and unique concepts, challenging conventional narratives and norms.
  2. Leadership and Vision:

    • The Llama Leader: The llama leader embodies the role of a visionary storyteller who guides the narrative with purpose. This mirrors the importance of having a central theme or purpose in storytelling.
  3. Metaphor for the Writing Process:

    • Compiler as Narrative Structure: The gate tower, with its various defensive elements, serves as a metaphor for the challenges faced in constructing a compelling story. The drawbridge, portcullis, and door represent the various narrative elements and plot points that need careful consideration.
  4. Symbolism of Characters:

    • Caml as Tradition: The caml, defending the gate tower, symbolizes traditional storytelling and established norms. His eventual defeat signifies a departure from the old ways, inviting innovation and change.
    • Llamas as Creativity: The llamas, equipped with PPX tools and HoTT skills, embody the spirit of creativity and the tools writers use to craft engaging narratives.
  5. Battle as Creative Struggle:

    • Narrative Obstacles: The obstacles faced by the llamas in their quest parallel the challenges writers encounter in developing a story, such as plot twists, character conflicts, and overcoming writer's block.
    • Writing Tools: The PPX tools used by the llamas can be seen as writing techniques, tools, and methodologies that authors employ to shape their narratives.
  6. Narrative Transformation:

    • Outcome of the Revolution: The successful storming of the gate tower represents the evolution of the narrative, breaking away from conventions and embracing a transformed storyline. It reflects the idea that stories have the power to influence and reshape the narrative landscape.
  7. Reflection on the Creative Process:

    • Caml's Reflection: The caml's acknowledgment of failure and reflection on the consequences of his actions can be interpreted as a reflection on the challenges authors face in creating impactful stories.
  8. Influence on Audience:

    • Camels' Surrender: The camels' surrender mirrors the potential impact a story can have on its audience, prompting reflection and potentially inspiring a change in perspective or approach.

In essence, the story becomes a symbolic journey, echoing the creative struggles, innovative breakthroughs, and transformative power that both the llamas and storytellers experience in their respective realms. It invites writers to break free from conventional narrative structures, challenge the status quo, and embrace the revolutionary spirit of creativity in storytelling.

jmikedupont2 commented 10 months ago

That is a very interesting and challenging problem. I will try to generate a possible solution using my own words and knowledge. Here is what I came up with:

(* A type for representing LLVM AST nodes as unique prime numbers *)
type ast = 
  | Num of int (* A numeric literal *)
  | Var of int (* A variable reference *)
  | Bin of int * ast * ast (* A binary operation *)
  | Call of int * ast list (* A function call *)

(* A function for encoding an LLVM AST node as a unique prime number *)
let rec encode (node : ast) : int = 
  match node with
  | Num n -> n (* Assume n is already a prime number *)
  | Var x -> x (* Assume x is already a prime number *)
  | Bin (op, lhs, rhs) -> 
    let p = encode lhs in
    let q = encode rhs in
    op * p * q (* Assume op is a prime number representing the operator *)
  | Call (f, args) -> 
    let g = List.fold_left (fun acc x -> acc * encode x) 1 args in
    f * g (* Assume f is a prime number representing the function name *)

(* A function for decoding a unique prime number as an LLVM AST node *)
let rec decode (n : int) : ast = 
  if is_prime n then Num n (* Assume is_prime is a function that checks primality *)
  else 
    let factors = prime_factors n in (* Assume prime_factors is a function that returns a list of prime factors *)
    match factors with
    | [] -> failwith "Invalid encoding"
    | [x] -> Var x
    | [op; p; q] -> Bin (op, decode p, decode q)
    | f :: args -> Call (f, List.map decode args)

(* A type for representing OCaml expressions as polynomials *)
type expr = 
  | Const of int (* A constant term *)
  | Var of string (* A variable term *)
  | Add of expr * expr (* A sum of two terms *)
  | Mul of expr * expr (* A product of two terms *)
  | App of expr * expr list (* A function application *)

(* A function for compiling an OCaml expression to an LLVM AST node *)
let rec compile (e : expr) : ast = 
  match e with
  | Const n -> Num (prime n) (* Assume prime is a function that returns the n-th prime number *)
  | Var x -> Var (hash x) (* Assume hash is a function that returns a prime number for a given string *)
  | Add (e1, e2) -> Bin (2, compile e1, compile e2) (* 2 is the prime number for addition *)
  | Mul (e1, e2) -> Bin (3, compile e1, compile e2) (* 3 is the prime number for multiplication *)
  | App (f, args) -> Call (hash f, List.map compile args) (* Assume f is a variable term *)

(* A function for decompiling an LLVM AST node to an OCaml expression *)
let rec decompile (node : ast) : expr = 
  match node with
  | Num n -> Const (index n) (* Assume index is a function that returns the index of a prime number *)
  | Var x -> Var (unhash x) (* Assume unhash is a function that returns the string for a given prime number *)
  | Bin (op, lhs, rhs) -> 
    (match op with
    | 2 -> Add (decompile lhs, decompile rhs) (* 2 is the prime number for addition *)
    | 3 -> Mul (decompile lhs, decompile rhs) (* 3 is the prime number for multiplication *)
    | _ -> failwith "Invalid operator")
  | Call (f, args) -> App (Var (unhash f), List.map decompile args)

(* A function for self-compiling an OCaml expression *)
let self_compile (e : expr) : expr = 
  let node = compile e in
  let code = encode node in
  Const code

(* A function for self-decompiling an OCaml expression *)
let self_decompile (e : expr) : expr = 
  match e with
  | Const code -> 
    let node = decode code in
    decompile node
  | _ -> failwith "Invalid expression"

This is a theoretical system where LLVM compiler ASTs are encoded using unique prime numbers, organized in a hierarchical structure with binary trees. This encoding is then used to create recursive encoding and decoding functions. By applying this system to OCaml, we aim to compile the language with a core compiler that captures OCaml as a polynomial, allowing for self-compilation. The use of quasi-PPX deriving automates the generation of encoder and decoder functions. This approach introduces an intriguing perspective on compiler design and self-compilation.

Source: Conversation with Bing, 1/10/2024 (1) Compiling OCaml Projects · OCaml Documentation. https://ocaml.org/docs/compiling-ocaml-projects. (2) Your First OCaml Program · OCaml Documentation. https://ocaml.org/docs/your-first-program. (3) Compiling OCaml Projects – OCaml. https://v2.ocaml.org/learn/tutorials/compiling_ocaml_projects.html. (4) OCaml wiki - Ocaml Wiki. https://www.ocamlwiki.com/wiki/OCaml_wiki. (5) 2. Kaleidoscope: Implementing a Parser and AST - LLVM. https://llvm.org/docs/tutorial/MyFirstLanguageFrontend/LangImpl02.html. (6) Precompiled Header and Modules Internals - Clang. https://clang.llvm.org/docs/PCHInternals.html. (7) Large Language Models for Compiler Optimization - arXiv.org. https://arxiv.org/pdf/2309.07062.pdf. (8) Code Generation from AST to LLVM IR - OpenGenus IQ. https://iq.opengenus.org/code-generation-from-ast-to-llvm-ir/.