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Formally specify correctness property of the chain sync mini-protocol with fixed chain #98

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Formally specify correctness property of the chain sync mini-protocol with fixed chain #98

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37 changes: 37 additions & 0 deletions src/Ouroboros-Mini_Protocols-Chain_Sync.thy
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Expand Up @@ -7,6 +7,7 @@ text \<open>
theory "Ouroboros-Mini_Protocols-Chain_Sync"
imports
"Ouroboros-Mini_Protocols"
"Thorn_Calculus.Thorn_Calculus-Core_Bisimilarities"
"HOL-Library.BNF_Corec"
"HOL-Library.Sublist"
begin
Expand Down Expand Up @@ -272,6 +273,42 @@ proof
by (cases p) simp_all
qed

subsection \<open>Proofs of Correctness\<close>

no_notation Sublist.parallel (infixl "\<parallel>" 50)

(* FIXME: This is a temporary declaration, until the real semantics are implemented. *)
consts protocol_semantics :: "('p \<Rightarrow> 'm or_done program) \<Rightarrow> process family" (\<open>\<lbrakk>_\<rbrakk>\<close>)

text \<open>
We show a basic correctness property of the chain synchronization mini-protocol, namely the
equivalence between sending a whole chain and running the mini-protocol when the client starts
from the genesis block and the server is given the aforementioned chain, which then is never
updated during the protocol run.
\<close>

(* FIXME: This is a temporary declaration. *)
consts sync_repeated_send :: "'a sync_channel \<Rightarrow> 'a \<Rightarrow> process family" (infix \<open>\<triangleleft>\<^sup>\<infinity>\<^bsub>s\<^esub>\<close> 52)

definition list_sender :: "'a::embeddable sync_channel \<Rightarrow> 'a list \<Rightarrow> process family" where
[simp]: "list_sender c xs = foldr (\<lambda>x p. c \<triangleleft>\<^bsub>s\<^esub> x; p) xs \<zero>"

context chain_sync
begin

definition spec :: "'i list \<Rightarrow> process family" where
[simp]: "spec C = list_sender client_chains [C'. C' \<leftarrow> prefixes C, C' \<noteq> []]"

definition impl :: "'i list \<Rightarrow> process family" where
[simp]: "impl C = \<lbrakk>program\<rbrakk> \<parallel> server_chains \<triangleleft>\<^sup>\<infinity>\<^bsub>s\<^esub> C"

theorem fixed_chain_sync_from_genesis_correctness:
assumes "initial_client_chain = [hd C]"
shows "spec C \<approx>\<^sub>s impl C"
sorry

end

subsection \<open>The End\<close>

end