{-# OPTIONS --safe #-}

open import Ledger.Conway.Specification.Gov.Base

module Ledger.Conway.Specification.Enact.Properties (gs : _) (open GovStructure gs) where

open import Ledger.Prelude

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

open EnactState

open Computational ⦃...⦄

instance
  Computational-ENACT : Computational _⊢_⇀⦇_,ENACT⦈_ String
  Computational-ENACT .computeProof Γᵉ s =
    let open EnactEnv Γᵉ renaming (treasury to t; epoch to e) in
    λ where
    $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#738}{\htmlId{554}{\htmlClass{InductiveConstructor}{\text{NoConfidence}}}}\, \\ \,\htmlId{569}{\htmlClass{Symbol}{\text{\_}}}\, \end{pmatrix}$                → success (_ , Enact-NoConf)
    $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#773}{\htmlId{625}{\htmlClass{InductiveConstructor}{\text{UpdateCommittee}}}}\, \\ (\,\href{Ledger.Conway.Specification.Enact.Properties.html#644}{\htmlId{644}{\htmlClass{Bound}{\text{new}}}}\, , \,\href{Ledger.Conway.Specification.Enact.Properties.html#650}{\htmlId{650}{\htmlClass{Bound}{\text{rem}}}}\, , \,\href{Ledger.Conway.Specification.Enact.Properties.html#656}{\htmlId{656}{\htmlClass{Bound}{\text{q}}}}\,) \end{pmatrix}$ →
      case ¿ ∀[ term ∈ range new ]
               term ≤ ccMaxTermLengthOf s +ᵉ' e ¿ of λ where
      (yes p) → success (-, Enact-UpdComm
        (subst (λ x → ∀[ term ∈ range new ] term ≤ x) (sym +ᵉ≡+ᵉ') p))
      (no ¬p) → failure "ENACT failed at ∀[ term ∈ range new ] term ≤ (ccMaxTermLengthOf s +ᵉ e)"
    $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#808}{\htmlId{978}{\htmlClass{InductiveConstructor}{\text{NewConstitution}}}}\, \\ \,\htmlId{996}{\htmlClass{Symbol}{\text{\_}}}\, \end{pmatrix}$ → success (-, Enact-NewConst)
    $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#843}{\htmlId{1038}{\htmlClass{InductiveConstructor}{\text{TriggerHF}}}}\,       \\ \,\htmlId{1056}{\htmlClass{Symbol}{\text{\_}}}\, \end{pmatrix}$ → success (-, Enact-HF)
    $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#878}{\htmlId{1092}{\htmlClass{InductiveConstructor}{\text{ChangePParams}}}}\,   \\ \,\htmlId{1110}{\htmlClass{Symbol}{\text{\_}}}\, \end{pmatrix}$ → success (-, Enact-PParams)
    $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#948}{\htmlId{1151}{\htmlClass{InductiveConstructor}{\text{Info}}}}\,            \\ \,\htmlId{1169}{\htmlClass{Symbol}{\text{\_}}}\, \end{pmatrix}$ → success (-, Enact-Info) 
    $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#913}{\htmlId{1208}{\htmlClass{InductiveConstructor}{\text{TreasuryWdrl}}}}\, \\ \,\href{Ledger.Conway.Specification.Enact.Properties.html#1223}{\htmlId{1223}{\htmlClass{Bound}{\text{wdrl}}}}\, \end{pmatrix}$ →
      case ¿ ∑[ x ← s .withdrawals ∪⁺ wdrl ] x ≤ t ¿ of λ where
        (yes p)             → success (-, Enact-Wdrl p)
        (no _)              → failure "ENACT failed at ∑[ x ← (s .withdrawals ∪⁺ wdrl) ᶠᵐ ] x ≤ t"
  Computational-ENACT .completeness Γᵉ s action _ p
    with action | p
  ... | $\begin{pmatrix} \,\htmlId{1535}{\htmlClass{DottedPattern Symbol}{\text{.}}}\,\,\href{Ledger.Conway.Specification.Gov.Actions.html#738}{\htmlId{1536}{\htmlClass{DottedPattern InductiveConstructor}{\text{NoConfidence}}}}\,    \\ \,\htmlId{1554}{\htmlClass{Symbol}{\text{\_}}}\,               \end{pmatrix}$ | Enact-NoConf   = refl
  ... | $\begin{pmatrix} \,\htmlId{1608}{\htmlClass{DottedPattern Symbol}{\text{.}}}\,\,\href{Ledger.Conway.Specification.Gov.Actions.html#773}{\htmlId{1609}{\htmlClass{DottedPattern InductiveConstructor}{\text{UpdateCommittee}}}}\, \\ (\,\href{Ledger.Conway.Specification.Enact.Properties.html#1628}{\htmlId{1628}{\htmlClass{Bound}{\text{new}}}}\, , \,\href{Ledger.Conway.Specification.Enact.Properties.html#1634}{\htmlId{1634}{\htmlClass{Bound}{\text{rem}}}}\, , \,\href{Ledger.Conway.Specification.Enact.Properties.html#1640}{\htmlId{1640}{\htmlClass{Bound}{\text{q}}}}\,) \end{pmatrix}$ | Enact-UpdComm p
    rewrite dec-yes
      (¿ ∀[ term ∈ range new ] term
           ≤ ccMaxTermLengthOf s +ᵉ' EnactEnv.epoch Γᵉ ¿)
      (subst (λ x → ∀[ term ∈ range new ] term ≤ x) +ᵉ≡+ᵉ' p) .proj₂
      = refl
  ... | $\begin{pmatrix} \,\htmlId{1871}{\htmlClass{DottedPattern Symbol}{\text{.}}}\,\,\href{Ledger.Conway.Specification.Gov.Actions.html#808}{\htmlId{1872}{\htmlClass{DottedPattern InductiveConstructor}{\text{NewConstitution}}}}\, \\ \,\htmlId{1890}{\htmlClass{Symbol}{\text{\_}}}\, \end{pmatrix}$ | Enact-NewConst = refl
  ... | $\begin{pmatrix} \,\htmlId{1930}{\htmlClass{DottedPattern Symbol}{\text{.}}}\,\,\href{Ledger.Conway.Specification.Gov.Actions.html#843}{\htmlId{1931}{\htmlClass{DottedPattern InductiveConstructor}{\text{TriggerHF}}}}\,       \\ \,\htmlId{1949}{\htmlClass{Symbol}{\text{\_}}}\, \end{pmatrix}$ | Enact-HF       = refl
  ... | $\begin{pmatrix} \,\htmlId{1989}{\htmlClass{DottedPattern Symbol}{\text{.}}}\,\,\href{Ledger.Conway.Specification.Gov.Actions.html#878}{\htmlId{1990}{\htmlClass{DottedPattern InductiveConstructor}{\text{ChangePParams}}}}\,   \\ \,\htmlId{2008}{\htmlClass{Symbol}{\text{\_}}}\, \end{pmatrix}$ | Enact-PParams  = refl
  ... | $\begin{pmatrix} \,\htmlId{2048}{\htmlClass{DottedPattern Symbol}{\text{.}}}\,\,\href{Ledger.Conway.Specification.Gov.Actions.html#948}{\htmlId{2049}{\htmlClass{DottedPattern InductiveConstructor}{\text{Info}}}}\,            \\ \,\htmlId{2067}{\htmlClass{Symbol}{\text{\_}}}\, \end{pmatrix}$ | Enact-Info     = refl
  ... | $\begin{pmatrix} \,\htmlId{2107}{\htmlClass{DottedPattern Symbol}{\text{.}}}\,\,\href{Ledger.Conway.Specification.Gov.Actions.html#913}{\htmlId{2108}{\htmlClass{DottedPattern InductiveConstructor}{\text{TreasuryWdrl}}}}\, \\ \,\href{Ledger.Conway.Specification.Enact.Properties.html#2123}{\htmlId{2123}{\htmlClass{Bound}{\text{wdrl}}}}\, \end{pmatrix}$ | Enact-Wdrl p
    rewrite dec-yes (¿ ∑[ x ← s .withdrawals ∪⁺ wdrl ] x ≤ EnactEnv.treasury Γᵉ ¿) p .proj₂
    = refl