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shelley-ledger.tex
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shelley-ledger.tex
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\documentclass[11pt,a4paper,dvipsnames,twosided]{article}
\usepackage[deliverable]{IOHKCoverPage}
% data for Deliverable header -- added by KH from an EU H2020 project template
\DeliverableNumber{SL-D5}
\DeliverableTitle{A Formal Specification of the Cardano Ledger}{Formal Cardano Ledger Spec.}
\DeliverableResponsible{Formal Methods Team}
\EditorName{Jared Corduan, \IOHK}
\Authors{Jared Corduan \quad \texttt{<[email protected]>}
\\[1em]
Polina Vinogradova \quad \texttt{<[email protected]>}
\\[1em]
Matthias G\"udemann \quad \texttt{<[email protected]>}
}
\DueDate{15$^{\textrm{th}}$ October 2019}
\SubmissionDate{8th October 2019}{2019/10/08}
\LeaderName{Philipp Kant, \IOHK}
\InstitutionAddress{\IOHK}
\Version{1.0}
\Project{Shelley Ledger}
\DisseminationPU
\usepackage[margin=2.5cm]{geometry}
\usepackage{lscape}
\usepackage{iohk}
\usepackage{microtype}
\usepackage{mathpazo} % nice fonts
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{latexsym}
\usepackage{mathtools}
\usepackage{stmaryrd}
\usepackage{extarrows}
\usepackage{slashed}
\usepackage[unicode=true,pdftex,pdfa,colorlinks=true]{hyperref}
\usepackage{xcolor}
\usepackage[capitalise,noabbrev,nameinlink]{cleveref}
\usepackage{float}
\floatstyle{boxed}
\restylefloat{figure}
\usepackage{tikz}
\usepackage{booktabs}
\usepackage{enumerate}
\usepackage{listings}
%%
%% Package `semantic` can be used for writing inference rules.
%%
\usepackage{semantic}
%% Setup for the semantic package
\setpremisesspace{20pt}
\usepackage{tocloft}
\addtolength{\cftsubsecnumwidth}{5pt}
%%
%% Types
%%
\newcommand{\Nothing}{\ensuremath{\Diamond}}
\newcommand{\N}{\ensuremath{\mathbb{N}}}
\newcommand{\Bool}{\type{Bool}}
\newcommand{\Npos}{\ensuremath{\mathbb{N}^{>0}}}
\newcommand{\Z}{\ensuremath{\mathbb{Z}}}
\newcommand{\Q}{\ensuremath{\mathbb{Q}}}
\newcommand{\R}{\ensuremath{\mathbb{R}}}
\newcommand{\Rnn}{\ensuremath{\mathbb{R}^{\geq 0}}}
\newcommand{\Tx}{\type{Tx}}
\newcommand{\TxBody}{\type{TxBody}}
\newcommand{\TxWitness}{\type{TxWitness}}
\newcommand{\Ix}{\type{Ix}}
\newcommand{\TxId}{\type{TxId}}
\newcommand{\Addr}{\type{Addr}}
\newcommand{\UTxO}{\type{UTxO}}
\newcommand{\Wdrl}{\type{Wdrl}}
\newcommand{\Coin}{\type{Coin}}
\newcommand{\PParams}{\type{PParams}}
\newcommand{\PParamsUpdate}{\type{PParamsUpdate}}
\newcommand{\ProposedPPUpdates}{\type{ProposedPPUpdates}}
\newcommand{\Slot}{\type{Slot}}
\newcommand{\StabilityWindow}{\ensuremath{\mathsf{StabilityWindow}}}
\newcommand{\RandomnessStabilisationWindow}{\ensuremath{\mathsf{RandomnessStabilisationWindow}}}
\newcommand{\SlotsPerEpoch}{\mathsf{SlotsPerEpoch}}
\newcommand{\SlotsPerKESPeriod}{\mathsf{SlotsPerKESPeriod}}
\newcommand{\MaxMajorPV}{\mathsf{MaxMajorPV}}
\newcommand{\ActiveSlotCoeff}{\mathsf{ActiveSlotCoeff}}
\newcommand{\Network}{\mathsf{Network}}
\newcommand{\NetworkId}{\mathsf{NetworkId}}
\newcommand{\BlockNo}{\type{BlockNo}}
\newcommand{\MaxKESEvo}{\ensuremath{\mathsf{MaxKESEvo}}}
\newcommand{\Quorum}{\ensuremath{\mathsf{Quorum}}}
\newcommand{\MaxLovelaceSupply}{\ensuremath{\mathsf{MaxLovelaceSupply}}}
\newcommand{\Duration}{\type{Duration}}
\newcommand{\StakePools}{\type{StakePools}}
\newcommand{\Seed}{\type{Seed}}
\newcommand{\seedOp}{\star}
\newcommand{\Ppm}{\type{Ppm}}
\newcommand{\ProtVer}{\ensuremath{\type{ProtVer}}}
\newcommand{\Metadatum}{\ensuremath{\type{Metadatum}}}
\newcommand{\Metadata}{\ensuremath{\type{Metadata}}}
\newcommand{\MetadataHash}{\ensuremath{\type{MetadataHash}}}
\newcommand{\Update}{\type{Update}}
\newcommand{\GenesisDelegation}{\type{GenesisDelegation}}
\newcommand{\FutGenesisDelegation}{\type{FutGenesisDelegation}}
\newcommand{\DCert}{\type{DCert}}
\newcommand{\DCertRegKey}{\type{DCert_{regkey}}}
\newcommand{\DCertDeRegKey}{\type{DCert_{deregkey}}}
\newcommand{\DCertDeleg}{\type{DCert_{delegate}}}
\newcommand{\DCertRegPool}{\type{DCert_{regpool}}}
\newcommand{\DCertRetirePool}{\type{DCert_{retirepool}}}
\newcommand{\DCertGen}{\type{DCert_{genesis}}}
\newcommand{\DCertMir}{\type{DCert_{mir}}}
\newcommand{\PoolParam}{\type{PoolParam}}
\newcommand{\PoolMD}{\type{PoolMD}}
\newcommand{\MIRPot}{\type{MIRPot}}
\newcommand{\InstantaneousRewards}{\type{InstantaneousRewards}}
\newcommand{\ReservesMIR}{\type{ReservesMIR}}
\newcommand{\TreasuryMIR}{\type{TreasuryMIR}}
\newcommand{\URL}{\type{Url}}
\newcommand{\UTxOState}{\ensuremath{\type{UTxOState}}}
\newcommand{\ledgerState}{\ensuremath{\type{ledgerState}}}
\newcommand{\AddrRWD}{\type{Addr_{rwd}}}
\newcommand{\AddrB}{\type{Addr_{base}}}
\newcommand{\AddrP}{\type{Addr_{ptr}}}
\newcommand{\AddrE}{\type{Addr_{enterprise}}}
\newcommand{\AddrBS}{\type{Addr_{bootstrap}}}
\newcommand{\Ptr}{\type{Ptr}}
\newcommand{\DState}{\type{DState}}
\newcommand{\DWEnv}{\type{DWEnv}}
\newcommand{\DPSEnv}{\type{DPSEnv}}
\newcommand{\DPEnv}{\type{DPEnv}}
\newcommand{\DEnv}{\type{DEnv}}
\newcommand{\PEnv}{\type{PEnv}}
\newcommand{\DPState}{\type{DPState}}
\newcommand{\PState}{\type{PState}}
\newcommand{\DCertBody}{\type{DCertBody}}
\newcommand{\TData}{\type{TData}}
\newcommand{\DPoolReap}{\ensuremath{\type{poolreap}}}
\newcommand{\UPIState}{\type{UPIState}}
\newcommand{\UpdatePayload}{\type{UpdatePayload}}
% multi-signature
\newcommand{\StakeCredential}{\type{Credential}_{stake}}
\newcommand{\txwitsVKey}[1]{\fun{txwitsVKey}~\var{#1}}
\newcommand{\txwitsScript}[1]{\fun{txwitsScript}~\var{#1}}
\newcommand{\AddrVKey}{\type{Addr^{vkey}}}
\newcommand{\AddrRWDVKey}{\type{Addr_{rwd}^{vkey}}}
\newcommand{\AddrRWDScr}{\type{Addr_{rwd}^{script}}}
\newcommand{\AddrVKeyB}{\type{Addr^{vkey}_{base}}}
\newcommand{\AddrVKeyP}{\type{Addr^{vkey}_{ptr}}}
\newcommand{\AddrVKeyE}{\type{Addr^{vkey}_{enterprise}}}
\newcommand{\AddrVKeyBS}{\type{Addr^{vkey}_{bootstrap}}}
\newcommand{\AddrScr}{\type{Addr^{script}}}
\newcommand{\AddrScrBase}{\type{Addr_{base}^{script}}}
\newcommand{\AddrScrEnterprise}{\type{Addr_{enterprise}^{script}}}
\newcommand{\AddrScrPtr}{\type{Addr_{ptr}^{script}}}
\newcommand{\HashScr}{\type{ScriptHash}}
\newcommand{\Script}{\type{Script}}
\newcommand{\MSig}{\type{MSig}}
\newcommand{\Credential}{\type{Credential}}
%% Adding witnesses
\newcommand{\TxIn}{\type{TxIn}}
\newcommand{\TxOut}{\type{TxOut}}
\newcommand{\VKey}{\type{VKey}}
\newcommand{\VKeyEv}{\type{VKey_{ev}}}
\newcommand{\VKeyGen}{\type{VKey_G}}
\newcommand{\SKey}{\type{SKey}}
\newcommand{\SKeyEv}{\type{SKey_{ev}}}
\newcommand{\KeyHash}{\type{KeyHash}}
\newcommand{\KeyHashGen}{\type{KeyHash_G}}
\newcommand{\KeyPair}{\type{KeyPair}}
\newcommand{\KeyPairEv}{\type{KeyPair_{ev}}}
\newcommand{\Sig}{\type{Sig}}
\newcommand{\Data}{\type{Data}}
\newcommand{\Ser}{\type{Ser}}
%% Adding delegation
\newcommand{\Epoch}{\type{Epoch}}
\newcommand{\KESPeriod}{\type{KESPeriod}}
%% Blockchain
\newcommand{\Acnt}{\type{Acnt}}
\newcommand{\Gkeys}{\var{G_{keys}}}
\newcommand{\Block}{\type{Block}}
\newcommand{\SlotId}{\type{SlotId}}
\newcommand{\PPUpdateState}{\type{PPUpdateState}}
\newcommand{\PPUpdateEnv}{\type{PPUpdateEnv}}
\newcommand{\UTxOEnv}{\type{UTxOEnv}}
\newcommand{\CEEnv}{\type{CEEnv}}
\newcommand{\CEState}{\type{CEState}}
\newcommand{\BDEnv}{\type{BDEnv}}
\newcommand{\BDState}{\type{BDState}}
\newcommand{\LEnv}{\type{LEnv}}
\newcommand{\LState}{\type{LState}}
\newcommand{\Proof}{\type{Proof}}
\newcommand{\Seedl}{\mathsf{Seed}_\ell}
\newcommand{\Seede}{\mathsf{Seed}_\eta}
\newcommand{\slotToSeed}[1]{\fun{slotToSeed}~ \var{#1}}
\newcommand{\prevHashToNonce}[1]{\fun{prevHashToNonce}~ \var{#1}}
\newcommand{\isOverlaySlot}[3]{\fun{isOverlaySlot}~\var{#1}~\var{#2}~\var{#3}}
\newcommand{\classifyOverlaySlot}[5]{\fun{classifyOverlaySlot}~\var{#1}~\var{#2}~\var{#3}~\var{#4}~\var{#5}}
\newcommand{\T}{\type{T}}
\newcommand{\vrf}[3]{\fun{vrf}_{#1} ~ #2 ~ #3}
\newcommand{\verifyVrf}[4]{\fun{verifyVrf}_{#1} ~ #2 ~ #3 ~#4}
\newcommand{\HashHeader}{\type{HashHeader}}
\newcommand{\HashBBody}{\type{HashBBody}}
\newcommand{\bhHash}[1]{\fun{bhHash}~ \var{#1}}
\newcommand{\bHeaderSize}[1]{\fun{bHeaderSize}~ \var{#1}}
\newcommand{\bSize}[1]{\fun{bSize}~ \var{#1}}
\newcommand{\bBodySize}[1]{\fun{bBodySize}~ \var{#1}}
\newcommand{\OCert}{\type{OCert}}
\newcommand{\BHeader}{\type{BHeader}}
\newcommand{\BHBody}{\type{BHBody}}
\newcommand{\bheader}[1]{\fun{bheader}~\var{#1}}
\newcommand{\hsig}[1]{\fun{hsig}~\var{#1}}
\newcommand{\bprev}[1]{\fun{bprev}~\var{#1}}
\newcommand{\bhash}[1]{\fun{bhash}~\var{#1}}
\newcommand{\bvkcold}[1]{\fun{bvkcold}~\var{#1}}
\newcommand{\bseedl}[1]{\fun{bseed}_{\ell}~\var{#1}}
\newcommand{\bprfn}[1]{\fun{bprf}_{n}~\var{#1}}
\newcommand{\bseedn}[1]{\fun{bseed}_{n}~\var{#1}}
\newcommand{\bprfl}[1]{\fun{bprf}_{\ell}~\var{#1}}
\newcommand{\bocert}[1]{\fun{bocert}~\var{#1}}
\newcommand{\bnonce}[1]{\fun{bnonce}~\var{#1}}
\newcommand{\bleader}[1]{\fun{bleader}~\var{#1}}
\newcommand{\hBbsize}[1]{\fun{hBbsize}~\var{#1}}
\newcommand{\bbodyhash}[1]{\fun{bbodyhash}~\var{#1}}
\newcommand{\overlaySchedule}[3]{\fun{overlaySchedule}~\var{#1}~\var{#2}~\var{#3}}
\newcommand{\OCertEnv}{\type{OCertEnv}}
\newcommand{\PrtclState}{\type{PrtclState}}
\newcommand{\PrtclEnv}{\type{PrtclEnv}}
\newcommand{\OverlayEnv}{\type{OverlayEnv}}
\newcommand{\VRFState}{\type{VRFState}}
\newcommand{\TickNonceState}{\type{TickNonceState}}
\newcommand{\TickNonceEnv}{\type{TickNonceEnv}}
\newcommand{\NewEpochState}{\type{NewEpochState}}
\newcommand{\UpdateNonceState}{\type{UpdateNonceState}}
\newcommand{\UpdateNonceEnv}{\type{UpdateNonceEnv}}
\newcommand{\PoolDistr}{\type{PoolDistr}}
\newcommand{\BBodyEnv}{\type{BBodyEnv}}
\newcommand{\BBodyState}{\type{BBodyState}}
\newcommand{\RUpdEnv}{\type{RUpdEnv}}
\newcommand{\ChainEnv}{\type{ChainEnv}}
\newcommand{\ChainState}{\type{ChainState}}
\newcommand{\ChainSig}{\type{ChainSig}}
\newcommand{\LastAppliedBlock}{\type{LastAppliedBlock}}
\newcommand{\lastAppliedHash}[1]{\fun{lastAppliedHash}~\var{#1}}
%%
%% Functions
%%
\newcommand{\txins}[1]{\fun{txins}~ \var{#1}}
\newcommand{\txouts}[1]{\fun{txouts}~ \var{#1}}
\newcommand{\txcerts}[1]{\fun{txcerts}~ \var{#1}}
\newcommand{\txid}[1]{\fun{txid}~ \var{#1}}
\newcommand{\outs}[1]{\fun{outs}~ \var{#1}}
\newcommand{\values}[1]{\fun{values}~ #1}
\newcommand{\ubalance}[1]{\fun{ubalance}~ \var{#1}}
\newcommand{\txttl}[1]{\fun{txttl}~ \var{#1}}
\newcommand{\firstSlot}[1]{\fun{firstSlot}~ \var{#1}}
\newcommand{\totalDeposits}[3]{\fun{totalDeposits}~ \var{#1} ~ \var{#2} ~ \var{#3}}
\newcommand{\keyRefund}[6]{\fun{keyRefund}~ {#1}~{#2}~{#3}~\var{#4}~\var{#5}~\var{#6}}
\newcommand{\refund}[4]{\fun{refund}~ \var{#1}~ \var{#2}~ {#3}~ {#4}}
\newcommand{\keyRefunds}[2]{\fun{keyRefunds}~ \var{#1}~ \var{#2}}
\newcommand{\consumed}[2]{\fun{consumed}~ \var{#1}~ \var{#2}}
\newcommand{\produced}[2]{\fun{produced}~ \var{#1}~ \var{#2}}
\newcommand{\applyFun}[2]{\fun{#1}~\var{#2}}
\newcommand{\RegKey}[1]{\textsc{RegKey}(#1)}
\newcommand{\DeregKey}[1]{\textsc{DeregKey}(#1)}
\newcommand{\Delegate}[1]{\textsc{Delegate}(#1)}
\newcommand{\RegPool}[1]{\textsc{RegPool}(#1)}
\newcommand{\RetirePool}[1]{\textsc{RetirePool}(#1)}
\newcommand{\cwitness}[1]{\fun{cwitness}~ \var{#1}}
\newcommand{\dpool}[1]{\fun{dpool}~ \var{#1}}
\newcommand{\poolParam}[1]{\fun{poolParam}~ \var{#1}}
\newcommand{\retire}[1]{\fun{retire}~ \var{#1}}
\newcommand{\addrRw}[1]{\fun{addr_{rwd}}~ \var{#1}}
\newcommand{\epoch}[1]{\fun{epoch}~\var{#1}}
\newcommand{\kesPeriod}[1]{\fun{kesPeriod}~\var{#1}}
%% UTxO witnesses
\newcommand{\inputs}[1]{\fun{inputs}~ \var{#1}}
\newcommand{\txwits}[1]{\fun{txwits}~ \var{#1}}
\newcommand{\verify}[3]{\fun{verify} ~ #1 ~ #2 ~ #3}
\newcommand{\sign}[2]{\fun{sign} ~ #1 ~ #2}
\newcommand{\verifyEv}[4]{\fun{verify_{ev}} ~ #1 ~ #2 ~ #3 ~ #4}
\newcommand{\signEv}[3]{\fun{sign_{ev}} ~ #1 ~ #2 ~ #3}
\newcommand{\serialised}[1]{\llbracket \var{#1} \rrbracket}
\newcommand{\hashKey}[1]{\fun{hashKey}~ \var{#1}}
\newcommand{\txbody}[1]{\fun{txbody}~ \var{#1}}
\newcommand{\txfee}[1]{\fun{txfee}~ \var{#1}}
\newcommand{\txwdrls}[1]{\fun{txwdrls}~ \var{#1}}
\newcommand{\minfee}[2]{\fun{minfee}~ \var{#1}~ \var{#2}}
\newcommand{\slotminus}[2]{\var{#1}~-_{s}~\var{#2}}
\DeclarePairedDelimiter\floor{\lfloor}{\rfloor}
% wildcard parameter
\newcommand{\wcard}[0]{\rule[-.5mm]{2mm}{.2mm}}
%% Adding ledgers...
\newcommand{\utxo}[1]{\fun{utxo}~ #1}
%% Delegation
\newcommand{\delegatesName}{\fun{delegates}}
\newcommand{\delegates}[3]{\delegatesName~#1~#2~#3}
\newcommand{\dwho}[1]{\fun{dwho}~\var{#1}}
\newcommand{\depoch}[1]{\fun{depoch}~\var{#1}}
\newcommand{\dval}{\ensuremath{d_{\mathsf{val}}}}
%% Delegation witnesses
\newcommand{\dbody}[1]{\fun{dbody}~\var{#1}}
\newcommand{\dwit}[1]{\fun{dwit}~\var{#1}}
%% Blockchain
\newcommand{\bwit}[1]{\fun{bwit}~\var{#1}}
\newcommand{\bslot}[1]{\fun{bslot}~\var{#1}}
\newcommand{\bblockno}[1]{\fun{bblockno}~\var{#1}}
\newcommand{\bbody}[1]{\fun{bbody}~\var{#1}}
\newcommand{\bhbody}[1]{\fun{bhbody}~\var{#1}}
\newcommand{\bdlgs}[1]{\fun{bdlgs}~\var{#1}}
%% ledgerstate constants
\newcommand{\genesisId}{\ensuremath{Genesis_{Id}}}
\newcommand{\genesisTxOut}{\ensuremath{Genesis_{Out}}}
\newcommand{\genesisUTxO}{\ensuremath{Genesis_{UTxO}}}
\newcommand{\genesisUTxOState}{(\genesisUTxO,\wcard,\wcard,\wcard)}
\newcommand{\emax}{\ensuremath{\mathsf{E_{max}}}}
\newcommand{\unitInterval}{\ensuremath{[0,~1]}}
\newcommand{\unitIntervalNonNull}{\ensuremath{(0,~1]}}
\newcommand{\nonnegReals}{\ensuremath{[0,~\infty)}}
\newcommand{\posReals}{\ensuremath{(0,~\infty)}}
\theoremstyle{definition}
\newtheorem{definition}{Definition}[section]
\newtheorem{lemma}[definition]{Lemma}
\newtheorem{theorem}[definition]{Theorem}
\newtheorem{property}{Property}[section]
\newcommand{\leteq}{\ensuremath{\mathrel{\mathop:}=}}
\begin{document}
\input{frontmatter.tex}
\include{intro}
\include{notation}
\include{crypto-primitives}
\include{address}
\include{protocol-parameters}
\include{transactions}
\include{update}
\include{utxo}
\include{delegation}
\include{ledger}
\include{epoch}
\include{chain}
\include{software-updates}
\include{sts-overview}
\include{properties}
\include{hand_proofs}
\include{leader-value}
\include{errata}
\clearpage
\addcontentsline{toc}{section}{References}
\bibliographystyle{habbrv}
\bibliography{references}
\clearpage
\begin{appendix}
\input{crypto-details}
\input{address-binary}
\input{bootstrap-witnesses}
\input{cddl}
\input{txsize}
\input{proofs}
\end{appendix}
\end{document}