[FRIAM] mental imagery

[Steve Smith]

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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