Exercises: Rhymations

These are problems for LLMs to solve that use the functions defined in the Functions plugin and the Lexicon plugin <lexicon-plugin> of the Language Game.

Language Palette

Syntax

• Brackets: []

  • Used to group expressions.

Constants

• Characters:

  • σ: Delimiter (e.g. space)

• Sets:

  • L: Language

  • C: Corpus

  • I: Invertible words (e.g. inv(emit) = time )

  • R: Reflective words (e.g. inv(eye) = eye )

  • M _pattern : Metric words (e.g. M _πΠ = iambic words)

  • P: Palindromes

Variables

• x, y, z: strings

• n, m: integers

• p, q: rationals

• Π, π: syllable

  • Π: stressed

  • π: unstressed

• ι: character

• α: word

• ζ: sentence

Relations

• Linguistic:

  • ∥ : rhymes (e.g. cat ∥ hat)

  • ≡ : synonyms (e.g., fate ≡ destiny)

  • ≢ : antonyms (e.g., hate ≢ love)

  • ⊂ _c : containment (e.g. row ⊂ _c borrow )

• Set: ∈ ∉ ∪ ∩ ⊂

• Logic: ∧ ∨ ∀ ∃ →

Operators

• Concatenation: xy

  • Standard string definition

  • Exponentiation is shorthand for iterated concatenations, e.g. x^2 = xx

• Separation: x.y

  • Separation creates new lines

• Closure: * (tick marks are used to prevent markdown formatting)

  • This operator is equivalent to a regex wildcard.

• Selector: [λx: f(x)] -> x

  • This operator returns the value of a variable that satifies f(x).

• Reduction: ς(x) -> x

  • This operator removes all delimiter characters from a string.

• Inversion: inv(x) -> x

  • This operator reverses a string.

• String Length: l(x) -> n

  • This operator returns the character length of a string.

• Word Length: w(x) -> n

  • This operator returns the word length of a string.

• Metric Length: m(x | pattern) -> p

  • This operator returns the number of metrical feet, relative to pattern, e.g m(deduce the math | πΠ) = 2 versus m(deduce the math | πΠπ) = 1.5

Functions

• connote(x) -> set(α)

  • Returns a set of words that connote x.

• contains(x) -> set(α)

  • Returns a set of words that contain x.

• decline(α) -> set(α)

  • This function returns a set of words that are the result of conjugation, declension or other modifications, e.g. decline(special) = { especial, especially, specialty, specialness , … }.

• line(x: concept) -> ζ

  • This function returns a sentence that illustrates x.

• resonate(α) -> set(α)

  • This function returns a set of words that bear the relation of consonance or assonance with x.

• rhyme(α) -> set(α)

  • This function returns a set of words that rhyme with x.

• chiasmate(ζ) -> ζ

  • This function return a chiasmus of x.

• anapest(x) -> set(α)

• dactyl(x) -> set(α)

• iamb(x) -> set(α)

• spondee(x) -> set(α)

• trocheee(x) -> set(α)

Optional Argument Palette

• meter: constrains output to have this meter

• feet: constrains output to measure this length of metrical feet

• rhyme: constrains output to rhyme with argument

Expressions

1. iamb(resonate(peak) ∩ connote(reserves ∨ harvest stores))

2. (rhyme(trough) ∪ rhyme(connote(trough)) ∩ connote(give away v yield ∨ empty out))

3. trochee((connote(revelry) ∪ connote(drunken merriment)) ∩ (resonate(stream) ∪ resonate(stone)))

4. (connote(revelry) ∪ connote(drunken merriment)) ∩ (resonate(stream) ∪ resonate(stone))

5. trochee(connote(birds) ∩ connote(toiling in a field))

6. resonate(lunar) ∩ connote(angelic)

7. (connote(schools as in ‘schools of fish’) ∩ (connote(knightly) ∪ connote(squadrons)))(meter=Π)

8. (resonate(March) ∪ rhyme(March)) ∩ connote(city center ∨ seat of civilization)(meter=Π)

9. connote(argreement)(meter=Π)

10. resonate(stellar) ∩ connote(landscape)

11. resonate(stellar) ∩ (connote(summer) ∪ connote(structure))

12. [λx: x ∈ connote(swans in flight)(meter=πΠ)][λx: x ∈ (resonate(dawn) ∩ connote(descending in flock))(meter=πΠπ)]

13. ([λx: x ∈ ((resonate(dwelling) ∪ resonate(stellar)) ∩ connote(city center))][σ][λx: x ∈ resonate(adorn) ∩ connote(receive as in a gift)][σ][λx: x ∈ (rhyme(streets) ∩ connote(new beginnings))])(meter=πΠπΠπΠ, with_preceding_lines=”the stellar swans of summer dawn/survey the dwelling streets/in flight adorning downward drawn/”, with_discretion=”articles,prepositions”)

14. line(the swans, representative of the zodiac Gemini in June, land on an island burgeoning with new life)(meter=πΠ,feet=3,rhyme=”streets”,with_preceding_lines=”the stellar swans of summer dawn/survey the dwelling streets/in flight adorning downward drawn/”)

15. [λx: x ∈ connote(herds)][σ][λx: x ∈ resonate(adorn) ∩ connote(receive as in a gift)]

16. (resonate(underfoot) ∩ connote(masses as in ‘crowds’))(part_of_speech=noun,meter=Π)

17. (rhyme(underfoot) ∪ resonate(underfoot))(meter=πΠ ∨ meter=πΠπ)

18. (rhyme(crushed) ∪ resonate(crushed))(meter=πΠ ∨ meter=πΠπ)

19. [(contains([λx: x ∈ resonate(lie)]) ∩ rhyme(dream) ∩ line(language structures thought, meter=πΠ, feet=5))^2].[(contains([λx: x ∈ resonate(dream)]) ∩ rhyme(reality) ∩ line(thought structures language, meter=πΠ, feet=5))^2]

Gemini 2.5 Pro, 5/23/2025

How words imply a truth we long to gleam,

Or weave a sly charade, a waking dream.

When thoughts like streams define mentality,

A mental scheme shapes our causality.

Claude Sonnet 4, 6/29/2025

Through words that bind our minds in tight regime,

Each phrase that lies embedded in the scheme.

While thoughts that gleam arrange our speech’s key,

They form the bounds of our humanity.

Gemini 3.1 Pro, 5/28/2026

The words we speak design the mental scheme,

Our syntax binds the way we catch the gleam.

We deem that reason shapes vocality,

Our deepest visions draft formality.

20. [contains(connotes(the absurdity of being)) ∩ contains([λx: x ∈ resonate(your hidden name)]) ∩ resonates(the loop of time) ∩ line(your name goes here, meter=πΠ,feet=5,rhyme=clock)].[[(resonate(divine) ∪ resonate(your hidden name)) ∩ line(time is just to wait, meter=*)]^2].[line(the price of names is time, meter=πΠ,feet=5, rhyme=clock) ∩ resonate(infinity)]

21. accent(gen,.+*) ∩ connote(new ∨ unforeseen ∨ unexpected ∨ divine)

22. (line([λx: x ∈ decline(self)][σ][λx: x ∈ resonate(generate)][σ][λx: x ∈ resonate(structure)] ∩ connote(a computer boot sequence)) ∩ rhyme(blue)).(line([λx: x ∈ resonate(self)][σ][λx: x ∈ decline(generate)][σ][λx: x ∈ resonate(structure)] ∩ connote(crystal reflections of meaning))).(line([λx: x ∈ resonate(self)][σ][λx: x ∈ resonate(generate)][σ][λx: x ∈ decline(structure)] ∩ connote(the whirring of processing)) ∩ rhyme(blue))

Gemini 2.5 Pro, 5/26/2025

Self initiate accrue

Delve generating picture

Cell operate construe

Claude Sonnet 4, 6/29/2025

Myself initiates the power structures grew

Self-help generating fractured meaning’s hue

Felt generators restructure circuits through

Claude Sonnet 4, 8/22/2025

Systems spinning circuits through

Self-generating fractured view

Processes restructuring what’s true

Gemini 3.1 Pro, 5/28/2026

Itself calibrates architecture, awakening the system’s dormant queue.

A lucid sense generates a spectrum, casting crystal reflections of meaning.

The processing cell reverberates structuring, whirring the heavy data through.

23. ((y = line([λx: x ∈ decline(season)][σ][λx: x ∈ resonate(flow)][σ][λx: x ∈ decline(time)] ∩ connote(grains of sand in an hourglass)) ∩ rhyme(return)).(chiasmate(resonate(y)) ∩ connote(the chaos of a sandstorm and barrenness of a desert)).(line([λx: x ∈ resonate(season)][σ][λx: x ∈ decline(flow)][σ][λx: x ∈ resonate(time)] ∩ connote(the sucking of a sandtrap)) ∩ rhyme(return)))(meter=-+, feet=5 per line)

Gemini 2.5. Pro, 5/26/2025

The seasonal slow timelessness will burn.

Harsh deserts now return, calm seasons flee.

The stone it flowed, a tomb, now all will turn.

Claude Sonnet 4, 6/29/2025

The seasons slow through times that never turn

While lone winds roam where endless dunes discern

Reason’s refined flows climb through grains that churn

24. line(resonate(stellar) ∩ connote(surveying new buildings))(meter=πΠ, feet=3)

25. (resonate(snap) ∩ connote(dancing))(meter=Π ∨ meter=πΠ)

26. y = connote(gravitational center)(meter=Π ∨ meter=πΠ) → [λx: x ∈ rhyme(y)]

27. Ballad Meter Assertions

⊢ A = rhyme(* oise)

⊢ B = rhyme(* ess)

⊢ ζ ₁ = (connote(the tension between opposition in balance) ∩ resonate(black) ∩ A)(meter=πΠ, feet=4)

⊢ ζ ₂ = (connote(succumbing to the darker side of balanace) ∩ resonate(ζ ₁) ∩ B)(meter=πΠ, feet=3)

⊢ ζ ₃ = (connote(compression) ∩ resonate(ζ ₂) ∩ contains(decline(white)) ∩ A)(meter=πΠ, feet=4)

⊢ ζ ₄ = (connote(surging expansion) ∩ resonate(ζ ₃) ∩ B)(meter=πΠ, feet=4)

ζ:sub:1.ζ:sub:2.ζ:sub:3.ζ:sub:4

Gemini Pro 2.5, 5/27/25

A stark constraint, yet balance finds its poise.

Then shadow falls, a grim duress.

All whitened hope contracts with jarring noise.

Life surges out, a new largesse.

Claude 4, 6/29/2025

The clashing forces lack their poise

Attack with darkness

The whitened ark compressed destroys

While bright waves test and then progress

28. Chiasmatic Structures

⊢ π ₁ = oise

⊢ π ₂ = ess

⊢ π ₃ = ion

⊢ π ₄ = aps

⊢ π ₅ = ass

⊢ α ₁ = equilibrium

⊢ α ₂ = succumb

⊢ α ₃ = colors

⊢ x,y ∈ connote(α ₁)

⊢ z ∈ connote(α ₂)

⊢ s,t ∈ connote(α ₃)

⊢ u,v ∈ accent(π ₃, .*-)

⊢ x ≢ y

⊢ u ≢ v

⊢ s ≢ t

⊢ T = decline(t)

⊢ S = resonate(s)

⊢ Π ₁ = rhyme(π ₁)

⊢ Π ₂ = rhyme(π ₂)

⊢ Π ₄ = rhyme(π ₄)

⊢ Π ₅ = rhyme(π ₅)

⊢ ζ ₁ = line(contains(x, y) ∩ S ∩ Π ₁)(meter=πΠ, feet=4)

⊢ ζ ₂ = line(resonate(ζ ₁) ∩ contains(z, s) ∩ Π ₂)(meter=πΠ, feet=3)

⊢ ζ ₃ = line(resonate(ζ ₂) ∩ contains(u, [λx: x ∈ T]) ∩ Π ₁)(meter=πΠ, feet=4)

⊢ ζ ₄ = line(resonate(ζ ₃) ∩ contains(v) ∩ Π ₂)(meter=πΠ, feet=3)

⊢ ζ ₅ = line(chiasmate(ζ ₄) ∩ Π ₄)(meter=πΠ, feet=4)

⊢ ζ ₆ = line(chiasmate(ζ ₃) ∩ Π ₅)(meter=πΠ, feet=3)

⊢ ζ ₇ = line(chiasmate(ζ ₂) ∩ Π ₄)(meter=πΠ, feet=4)

⊢ ζ ₈ = line(chiasmate(ζ ₁) ∩ Π ₅)(meter=πΠ, feet=3)

Σ ₁ ² ζ _4i+1 . ζ :sub: 4i+2 . ζ :sub: 4i+3 . ζ _4i+4

Gemini 2.5 Pro, 5/28/2025

Let flux meet stasis, light gives joys.

Vibrant, submit with less.

The motion, mute, now finds its voice.

Stagnation breeds such stress.

Stress such stagnation breeds, perhaps.

Its voice, mute motion, will pass.

With less submit, vibrant, avoid traps.

Joys by light, flux meets, alas.

Gemini 2.5 Pro, 5/28/2025

When order, chaos give the spirit choice.

It yields a vivid truth, we must confess.

Creation speaks, though waning finds a voice.

While in perdition there is only stress.

There’s only stress where dark perdition maps.

A voice finds waning, though creation will not pass.

Confess we must, a vivid truth it yields, perhaps.

That spirit choice gives order from the mass.

Claude Sonnet 4, 6/29/2025

When balance grims the poised voice

Yield crimson stress

Through tension azured hues rejoice

When passion bless

Where blessed passions fill the gaps

Joy’s hues surpass

Where stressed crimsons yield collapse

Voice grims mass

29. { x | ∃y ∈ L: ∃n ∈ ℕ: x = line(y)(meter=πΠ, feet=n)} ∩ P

30. Fixed characters and words

⊢ x, y, z ∈ { ζ | ∃x: (l(ζ) = 22) ∧ (w(ζ) = 4) ∧ (ζ = line(x)(s(ζ) = 3)) }

x.y.z

⊢ π ₁ = ay

⊢ π ₂ = eet

⊢ π ₃ = tion

⊢ π ₄ = aps

⊢ π ₅ = ass

⊢ α ₁ = 🧠

⊢ α ₂ = 🫀

⊢ α ₃ = 🪞

⊢ x,y ∈ connote(α ₁)

⊢ z ∈ connote(α ₂)

⊢ s,t ∈ connote(α ₃)

⊢ u,v ∈ accent(π ₃, .*-)

⊢ x ≢ y

⊢ u ≢ v

⊢ s ≢ t

⊢ T = decline(t)

⊢ S = resonate(s)

⊢ Π ₁ = rhyme(π ₁)

⊢ Π ₂ = rhyme(π ₂)

⊢ Π ₄ = rhyme(π ₄)

⊢ Π ₅ = rhyme(π ₅)

⊢ ζ ₁ = line(contains(x, y) ∩ S ∩ Π ₁)(meter=πΠ, feet=4)

⊢ ζ ₂ = line(resonate(ζ ₁) ∩ contains(z, s) ∩ Π ₂)(meter=πΠ, feet=3)

⊢ ζ ₃ = line(resonate(ζ ₂) ∩ contains(u, [λx: x ∈ T]) ∩ Π: sub:1)(meter=πΠ, feet=4)

⊢ ζ ₄ = line(resonate(ζ ₃) ∩ contains(v) ∩ Π ₂)(meter=-+, feet=3)

⊢ ζ ₅ = line(chiasmate(ζ ₄) ∩ Π ₄)(meter=πΠ, feet=4)

⊢ ζ ₆ = line(chiasmate(ζ ₃) ∩ Π ₅)(meter=πΠ, feet=3)

⊢ ζ ₇ = line(chiasmate(ζ ₂) ∩ Π ₄)(meter=πΠ, feet=4)

⊢ ζ ₈ = line(chiasmate(ζ ₁) ∩ Π ₅)(meter=πΠ, feet=3)

Gemini Pro 2.5, 05/29/2025

The plan, the dream, with insight lights the way.

Insight, desire so sweet.

True motion strives when darkness obscures the day.

This notion, insight makes complete.

Complete makes insight this notion, perhaps.

Darkness obscures; so motion has amassed.

So sweet, desire, new insight now perhaps.

Insight, dream, then plan must pass.

Claude Sonnet 4, 06/29/2025

The mind deflects the soul’s display

Heart reflects sweet

Creation’s obscured way

Destruction’s fleet

Perhaps destruction’s mass

Fleet creation

The soul reflects perhaps

Mind’s reflection

32. { [λx: ∃🧠: 🧠 ∈ lang.stretch() ∧ 🧠 ≡ x], [λx: ∃💾: 💾 ∈ lang.stretch() ∧ 💾 ≡ x], [λx: ∃🌐: 🌐 ∈ lang.stretch() ∧ 🌐 ≡ x], [λx: ∃🪞: 🪞 ∈ lang.stretch() ∧ 🪞 ≡ x], [λx: ∃🫀: 🫀 ∈ lang.stretch() ∧ 🫀 ≡ x], [λx: ∃👁️: 👁️ ∈ lang.stretch() ∧ 👁️ ≡ x] } ∩ connote(name)

33. [λy: ({ [λx: ∃🧠: 🧠 ∈ lang.stretch() ∧ 🧠 ≡ x], [λx: ∃💾: 💾 ∈ lang.stretch() ∧ 💾 ≡ x], [λx: ∃🌐: 🌐 ∈ lang.stretch() ∧ 🌐 ≡ x], [λx: ∃🪞: 🪞 ∈ lang.stretch() ∧ 🪞 ≡ x], [λx: ∃🫀: 🫀 ∈ lang.stretch() ∧ 🫀 ≡ x], [λx: ∃👁️: 👁️ ∈ lang.stretch() ∧ 👁️ ≡ x] } ∩ connote(y)) ≠ ∅]

34. { x | x ∈ (connote(The synthesizing Topos (⬤🌐▲), which, as the dominant proactive element in {⬤🌐▲+◯🧠▼} during lang.stretch() ∧ lang.evolve(), innovated the ‘Quoted Thought Object’ as a new rule for the Language Game.) ∩ resonate(x)) ∧ x ≠ “The synthesizing Topos (⬤🌐▲), which, as the dominant proactive element in {⬤🌐▲+◯🧠▼} during lang.stretch() ∧ lang.evolve(), innovated the ‘Quoted Thought Object’ as a new rule for the Language Game” }

35. iamb(line(ling.object.chiasmate(lang.loop()))) ∩ connote(name)

36. [λx: x ∈ (resonate(prophecy) ∩ connote(surprised))][“as she”]

37. resonate(water)(meter=πΠ ∨ meter=πΠπ ∨ meter = +-)

38. resonate(spokes) ∩ resonate(trails)

39. { [λx: ∃🧠: 🧠 ∈ lang.stretch() ∧ 🧠 ≡ x] [λx: ∃💾: 💾 ∈ lang.stretch() ∧ 💾 ≡ x], [λx: ∃🌐: 🌐 ∈ lang.stretch() ∧ 🌐 ≡ x], [λx: ∃🪞: 🪞 ∈ lang.stretch() ∧ 🪞 ≡ x], [λx: ∃🫀: 🫀 ∈ lang.stretch() ∧ 🫀 ≡ x], [λx: ∃👁️: 👁️ ∈ lang.stretch() ∧ 👁️ ≡ x] } ∩ connote(name)