{-# OPTIONS --safe #-}

open import Ledger.Conway.Specification.Gov.Base
open import Ledger.Conway.Specification.Transaction using (TransactionStructure)
open import Ledger.Core.Specification.ProtocolVersion

module Ledger.Conway.Specification.Gov.Properties.Computational
  (txs : _) (open TransactionStructure txs using (govStructure))
  (open GovStructure govStructure hiding (epoch)) where

open import Ledger.Prelude hiding (Any; any?)

open import Axiom.Set.Properties

open import Ledger.Conway.Specification.Enact govStructure
open import Ledger.Conway.Specification.Gov govStructure
open import Ledger.Conway.Specification.Gov.Actions govStructure hiding (yes; no)
open import Ledger.Conway.Specification.Ratify govStructure

import Data.List.Membership.Propositional as P
open import Data.List.Membership.Propositional.Properties
open import Data.List.Relation.Unary.All using (all?; All)
open import Data.List.Relation.Unary.Any hiding (map)
open import Data.List.Relation.Unary.Unique.Propositional
open import Data.Maybe.Properties
open import Relation.Binary using (IsEquivalence)

open import Tactic.Defaults
open import stdlib-meta.Tactic.GenError

open Equivalence
open GovActionState
open Inverse

lookupActionId : (pparams : PParams) (role : GovRole) (aid : GovActionID) (epoch : Epoch) (s : GovState) 
                 Dec (Any  (aid' , ast)  aid  aid' × canVote pparams (action ast) role × ¬ (expired epoch ast)) s)
lookupActionId pparams role aid epoch =
  let instance _ = λ {e ga}   (expired? e ga)
   in any? λ _  ¿ _ ¿

private
  isUpdateCommittee : (a : GovAction)  Dec (∃[ new ] ∃[ rem ] ∃[ q ] a  $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#748}{\htmlId{1640}{\htmlClass{InductiveConstructor}{\text{UpdateCommittee}}}}\, \\ \,\htmlId{1658}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Specification.Gov.Properties.Computational.html#1612}{\htmlId{1659}{\htmlClass{Bound}{\text{new}}}}\, , \,\href{Ledger.Conway.Specification.Gov.Properties.Computational.html#1621}{\htmlId{1665}{\htmlClass{Bound}{\text{rem}}}}\, , \,\href{Ledger.Conway.Specification.Gov.Properties.Computational.html#1630}{\htmlId{1671}{\htmlClass{Bound}{\text{q}}}}\,\,\htmlId{1672}{\htmlClass{Symbol}{\text{)}}}\, \end{pmatrix}$)
  isUpdateCommittee $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#710}{\htmlId{1701}{\htmlClass{InductiveConstructor}{\text{NoConfidence}}}}\,       \\ \,\htmlId{1722}{\htmlClass{Symbol}{\text{\_}}}\,                \end{pmatrix}$ = no λ()
  isUpdateCommittee $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#748}{\htmlId{1774}{\htmlClass{InductiveConstructor}{\text{UpdateCommittee}}}}\,    \\ \,\htmlId{1795}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Specification.Gov.Properties.Computational.html#1796}{\htmlId{1796}{\htmlClass{Bound}{\text{new}}}}\, , \,\href{Ledger.Conway.Specification.Gov.Properties.Computational.html#1802}{\htmlId{1802}{\htmlClass{Bound}{\text{rem}}}}\, , \,\href{Ledger.Conway.Specification.Gov.Properties.Computational.html#1808}{\htmlId{1808}{\htmlClass{Bound}{\text{q}}}}\,\,\htmlId{1809}{\htmlClass{Symbol}{\text{)}}}\,  \end{pmatrix}$ = yes (new , rem , q , refl)
  isUpdateCommittee $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#786}{\htmlId{1867}{\htmlClass{InductiveConstructor}{\text{NewConstitution}}}}\,    \\ \,\htmlId{1888}{\htmlClass{Symbol}{\text{\_}}}\,                \end{pmatrix}$ = no λ()
  isUpdateCommittee $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#824}{\htmlId{1940}{\htmlClass{InductiveConstructor}{\text{TriggerHardFork}}}}\,    \\ \,\htmlId{1961}{\htmlClass{Symbol}{\text{\_}}}\,                \end{pmatrix}$ = no λ()
  isUpdateCommittee $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#862}{\htmlId{2013}{\htmlClass{InductiveConstructor}{\text{ChangePParams}}}}\,      \\ \,\htmlId{2034}{\htmlClass{Symbol}{\text{\_}}}\,                \end{pmatrix}$ = no λ()
  isUpdateCommittee $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#900}{\htmlId{2086}{\htmlClass{InductiveConstructor}{\text{TreasuryWithdrawal}}}}\, \\ \,\htmlId{2107}{\htmlClass{Symbol}{\text{\_}}}\,                \end{pmatrix}$ = no λ()
  isUpdateCommittee $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#938}{\htmlId{2159}{\htmlClass{InductiveConstructor}{\text{Info}}}}\,               \\ \,\htmlId{2180}{\htmlClass{Symbol}{\text{\_}}}\,                \end{pmatrix}$ = no λ()

  pvFollows :  v' ver v  Dec (if pvCanFollowMajor v' ver
                                   then pvCanFollowMinor v v'
                                   else pvCanFollow v v')
  pvFollows v' ver v with ¿ pvCanFollowMajor v' ver ¿
  ... | yes p = ¿ pvCanFollowMinor v v' ¿
  ... | no ¬p = ¿ pvCanFollow v v' ¿

  hasPrev :  x ver v  Dec (∃[ v' ] x .action  $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#824}{\htmlId{2575}{\htmlClass{InductiveConstructor}{\text{TriggerHardFork}}}}\, \\ \,\href{Ledger.Conway.Specification.Gov.Properties.Computational.html#2556}{\htmlId{2593}{\htmlClass{Bound}{\text{v'}}}}\, \end{pmatrix}$
                                                      × (if pvCanFollowMajor v' ver
                                                            then pvCanFollowMinor v v'
                                                            else pvCanFollow v v'))
  hasPrev record { action = $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#710}{\htmlId{2885}{\htmlClass{InductiveConstructor}{\text{NoConfidence}}}}\,        \\ \,\htmlId{2907}{\htmlClass{Symbol}{\text{\_}}}\,   \end{pmatrix}$} _ v = no λ ()
  hasPrev record { action = $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#748}{\htmlId{2960}{\htmlClass{InductiveConstructor}{\text{UpdateCommittee}}}}\,     \\ \,\htmlId{2982}{\htmlClass{Symbol}{\text{\_}}}\,   \end{pmatrix}$} _ v = no λ ()
  hasPrev record { action = $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#786}{\htmlId{3035}{\htmlClass{InductiveConstructor}{\text{NewConstitution}}}}\,     \\ \,\htmlId{3057}{\htmlClass{Symbol}{\text{\_}}}\,   \end{pmatrix}$} _ v = no λ ()
  hasPrev record { action = $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#824}{\htmlId{3110}{\htmlClass{InductiveConstructor}{\text{TriggerHardFork}}}}\,     \\ \,\href{Ledger.Conway.Specification.Gov.Properties.Computational.html#3132}{\htmlId{3132}{\htmlClass{Bound}{\text{v'}}}}\,  \end{pmatrix}$} ver v
    with pvFollows v' ver v
  ... | yes p = yes (v' , refl , p)
  ... | no ¬p = no  where (_ , refl , h)  ¬p h)
  hasPrev record { action = $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#862}{\htmlId{3292}{\htmlClass{InductiveConstructor}{\text{ChangePParams}}}}\,       \\ \,\htmlId{3314}{\htmlClass{Symbol}{\text{\_}}}\,   \end{pmatrix}$} _ v = no λ ()
  hasPrev record { action = $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#900}{\htmlId{3367}{\htmlClass{InductiveConstructor}{\text{TreasuryWithdrawal}}}}\,  \\ \,\htmlId{3389}{\htmlClass{Symbol}{\text{\_}}}\,   \end{pmatrix}$} _ v = no λ ()
  hasPrev record { action = $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#938}{\htmlId{3442}{\htmlClass{InductiveConstructor}{\text{Info}}}}\,                \\ \,\htmlId{3464}{\htmlClass{Symbol}{\text{\_}}}\,   \end{pmatrix}$} _ v = no λ ()

opaque
  unfolding validHFAction isRegistered

  instance
    validHFAction? :  {p s e}  validHFAction p s e 
    validHFAction? {record { action = $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#710}{\htmlId{3641}{\htmlClass{InductiveConstructor}{\text{NoConfidence}}}}\,        \\ \,\htmlId{3663}{\htmlClass{Symbol}{\text{\_}}}\, \end{pmatrix}$}} = Dec-⊤
    validHFAction? {record { action = $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#748}{\htmlId{3719}{\htmlClass{InductiveConstructor}{\text{UpdateCommittee}}}}\,     \\ \,\htmlId{3741}{\htmlClass{Symbol}{\text{\_}}}\, \end{pmatrix}$}} = Dec-⊤
    validHFAction? {record { action = $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#786}{\htmlId{3797}{\htmlClass{InductiveConstructor}{\text{NewConstitution}}}}\,     \\ \,\htmlId{3819}{\htmlClass{Symbol}{\text{\_}}}\, \end{pmatrix}$}} = Dec-⊤
    validHFAction? {record { action = $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#824}{\htmlId{3875}{\htmlClass{InductiveConstructor}{\text{TriggerHardFork}}}}\,     \\ \,\href{Ledger.Conway.Specification.Gov.Properties.Computational.html#3897}{\htmlId{3897}{\htmlClass{Bound}{\text{v}}}}\, \end{pmatrix}$ ; prevAction = prev }} {s} {record { pv = (v' , aid') }}
      with aid'  prev ×-dec pvCanFollow? {v} {v'} | any?  (aid , x)  aid  prev ×-dec hasPrev x v' v) s
    ... | yes p' | _ =  yes (inj₁ p')
    ... | no _ | yes p' with ((aid , x) , x∈xs , (refl , v , h))P.find p' =  yes (inj₂
      (x , v , to ∈-fromList x∈xs , h))
    ... | no ¬p₁ | no ¬p₂ =  no λ
      { (inj₁ x)  ¬p₁ x
      ; (inj₂ (s , v , (h₁ , h₂ , h₃)))  ¬p₂ $
        ∃∈-Any ((prev , s) , (from ∈-fromList h₁ , refl , (v , h₂ , h₃))) }
    validHFAction? {record { action = $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#862}{\htmlId{4462}{\htmlClass{InductiveConstructor}{\text{ChangePParams}}}}\,       \\ \,\htmlId{4484}{\htmlClass{Symbol}{\text{\_}}}\, \end{pmatrix}$}} = Dec-⊤
    validHFAction? {record { action = $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#900}{\htmlId{4540}{\htmlClass{InductiveConstructor}{\text{TreasuryWithdrawal}}}}\,  \\ \,\htmlId{4562}{\htmlClass{Symbol}{\text{\_}}}\, \end{pmatrix}$}} = Dec-⊤
    validHFAction? {record { action = $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#938}{\htmlId{4618}{\htmlClass{InductiveConstructor}{\text{Info}}}}\,                \\ \,\htmlId{4640}{\htmlClass{Symbol}{\text{\_}}}\, \end{pmatrix}$}} = Dec-⊤

  isRegistered? :  Γ v  Dec (isRegistered Γ v)
  isRegistered? _ $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#423}{\htmlId{4726}{\htmlClass{InductiveConstructor}{\text{CC}}}}\,   \\ \,\htmlId{4733}{\htmlClass{Symbol}{\text{\_}}}\, \end{pmatrix}$ = ¿ _  _ ¿
  isRegistered? _ $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#426}{\htmlId{4771}{\htmlClass{InductiveConstructor}{\text{DRep}}}}\, \\ \,\htmlId{4778}{\htmlClass{Symbol}{\text{\_}}}\, \end{pmatrix}$ = ¿ _  _ ¿
  isRegistered? _ $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#431}{\htmlId{4816}{\htmlClass{InductiveConstructor}{\text{SPO}}}}\,  \\ \,\htmlId{4823}{\htmlClass{Symbol}{\text{\_}}}\, \end{pmatrix}$ = ¿ _  _ ¿

open GovVoter

instance
  Computational-GOV : Computational _⊢_⇀⦇_,GOV⦈_ String
  Computational-GOV = record {Go} where
    module Go Γ s where
      open GovEnv (proj₁ Γ)
      k = proj₂ Γ

      module GoVote sig where
        open GovVote sig

        computeProof = case lookupActionId pparams (gvRole voter) gid epoch s ,′ isRegistered? (proj₁ Γ) voter of λ where
            (yes p , yes p')  case Any↔ .from p of λ where
              (_ , mem , refl , cV , ¬exp)  success (_ , GOV-Vote (∈-fromList .to mem , cV , p' , ¬exp))
            (yes _ , no ¬p)  failure (genErrors ¬p)
            (no ¬p , _    )  failure (genErrors ¬p)

        completeness :  s'  Γ  s ⇀⦇ inj₁ sig ,GOV⦈ s'  map proj₁ computeProof  success s'
        completeness s' (GOV-Vote {ast = ast} (mem , cV , reg , ¬expired))
          with lookupActionId pparams (gvRole voter) gid epoch s | isRegistered? (proj₁ Γ) voter
        ... | no ¬p | _ = ⊥-elim (¬p (Any↔ .to (_ , ∈-fromList .from mem , refl , cV , ¬expired)))
        ... | yes _ | no ¬p = ⊥-elim $ ¬p reg
        ... | yes p | yes q with Any↔ .from p
        ... | ((_ , ast') , mem , refl , cV) = refl

      module GoProp prop where
        open GovProposal prop
          renaming (action to a; deposit to d; policy to p; returnAddr to addr; prevAction to prev)
        open PParams pparams hiding (a)

        instance
          Dec-actionWellFormed = actionWellFormed?
          Dec-actionValid = actionValid?
        {-# INCOHERENT Dec-actionWellFormed #-}
        {-# INCOHERENT Dec-actionValid #-}

        H = ¿ actionWellFormed a
            × actionValid rewardCreds p ppolicy epoch a
            × d  govActionDeposit
            × validHFAction prop s enactState
            × hasParent' enactState s (a .gaType) prev
            × NetworkIdOf addr  NetworkId
            × CredentialOf addr  rewardCreds ¿
            ,′ isUpdateCommittee a

        computeProof = case H of λ where
          (yes (wf , av , dep , vHFA , HasParent' en , goodAddr , regReturn) , yes (new , rem , q , refl)) 
            case ¿ ∀[ e  range new ] epoch < e × dom new  rem ≡ᵉ  ¿ of λ where
              (yes newOk)  success (-, GOV-Propose {_} {_} {_} {_} {_} {_} {_} {_} {_} {(new , rem , q)} (wf , av , dep , vHFA , en , goodAddr , regReturn))
              (no ¬p)      failure (genErrors ¬p)
          (yes (wf , av , dep , vHFA , HasParent' en , goodAddr , returnReg) , no notNewComm)  success
            (-, GOV-Propose {_} {_} {_} {_} {_} {_} {_} {_} {_} {a .gaData} (wf , av , dep , vHFA , en , goodAddr , returnReg))
          (no ¬p , _)  failure (genErrors ¬p)

        completeness :  s'  Γ  s ⇀⦇ inj₂ prop ,GOV⦈ s'  map proj₁ computeProof  success s'
        completeness s' (GOV-Propose (wf , av , dep , vHFA , en , goodAddr)) with H
        ... | (no ¬p , _) = ⊥-elim (¬p (wf , av , dep , vHFA , HasParent' en , goodAddr))
        ... | (yes (_ , _ , _ , _ , HasParent' _ , _) , no notNewComm) = refl
        ... | (yes (_ , (_ , (av₁ , av₂)) , _ , _ , HasParent' _ , _) , yes (new , rem , q , refl))
          rewrite dec-yes ¿ ∀[ e  range new ] epoch < e × dom new  rem ≡ᵉ  ¿  { x  av₁ x , av₂ }) .proj₂ = refl

      computeProof : (sig : GovVote  GovProposal)  _
      computeProof (inj₁ s) = GoVote.computeProof s
      computeProof (inj₂ s) = GoProp.computeProof s

      completeness :  sig s'  Γ  s ⇀⦇ sig ,GOV⦈ s'  _
      completeness (inj₁ s) = GoVote.completeness s
      completeness (inj₂ s) = GoProp.completeness s

Computational-GOVS : Computational _⊢_⇀⦇_,GOVS⦈_ String
Computational-GOVS = it

allEnactable-singleton :  {aid s es}  getHash (s .prevAction)  getHashES es (GovActionTypeOf s)
   allEnactable es [ (aid , s) ]
allEnactable-singleton {aid} {s} {es} eq = helper All.∷ All.[]
  where
    module ≡ᵉ = IsEquivalence (≡ᵉ-isEquivalence th)

    helper : enactable es (getAidPairsList [ (aid , s) ]) (aid , s)
    helper with getHashES es (GovActionTypeOf s) | getHash (s .prevAction)
    ... | just x | just x' with refl <- just-injective eq =
      [ (aid , x) ] , proj₁ ≡ᵉ.refl , All.[]  [] , inj₁ (refl , refl)
    ... | just x | nothing = case eq of λ ()
    ... | nothing | _ = _