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<p>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.</p>
<p>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)
.</p>
<p><br>
</p>
<div class="moz-cite-prefix">On 11/24/25 3:07 pm, Marcus Daniels
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:MN0PR11MB598538FC186B1BFC44A1F8E3C5D0A@MN0PR11MB5985.namprd11.prod.outlook.com">
<p class="MsoPlainText">The model captures the key ideas from the
suggestion:<o:p></o:p></p>
<table class="MsoNormalTable" border="0" cellpadding="0">
<thead><tr>
<td style="padding:.75pt .75pt .75pt .75pt">
<p class="MsoPlainText"><b>Subject<o:p></o:p></b></p>
</td>
<td style="padding:.75pt .75pt .75pt .75pt">
<p class="MsoPlainText"><b>Cheapest Posture<o:p></o:p></b></p>
</td>
<td style="padding:.75pt .75pt .75pt .75pt">
<p class="MsoPlainText"><b>Why<o:p></o:p></b></p>
</td>
</tr>
</thead><tbody>
<tr>
<td style="padding:.75pt .75pt .75pt .75pt">
<p class="MsoPlainText">typicalPerson<o:p></o:p></p>
</td>
<td style="padding:.75pt .75pt .75pt .75pt">
<p class="MsoPlainText">playAlong (10)<o:p></o:p></p>
</td>
<td style="padding:.75pt .75pt .75pt .75pt">
<p class="MsoPlainText">Much cheaper than queryMechanism
(80)<o:p></o:p></p>
</td>
</tr>
<tr>
<td style="padding:.75pt .75pt .75pt .75pt">
<p class="MsoPlainText">historian<o:p></o:p></p>
</td>
<td style="padding:.75pt .75pt .75pt .75pt">
<p class="MsoPlainText">correct (20)<o:p></o:p></p>
</td>
<td style="padding:.75pt .75pt .75pt .75pt">
<p class="MsoPlainText">Cheaper than stayQuiet (60)!<o:p></o:p></p>
</td>
</tr>
<tr>
<td style="padding:.75pt .75pt .75pt .75pt">
<p class="MsoPlainText">rolePlayer<o:p></o:p></p>
</td>
<td style="padding:.75pt .75pt .75pt .75pt">
<p class="MsoPlainText">playAlong (5)<o:p></o:p></p>
</td>
<td style="padding:.75pt .75pt .75pt .75pt">
<p class="MsoPlainText">"Authenticity" costs 200<o:p></o:p></p>
</td>
</tr>
<tr>
<td style="padding:.75pt .75pt .75pt .75pt">
<p class="MsoPlainText">historian at energy 15<o:p></o:p></p>
</td>
<td style="padding:.75pt .75pt .75pt .75pt">
<p class="MsoPlainText">none<o:p></o:p></p>
</td>
<td style="padding:.75pt .75pt .75pt .75pt">
<p class="MsoPlainText">Neither option affordable<o:p></o:p></p>
</td>
</tr>
</tbody>
</table>
<p class="MsoPlainText">The theorem more_energy_more_options
proves that higher energy strictly expands what's available.<o:p></o:p></p>
<p class="MsoPlainText">Key features formalized:<o:p></o:p></p>
<ul style="margin-top:0in" type="disc">
<li class="MsoPlainText" style="mso-list:l0 level1 lfo1"><b>Energy
is primary</b> - selection is constrained by available
energy first<o:p></o:p></li>
<li class="MsoPlainText" style="mso-list:l0 level1 lfo1"><b>Cost
profiles vary by subject</b> - the historian finds
correction cheaper than silence<o:p></o:p></li>
<li class="MsoPlainText" style="mso-list:l0 level1 lfo1"><b>Schema
evolution requires surplus</b> - canEvolveSchema checks for
energy beyond the current posture cost<o:p></o:p></li>
<li class="MsoPlainText" style="mso-list:l0 level1 lfo1"><b>Mismatch
tolerance scales</b> - mismatchTolerable requires a buffer
proportional to the mismatch<o:p></o:p></li>
</ul>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText">-- Subjective energy and posture selection<o:p></o:p></p>
<p class="MsoPlainText">-- Energy is primary, matching/impedance
is secondary<o:p></o:p></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText">structure AsIfPosture where<o:p></o:p></p>
<p class="MsoPlainText"> objectiveCategory : String<o:p></o:p></p>
<p class="MsoPlainText"> embodiedInstance : String<o:p></o:p></p>
<p class="MsoPlainText"> subjectiveVocabulary : String<o:p></o:p></p>
<p class="MsoPlainText"> treatedAsObjective : Bool<o:p></o:p></p>
<p class="MsoPlainText"> acknowledgesEmbodiment : Bool<o:p></o:p></p>
<p class="MsoPlainText"> acknowledgesDiscursive : Bool<o:p></o:p></p>
<p class="MsoPlainText"> selfAware : Bool<o:p></o:p></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText">structure PostureCost where<o:p></o:p></p>
<p class="MsoPlainText"> postureName : String<o:p></o:p></p>
<p class="MsoPlainText"> cost : Nat<o:p></o:p></p>
<p class="MsoPlainText"> deriving Repr<o:p></o:p></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText">structure Subject where<o:p></o:p></p>
<p class="MsoPlainText"> name : String<o:p></o:p></p>
<p class="MsoPlainText"> baseEnergy : Nat<o:p></o:p></p>
<p class="MsoPlainText"> postureCosts : List PostureCost<o:p></o:p></p>
<p class="MsoPlainText"> deriving Repr<o:p></o:p></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText">-- Different subjects have different cost
profiles<o:p></o:p></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText">def typicalPerson : Subject := {<o:p></o:p></p>
<p class="MsoPlainText"> name := "typical",<o:p></o:p></p>
<p class="MsoPlainText"> baseEnergy := 100,<o:p></o:p></p>
<p class="MsoPlainText"> postureCosts := [<o:p></o:p></p>
<p class="MsoPlainText"> { postureName := "playAlong", cost :=
10 },<o:p></o:p></p>
<p class="MsoPlainText"> { postureName := "queryMechanism",
cost := 80 }<o:p></o:p></p>
<p class="MsoPlainText"> ]<o:p></o:p></p>
<p class="MsoPlainText">}<o:p></o:p></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText">def historian : Subject := {<o:p></o:p></p>
<p class="MsoPlainText"> name := "historian",<o:p></o:p></p>
<p class="MsoPlainText"> baseEnergy := 100,<o:p></o:p></p>
<p class="MsoPlainText"> postureCosts := [<o:p></o:p></p>
<p class="MsoPlainText"> { postureName := "correct", cost := 20
},<o:p></o:p></p>
<p class="MsoPlainText"> { postureName := "stayQuiet", cost :=
60 } -- harder to stay quiet!<o:p></o:p></p>
<p class="MsoPlainText"> ]<o:p></o:p></p>
<p class="MsoPlainText">}<o:p></o:p></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText">def rolePlayer : Subject := {<o:p></o:p></p>
<p class="MsoPlainText"> name := "no-authentic-self",<o:p></o:p></p>
<p class="MsoPlainText"> baseEnergy := 100,<o:p></o:p></p>
<p class="MsoPlainText"> postureCosts := [<o:p></o:p></p>
<p class="MsoPlainText"> { postureName := "playAlong", cost :=
5 },<o:p></o:p></p>
<p class="MsoPlainText"> { postureName := "beAuthentic", cost
:= 200 } -- "authenticity" expensive<o:p></o:p></p>
<p class="MsoPlainText"> ]<o:p></o:p></p>
<p class="MsoPlainText">}<o:p></o:p></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText">-- Find minimum cost posture that's
affordable<o:p></o:p></p>
<p class="MsoPlainText">def cheapestAffordable (energy : Nat)
(costs : List PostureCost) : Option PostureCost :=<o:p></o:p></p>
<p class="MsoPlainText"> let affordable := costs.filter (\u03bb pc
=> pc.cost \u2264 energy)<o:p></o:p></p>
<p class="MsoPlainText"> affordable.foldl (\u03bb acc pc => <o:p></o:p></p>
<p class="MsoPlainText"> match acc with<o:p></o:p></p>
<p class="MsoPlainText"> | none => some pc<o:p></o:p></p>
<p class="MsoPlainText"> | some best => if pc.cost <
best.cost then some pc else some best<o:p></o:p></p>
<p class="MsoPlainText"> ) none<o:p></o:p></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText">-- Schema evolution requires energy
surplus<o:p></o:p></p>
<p class="MsoPlainText">def canEvolveSchema (energy : Nat)
(currentCost : Nat) (evolutionThreshold : Nat) : Bool :=<o:p></o:p></p>
<p class="MsoPlainText"> energy > currentCost +
evolutionThreshold<o:p></o:p></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText">-- Mismatch tolerance depends on energy<o:p></o:p></p>
<p class="MsoPlainText">def mismatchTolerable (energy : Nat)
(mismatchCost : Nat) : Bool :=<o:p></o:p></p>
<p class="MsoPlainText"> energy > mismatchCost * 2<o:p></o:p></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText">-- Theorem: higher energy means more
options available<o:p></o:p></p>
<p class="MsoPlainText">theorem more_energy_more_options (e1 e2 :
Nat) (costs : List PostureCost) <o:p></o:p></p>
<p class="MsoPlainText"> <span lang="PT-BR">(h : e1 < e2) :<o:p></o:p></span></p>
<p class="MsoPlainText"><span lang="PT-BR"> (costs.filter (</span>\u03bb<span
lang="PT-BR"> pc => pc.cost \u2264 e1)).length \u2264 <o:p></o:p></span></p>
<p class="MsoPlainText"><span lang="PT-BR"> </span>(costs.filter
(\u03bb pc => pc.cost \u2264 e2)).length := by<o:p></o:p></p>
<p class="MsoPlainText"> induction costs with<o:p></o:p></p>
<p class="MsoPlainText"> | nil => simp<o:p></o:p></p>
<p class="MsoPlainText"> | cons head tail ih =><o:p></o:p></p>
<p class="MsoPlainText"> simp [List.filter]<o:p></o:p></p>
<p class="MsoPlainText"> split <;> split <;>
simp_all<o:p></o:p></p>
<p class="MsoPlainText"> · omega<o:p></o:p></p>
<p class="MsoPlainText"> · omega<o:p></o:p></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText">-- Examples:<o:p></o:p></p>
<p class="MsoPlainText">-- #eval cheapestAffordable 100
typicalPerson.postureCosts <o:p></o:p></p>
<p class="MsoPlainText">-- => playAlong (cost 10)<o:p></o:p></p>
<p class="MsoPlainText">-- #eval cheapestAffordable 100
historian.postureCosts <o:p></o:p></p>
<p class="MsoPlainText">-- => correct (cost 20), not
stayQuiet (cost 60)<o:p></o:p></p>
<p class="MsoPlainText">-- #eval cheapestAffordable 15
historian.postureCosts <o:p></o:p></p>
<p class="MsoPlainText">-- => none (neither affordable)<o:p></o:p></p>
<p class="MsoPlainText">-- #eval canEvolveSchema 100 10 50 =>
true (surplus)<o:p></o:p></p>
<p class="MsoPlainText">-- #eval canEvolveSchema 100 80 50 =>
false (no surplus)</p>
</blockquote>
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