{-# OPTIONS --safe #-}

open import Ledger.Dijkstra.Specification.Gov.Base
open import Ledger.Dijkstra.Specification.Transaction using (TransactionStructure)

module Ledger.Dijkstra.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.Dijkstra.Specification.Enact govStructure
open import Ledger.Dijkstra.Specification.Gov govStructure
open import Ledger.Dijkstra.Specification.Gov.Actions govStructure hiding (yes; no)
open import Ledger.Dijkstra.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 Inverse

lookupActionId :
  (pparams  : PParams)
  (role     : GovRole)
  (aid      : GovActionID)
  (epoch    : Epoch)
  (s        : GovState)
  → Dec (Any ( λ (aid' , ast) →  aid ≡ aid'
                                 × canVote pparams (GovActionOf 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 ≡ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Gov.Actions.html#609}{\htmlId{1677}{\htmlClass{InductiveConstructor}{\text{UpdateCommittee}}}}\, \\ \,\htmlId{1695}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Dijkstra.Specification.Gov.Properties.Computational.html#1649}{\htmlId{1696}{\htmlClass{Bound}{\text{new}}}}\, , \,\href{Ledger.Dijkstra.Specification.Gov.Properties.Computational.html#1658}{\htmlId{1702}{\htmlClass{Bound}{\text{rem}}}}\, , \,\href{Ledger.Dijkstra.Specification.Gov.Properties.Computational.html#1667}{\htmlId{1708}{\htmlClass{Bound}{\text{q}}}}\,\,\htmlId{1709}{\htmlClass{Symbol}{\text{)}}}\, \end{pmatrix}$)
  -- (new , rem , q) : (Credential ⇀ Epoch) × ℙ Credential × ℚ

  isUpdateCommittee $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Gov.Actions.html#571}{\htmlId{1802}{\htmlClass{InductiveConstructor}{\text{NoConfidence}}}}\,       \\ \,\htmlId{1823}{\htmlClass{Symbol}{\text{\_}}}\,                \end{pmatrix}$ = no λ()
  isUpdateCommittee $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Gov.Actions.html#609}{\htmlId{1875}{\htmlClass{InductiveConstructor}{\text{UpdateCommittee}}}}\,    \\ \,\htmlId{1896}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Dijkstra.Specification.Gov.Properties.Computational.html#1897}{\htmlId{1897}{\htmlClass{Bound}{\text{new}}}}\, , \,\href{Ledger.Dijkstra.Specification.Gov.Properties.Computational.html#1903}{\htmlId{1903}{\htmlClass{Bound}{\text{rem}}}}\, , \,\href{Ledger.Dijkstra.Specification.Gov.Properties.Computational.html#1909}{\htmlId{1909}{\htmlClass{Bound}{\text{q}}}}\,\,\htmlId{1910}{\htmlClass{Symbol}{\text{)}}}\,  \end{pmatrix}$ = yes (new , rem , q , refl)
  isUpdateCommittee $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Gov.Actions.html#647}{\htmlId{1968}{\htmlClass{InductiveConstructor}{\text{NewConstitution}}}}\,    \\ \,\htmlId{1989}{\htmlClass{Symbol}{\text{\_}}}\,                \end{pmatrix}$ = no λ()
  isUpdateCommittee $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Gov.Actions.html#685}{\htmlId{2041}{\htmlClass{InductiveConstructor}{\text{TriggerHardFork}}}}\,    \\ \,\htmlId{2062}{\htmlClass{Symbol}{\text{\_}}}\,                \end{pmatrix}$ = no λ()
  isUpdateCommittee $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Gov.Actions.html#723}{\htmlId{2114}{\htmlClass{InductiveConstructor}{\text{ChangePParams}}}}\,      \\ \,\htmlId{2135}{\htmlClass{Symbol}{\text{\_}}}\,                \end{pmatrix}$ = no λ()
  isUpdateCommittee $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Gov.Actions.html#761}{\htmlId{2187}{\htmlClass{InductiveConstructor}{\text{TreasuryWithdrawal}}}}\, \\ \,\htmlId{2208}{\htmlClass{Symbol}{\text{\_}}}\,                \end{pmatrix}$ = no λ()
  isUpdateCommittee $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Gov.Actions.html#799}{\htmlId{2260}{\htmlClass{InductiveConstructor}{\text{Info}}}}\,               \\ \,\htmlId{2281}{\htmlClass{Symbol}{\text{\_}}}\,                \end{pmatrix}$ = no λ()

  hasPrev : (ast : GovActionState) (v : ProtVer)
    → Dec (∃[ v' ] (GovActionOf ast) ≡ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Gov.Actions.html#685}{\htmlId{2402}{\htmlClass{InductiveConstructor}{\text{TriggerHardFork}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Gov.Properties.Computational.html#2375}{\htmlId{2420}{\htmlClass{Bound}{\text{v'}}}}\, \end{pmatrix}$ × pvCanFollow v' v)

  hasPrev record { action = $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Gov.Actions.html#571}{\htmlId{2478}{\htmlClass{InductiveConstructor}{\text{NoConfidence}}}}\,        \\ \,\htmlId{2500}{\htmlClass{Symbol}{\text{\_}}}\,   \end{pmatrix}$} v = no λ ()
  hasPrev record { action = $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Gov.Actions.html#609}{\htmlId{2551}{\htmlClass{InductiveConstructor}{\text{UpdateCommittee}}}}\,     \\ \,\htmlId{2573}{\htmlClass{Symbol}{\text{\_}}}\,   \end{pmatrix}$} v = no λ ()
  hasPrev record { action = $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Gov.Actions.html#647}{\htmlId{2624}{\htmlClass{InductiveConstructor}{\text{NewConstitution}}}}\,     \\ \,\htmlId{2646}{\htmlClass{Symbol}{\text{\_}}}\,   \end{pmatrix}$} v = no λ ()
  hasPrev record { action = $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Gov.Actions.html#685}{\htmlId{2697}{\htmlClass{InductiveConstructor}{\text{TriggerHardFork}}}}\,     \\ \,\href{Ledger.Dijkstra.Specification.Gov.Properties.Computational.html#2719}{\htmlId{2719}{\htmlClass{Bound}{\text{v'}}}}\,  \end{pmatrix}$} v =
    case pvCanFollow? {v'} {v} of λ where
      (yes p) → yes (-, refl , p)
      (no ¬p) → no  (λ where (_ , refl , h) → ¬p h)
  hasPrev record { action = $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Gov.Actions.html#723}{\htmlId{2890}{\htmlClass{InductiveConstructor}{\text{ChangePParams}}}}\,       \\ \,\htmlId{2912}{\htmlClass{Symbol}{\text{\_}}}\,   \end{pmatrix}$} v = no λ ()
  hasPrev record { action = $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Gov.Actions.html#761}{\htmlId{2963}{\htmlClass{InductiveConstructor}{\text{TreasuryWithdrawal}}}}\,  \\ \,\htmlId{2985}{\htmlClass{Symbol}{\text{\_}}}\,   \end{pmatrix}$} v = no λ ()
  hasPrev record { action = $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Gov.Actions.html#799}{\htmlId{3036}{\htmlClass{InductiveConstructor}{\text{Info}}}}\,                \\ \,\htmlId{3058}{\htmlClass{Symbol}{\text{\_}}}\,   \end{pmatrix}$} v = no λ ()


opaque
  unfolding validHFAction isRegistered

  instance
    validHFAction? : ∀ {p : GovProposal} {s : GovState} {e : EnactState}
      → validHFAction p s e ⁇

    validHFAction?  {record { action = $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Gov.Actions.html#571}{\htmlId{3284}{\htmlClass{InductiveConstructor}{\text{NoConfidence}}}}\,     \\ \,\htmlId{3303}{\htmlClass{Symbol}{\text{\_}}}\, \end{pmatrix}$}} = Dec-⊤
    validHFAction?  {record { action = $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Gov.Actions.html#609}{\htmlId{3360}{\htmlClass{InductiveConstructor}{\text{UpdateCommittee}}}}\,  \\ \,\htmlId{3379}{\htmlClass{Symbol}{\text{\_}}}\, \end{pmatrix}$}} = Dec-⊤
    validHFAction?  {record { action = $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Gov.Actions.html#647}{\htmlId{3436}{\htmlClass{InductiveConstructor}{\text{NewConstitution}}}}\,  \\ \,\htmlId{3455}{\htmlClass{Symbol}{\text{\_}}}\, \end{pmatrix}$}} = Dec-⊤
    validHFAction?  {record { action = $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Gov.Actions.html#685}{\htmlId{3512}{\htmlClass{InductiveConstructor}{\text{TriggerHardFork}}}}\,  \\ \,\href{Ledger.Dijkstra.Specification.Gov.Properties.Computational.html#3531}{\htmlId{3531}{\htmlClass{Bound}{\text{v}}}}\, \end{pmatrix}$ ; prevAction = prev }}
                    {s} {record { pv = (v' , aid') }}
      with    aid' ≟ prev ×-dec pvCanFollow? {v'} {v}
           |  any? (λ (aid , x) → aid ≟ prev ×-dec hasPrev x 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 = $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Gov.Actions.html#723}{\htmlId{4345}{\htmlClass{InductiveConstructor}{\text{ChangePParams}}}}\,       \\ \,\htmlId{4367}{\htmlClass{Symbol}{\text{\_}}}\, \end{pmatrix}$}} = Dec-⊤
    validHFAction? {record { action = $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Gov.Actions.html#761}{\htmlId{4423}{\htmlClass{InductiveConstructor}{\text{TreasuryWithdrawal}}}}\,  \\ \,\htmlId{4445}{\htmlClass{Symbol}{\text{\_}}}\, \end{pmatrix}$}} = Dec-⊤
    validHFAction? {record { action = $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Gov.Actions.html#799}{\htmlId{4501}{\htmlClass{InductiveConstructor}{\text{Info}}}}\,                \\ \,\htmlId{4523}{\htmlClass{Symbol}{\text{\_}}}\, \end{pmatrix}$}} = Dec-⊤

  isRegistered? : ∀ Γ v → Dec (isRegistered Γ v)
  isRegistered? _ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Gov.Actions.html#373}{\htmlId{4609}{\htmlClass{InductiveConstructor}{\text{CC}}}}\,   \\ \,\htmlId{4616}{\htmlClass{Symbol}{\text{\_}}}\, \end{pmatrix}$ = ¿ _ ∈ _ ¿
  isRegistered? _ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Gov.Actions.html#376}{\htmlId{4654}{\htmlClass{InductiveConstructor}{\text{DRep}}}}\, \\ \,\htmlId{4661}{\htmlClass{Symbol}{\text{\_}}}\, \end{pmatrix}$ = ¿ _ ∈ _ ¿
  isRegistered? _ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Gov.Actions.html#381}{\htmlId{4699}{\htmlClass{InductiveConstructor}{\text{SPO}}}}\,  \\ \,\htmlId{4706}{\htmlClass{Symbol}{\text{\_}}}\, \end{pmatrix}$ = ¿ _ ∈ _ ¿

open GovVoter

instance
  Computational-GOV : Computational _⊢_⇀⦇_,GOV⦈_ String
  Computational-GOV = record {Go} where
    module Go (Γk : GovEnv × ℕ) (s : GovState) where
      Γ : GovEnv
      Γ = proj₁ Γk

      k : ℕ
      k = proj₂ Γk

      module GoVote sig where
        open GovVote sig

        computeProof = case lookupActionId (PParamsOf Γ) (gvRole voter) gid (EpochOf Γ) s ,′ isRegistered? 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 , k) ⊢ s ⇀⦇ inj₁ sig ,GOV⦈ s' → map proj₁ computeProof ≡ success s'
        completeness s' (GOV-Vote {ast = ast} (mem , cV , reg , ¬expired))
          with lookupActionId (PParamsOf Γ) (gvRole voter) gid (EpochOf Γ) s | isRegistered? 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 PParams (PParamsOf Γ)

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

        H = ¿ actionWellFormed (GovActionOf prop)
            × actionValid (RewardCredentialsOf Γ) (PolicyOf prop) (GovEnv.ppolicy Γ) (EpochOf Γ) (GovActionOf prop)
            × (DepositOf prop) ≡ govActionDeposit
            × validHFAction prop s (EnactStateOf Γ)
            × hasParent' (EnactStateOf Γ) s ((GovActionOf prop) .gaType) (GovProposal.prevAction prop)
            × NetworkIdOf (RewardAddressOf prop) ≡ NetworkId
            × CredentialOf (RewardAddressOf prop) ∈ (RewardCredentialsOf Γ) ¿
            ,′ isUpdateCommittee (GovActionOf prop)

        pattern gov-propose  {zz} xx = GOV-Propose {_} {_} {_} {_} {_} {_} {_} {_} {_} {zz} xx
        -- The inferred variables in both cases below are
        -- { Γ } { RewardAddressOf prop } { GovActionOf prop } { AnchorOf prop } { PolicyOf prop } { DepositOf prop } { (GovProposal.prevAction prop) } { s } { k }

        computeProof = case H of λ where
          (yes (wf , av , dep , vHFA , HasParent' en , goodAddr , regReturn) , yes (new , rem , q , refl)) →
            case ¿ ∀[ e ∈ range new ] (EpochOf Γ) < 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 {(GovActionOf prop) .gaData} (wf , av , dep , vHFA , en , goodAddr , returnReg))
          (no ¬p , _) → failure (genErrors ¬p)

        completeness : ∀ s' → (Γ , k) ⊢ 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 ] (EpochOf Γ) < e × dom new ∩ rem ≡ᵉ ∅ ¿ (λ { 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 , k) ⊢ 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 : GovActionID} {s : GovActionState} {es : EnactState}
  → getHash (GovActionState.prevAction s) ≡ 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 (GovActionState.prevAction s)
    ... | 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 | _ = _