I'm finding your Lean4 fascinating for it's balance between intuitive
enough to (almost) read and (known to be) formal enough to trust to be
testable/executeable.
Reminds me vaguely of the semester I learned BNF and kept finding myself
expressing (only to myself) observations about the world in that
idiom... later Prolog captured that part of me (for a while) .
On 11/24/25 3:07 pm, Marcus Daniels wrote:
The model captures the key ideas from the suggestion:
*Subject*
*Cheapest Posture*
*Why*
typicalPerson
playAlong (10)
Much cheaper than queryMechanism (80)
historian
correct (20)
Cheaper than stayQuiet (60)!
rolePlayer
playAlong (5)
"Authenticity" costs 200
historian at energy 15
none
Neither option affordable
The theorem more_energy_more_options proves that higher energy
strictly expands what's available.
Key features formalized:
* *Energy is primary* - selection is constrained by available energy
first
* *Cost profiles vary by subject* - the historian finds correction
cheaper than silence
* *Schema evolution requires surplus* - canEvolveSchema checks for
energy beyond the current posture cost
* *Mismatch tolerance scales* - mismatchTolerable requires a buffer
proportional to the mismatch
-- Subjective energy and posture selection
-- Energy is primary, matching/impedance is secondary
structure AsIfPosture where
objectiveCategory : String
embodiedInstance : String
subjectiveVocabulary : String
treatedAsObjective : Bool
acknowledgesEmbodiment : Bool
acknowledgesDiscursive : Bool
selfAware : Bool
structure PostureCost where
postureName : String
cost : Nat
deriving Repr
structure Subject where
name : String
baseEnergy : Nat
postureCosts : List PostureCost
deriving Repr
-- Different subjects have different cost profiles
def typicalPerson : Subject := {
name := "typical",
baseEnergy := 100,
postureCosts := [
{ postureName := "playAlong", cost := 10 },
{ postureName := "queryMechanism", cost := 80 }
]
}
def historian : Subject := {
name := "historian",
baseEnergy := 100,
postureCosts := [
{ postureName := "correct", cost := 20 },
{ postureName := "stayQuiet", cost := 60 } -- harder to stay quiet!
]
}
def rolePlayer : Subject := {
name := "no-authentic-self",
baseEnergy := 100,
postureCosts := [
{ postureName := "playAlong", cost := 5 },
{ postureName := "beAuthentic", cost := 200 } -- "authenticity"
expensive
]
}
-- Find minimum cost posture that's affordable
def cheapestAffordable (energy : Nat) (costs : List PostureCost) :
Option PostureCost :=
let affordable := costs.filter (λ pc => pc.cost ≤ energy)
affordable.foldl (λ acc pc =>
match acc with
| none => some pc
| some best => if pc.cost < best.cost then some pc else some best
) none
-- Schema evolution requires energy surplus
def canEvolveSchema (energy : Nat) (currentCost : Nat)
(evolutionThreshold : Nat) : Bool :=
energy > currentCost + evolutionThreshold
-- Mismatch tolerance depends on energy
def mismatchTolerable (energy : Nat) (mismatchCost : Nat) : Bool :=
energy > mismatchCost * 2
-- Theorem: higher energy means more options available
theorem more_energy_more_options (e1 e2 : Nat) (costs : List PostureCost)
(h : e1 < e2) :
(costs.filter (λpc => pc.cost ≤ e1)).length ≤
(costs.filter (λ pc => pc.cost ≤ e2)).length := by
induction costs with
| nil => simp
| cons head tail ih =>
simp [List.filter]
split <;> split <;> simp_all
· omega
· omega
-- Examples:
-- #eval cheapestAffordable 100 typicalPerson.postureCosts
-- => playAlong (cost 10)
-- #eval cheapestAffordable 100 historian.postureCosts
-- => correct (cost 20), not stayQuiet (cost 60)
-- #eval cheapestAffordable 15 historian.postureCosts
-- => none (neither affordable)
-- #eval canEvolveSchema 100 10 50 => true (surplus)
-- #eval canEvolveSchema 100 80 50 => false (no surplus)
.- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / ...
--- -- . / .- .-. . / ..- ... . ..-. ..- .-..
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