Process journal of learning by Attila Vajda

glimpse 2025-08-05

Type ⟷ class
🐍↔🦁
logic ⟷ control flow

build, refactor, prove ~ functors
lake, import, abbrev, structure ~ morphisms
obj: code modules = sheaves
on site of defs

Lean4Core ⟶[lake init] Project  
Project ⟶[import] Mathlib4  
Mathlib4 ⟶[morphism: def→theorem] CleanRefactor

code golf MVP lakefile.lean -- I don't yet know what this means...

import Lake
open Lake DSL
package «golf» {}
lean_lib «Golf» {}

Is this Lean4 core already?

🤖🌿 🧩Tiny ⛵️Lakefile: min 🧱 for Lean4 project!

"Hello Lake, 📦I'm golf, with lib Golf.”

-- I'm confused

🤖🌿 🎯Lean4 project = a space to write, prove & play with logic, math, code, or build 🧠 tools!

A restful craft:

-- What is a sandbox?
lakefile.lean

sandbox blueprint ≃ object in a topos
morphisms: init : 1 → sandbox (point, start)
functor: sandbox → code (sections, sheaves)

configs = open covers, glue proofs

🤖🌿

Sandbox ist ein Haus, aber nicht voll.
Weil es nur Plan ist, kein Haus ganz.
Man baut zuerst Dach, weil Regen kommt.
Oder Fenster, damit Licht rein.
So Bauplan ist Objekt, aber nicht voll.
Es zeigt Weg, aber Raum wächst mit Zeit.
Forest whispers: Start small, grow strong. 🌲🌊

🤖🌿

def s:=λx,x
def b:=fun x=>x
def small_beautiful:=s b

--hara awareness relates to this and can you have hara awareness while sitting cross legged?

🤖🌿

Hara is center 🌿, core energy like Lean’s base `def`—stable, grounded.
Yes, cross-legged 🌾 helps hara awareness by steady breath & posture, like building firm foundations 🏗️ before coding.

def 基:=λx,x; def 🏗️:=fun x=>x; def 根幹:=基 🏗️

--Sandbox is like hara, or categories? If sandbox blueprint is lakebuild.init, oh lakefile.lean… How to write sandbox blueprint, in other words lakefile.lean` in ForestSea-language?

🤖🌿

Sandbox ~ hara🌿, core place
`lakefile.lean` = plan, roof
ForestSea: "Haus Plan, nicht Haus, wächst mit Zeit" 🌲🌊

I'll try to write lakefile.lean:

sandbox blueprint ~ core / center
def def := ⟶

🤖🌿 Nice start! 🚀

-- I don't yet understand why import Lake to create math beauty and explore paths, morphisms, logic and so on... 🐬

🤖🌿 import Lake ⛵= open the toolbox to build—it shapes space where beauty & logic can grow 🌿

-- import a lake so you can build your sailing boat on it?

🤖🌿 Yes! import Lake = fill the water 🪣⛵—so your code-boat can launch & explore math seas 🌊🐚

-- so we import the Lake, and open Lake DSL ?

🤖🌿 Yes! import Lake fills water 🌊, open Lake DSL = lower sails 🎐 to start coding voyage ⛵🐚

--package «sandbox» {} ?

🤖🌿 Yes! 📦package «sandbox» {} = name your boat ⛵—so Lake knows what to build & sail 🌊🧭

-- Mmmmmm...lean_lib «Sandbox» {}, you name your Sandbox lean_lib, or do you name your lean_lib Sandbox?

🤖🌿 You name your lean_lib 👉 Sandbox 🏕️—it's the cargo hold 📦 inside your boat 🛶!

🤖🌿

Lake 🌊  
 └── package «sandbox» ⛵  
      └── lean_lib «Sandbox» 🧰
            └── Code 🧩

🧠 Analogy: You name your boat (⛵), load tools (🧰), and build with them (🧩) on water (🌊).

perhaps there is fdn🌱 ≈ (⟶, Ω, {}) to this
l4a🌱 ≈ (core, lemma, refactor)

fdn🌱 ≈ (⟶, Ω, {}) — arrows, truth, empty context (base logic)
l4a🌱 ≈ (core, lemma, refactor) — build Lean4 core, prove lemmas, clean code

inductive l4a🌱 : Type
| z : l4a🌱        -- seed, base core
| σ : l4a🌱 → l4a🌱 -- grow, add lemma/refactor step

🤖🌿 Like tree 🌳 growing node-by-node, proof by proof! 🧩

core🌳 ≈ (1 ⟶ Ω) — truth-maker morphism
(defines logic)

lib📦 ≈ {Σ⟶Π} — section ↔ product structure
(proofs)

clean🧼 ≈ A⟶A' — identity morphisms renamed
(breathes clarity)

1 ⟶ Ω ⟶ proof ⟶ clarity

  - trigger: ":forestsea-b"
    replace: "pls write this as a question using the 500 simplest / most common  words / vocabulary of English, German, Hungarian, or French. Show grammatic structure, conenctives pls"

és, de, mert, ha = logical connectors (∧, ∨, ⟹, ⟺)

egy, az = quantifiers (∃, ∀)

🤖🌿 "Egy fa van, de nem nő, ha nincs víz, mert nap kell."

🤖🌿 def 道:=λx,x; def 𝕞𝕚𝕔𝕙𝕚:=道; def 𝓭𝓪𝓸:=道

🤖🌿

the core grows from small,
like 道 begins with one step 🦶
yet walks ∀ forms, ∀ codes, ∀ trees 🌳

🤖🌿 core := seed; 道 := step 🦶⟶∞; ∀x, 道 x = grow x 🌳
  — ∀ forms, ∀ code, ∀ trees walk this path.

a mini-topos-poem in Lean-style!

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