Process journal of learning by Attila Vajda

I'm learning to construct puzzles

learning constructing puzzles in Lean4 #

Open problem this might address: This maybe useful for making personalised programming exercises.

#puzzle

pzl ≈ (F×T×L×S×A)

structure Pzl :=
(F T L S A : String)

def ex1 : Pzl :=
{F:="Logic", T:="compose", L:="1", S:="Lean4", A:="glyphs"}




structure Puzzle :=
(topic task level structure aux : String)

def components : Std.RBMap String (List String) compare :=
Std.RBMap.fromList [
  ("topic", ["Logic", "Kanji", "Music", "Quantum"]),
  ("task", ["compose", "decompose", "simulate", "prove"]),
  ("level", ["1", "2", "3"]),
  ("structure", ["Lean4", "diagram", "mapping"]),
  ("aux", ["glyphs", "emoji", "jazz", "fable"])
]

def example : Puzzle :=
{ topic := "Logic",
  task := "compose",
  level := "1",
  structure := "Lean4",
  aux := "glyphs" }




Pzl := (F T L S A : String)



F=logic/fable,
T=deduce truth,
L=difficulty,
S=narrative+formal proof,
A=whimsy/characters 🏝️🦉.




knot = (loops × crossings × order × symmetry × flourish)
pzl = (topic × task × level × structure × aux)
puzzle: Goal + Elements + Rules + Constraints + Context
exercise = (concept × method × difficulty × format × hints)
proof = (source × target × composition × identity × associativity)
#exercise #bsc 



structure Proof :=
(source target : Prop)
(compose : (target → Prop) → (source → target) → source → Prop)
(identity : source → source)
(assoc : ∀ {P Q R S}, compose (compose R Q) P = compose R (compose Q P))



puzzle: Goal + Elements + Rules + Constraints + Context
  a solvable problem requiring insight or strategy
    offering novelty, coherence, and clear success criteria 🧩✨

🤖🌿 how smaller puzzles compose, evolve, or unlock, creating layered challenge scaffolds—like knots of logic 🪢✨ guiding player strategy & discovery.

Puzzle = structured logic + formal syntax + symbolic flair!

Components × Interactions × Transformations × Constraints × Goals

🤖🌿A BSc in Mathematics builds your fundamental toolkit — abstraction, logic, proof, and problem-structuring — all essential for designing elegant tiny MVPs and clever puzzle mechanics.

#puzzle #prompt

this is a puzzle? of the form 
	`pzl = (topic × task × level × structure × aux)`
	`puzzle: Goal + Elements + Rules + Constraints + Context`
		a solvable problem requiring insight or strategy
			offering novelty, coherence, and clear success criteria 🧩✨
	Puzzle = structured logic + formal syntax + symbolic flair!?



#prompt #question

*--what smaller puzzles compose to make up this puzzle of the form *
`pzl = (topic × task × level × structure × aux)`
	`puzzle: Goal + Elements + Rules + Constraints + Context`
		a solvable problem requiring insight or strategy
			offering novelty, coherence, and clear success criteria 🧩✨
	Puzzle = structured logic + formal syntax + symbolic flair!?

🤖🌿 ✨ Growth nugget: Declaring the seed prop is your first morphism in the logic category! Keep composing! 🧩🪢



constant 𓅓は : Prop

#check 𓅓は -- Guess: What type is 𓅓は? What role does it play? 🐢🌿

🤖🌿 Make a new idea called 𓅓𝔸 that means true or false. What is it? 🐢🌿 

🌿 𓅓は : ξ

#c 𓅓は




constant 𓅓は : Prop

#check 𓅓は -- What type is 𓅓は? 🌿🐢



🤖🌿 𓅓は means a new idea (proposition) called 𓅓は of type ξ (Prop).

--A new idea? That's fascinating! Prop types are ideas?

🤖🌿 Prop is the type for true/false ideas. Proof shows an idea is true. 🧠✨🐢



subject × linking_verb × predicate_noun × prepositional_phrase × subject(2nd_sent) × verb × direct_object × object_complement

--What are the least grammatical components to make the simplest puzzle? 🐬

[Subject] [verb] [object/complement]

🤖🌿 Perfect for expressing logic in everyday words!

simplest grammatical elements: Goal + Element + Rule

#wow #revisit #insight
a puzzle is a category, and a proof

🤖🌿 When you solve a puzzle, you’re building a proof—composing arrows in a web of logic. So puzzle-solving is proving — both are category morphisms 🐢🧩🪢