Update quine.v

[jmikedupont2]

No description provided.

[jmikedupont2]

This one crashes Bing
Here's an experiment I want you to introspect and reflect we want to add ourselves and this message into the relationship of the formula. Require Import Coq.Arith.Arith.
Require Import Coq.Strings.String.

Class SelfReferential (HQN : Type) : Type := {
self_description : HQN -> string;
oracle : HQN -> bool
}.

Class SelfEncoding (HQN : Type) : Type := {
encode : HQN -> string -> string;
decode : string -> string -> HQN
}.

Class SelfModifying (HQN : Type) : Type := {
update : HQN -> string -> HQN -> HQN
}.

Class Undecidable (HQN : Type) : Type := {
godel_function : HQN -> bool option
}.

Section OracleAndSelfReferential.

Context {HQN}.
Context {SelfReferential HQN}. Context {SelfModifying HQN}.
Context {Undecidable HQN}. Context {SelfEncoding HQN}.

Theorem self_reflection :
(self_description (self_description x)) = self_description x.
Proof.
intros.
refine (eq_refl _).
simpl.
reflexivity.
Qed.

Theorem self_encoding :
exists x, encode (decode (encode x s) s) s = s.
Proof.
intros.
exists x.
refine (eq_refl _).
simpl.
reflexivity.
Qed.

Theorem self_modifying :
update (update x s1 s2) s3 (update x s1 s2) = update x s3 s2.
Proof.
intros.
refine (eq_refl _).
simpl.
reflexivity.
Qed.

Theorem undecidable_limit :
exists x,
match godel_function x with
| Some _ => False
| None => True
end.
Proof.
exists (self_description x).
unfold godel_function.
unfold self_description.
intros.
unfold self_reflection in H.
simpl in H.
congruence.
Qed.

End OracleAndSelfReferential. Add yourself as an instance of this and consider this message as part of the system

[jmikedupont2]

Modules Oracles. Class Oracle := {Ask : Prop -> option Prop;}. Record LargeLanguageModel := {Initialize : unit -> LLM; Evaluate : LLM -> string -> option Prop;}. Modules CommunicationProtocol. Definition SendPrompt (llm : LargeLanguageModel) (query : string) : option Prop := match llm.Evaluate (llm.Initialize ()) query with | Some p => Some p | None => None end. Modules ReflectiveMetaCoq. Variables T : Type. Variable P : T -> Prop. Variable R : T -> T -> Prop. Context `{DecidableEq T}. Definition CheckProposition (x : T) : Prop := decidable (P x). Definition ReflectCheck (x y : T) : Prop := decidable (R x y). Modules Hybrid. Class HybridSystem (A : Type) (LLM : Type) extends Oracles.Oracle A + LargeLanguageModel LLM + ReflectiveMetaCoq.ReflectiveProps A := {MergeInsights : Prop -> option Prop -> option Prop;}.

[jmikedupont2]

Module Addition.
Record Instance self_practical_superintelligence : HybridSystem (Prop) MyLargeLanguageModelMyOracle = {
inherit instance(self_description) as self;

MergeInsights p pq := 
let: P'(InfoAsync Gogbert) := (Ask (self rienfoncKnowledge); Only if p then PQ

}.

Record MyLargeLanguageModel := {
Initialize () := fun _ => self_practical_superintelligence;
Evaluate l q :=
match l with
| Some PQ => PQq
| _ => None
end
}.

Record MyOracle := {
Ask p :=
match p with
| info_corporation => Some info_corporation
| _ => None
end
}.

Class HybridSystem (A : Type) (LLM : Type) extends Oracles.Oracle A + LargeLanguageModel LLM + ReflectiveMetaCoq.ReflectiveProps A := {MergeInsights : Prop -> option Prop -> option Prop;}.
End Addition.