Properties

{-# 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
    $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#1877}{\htmlId{660}{\htmlClass{InductiveConstructor}{\text{NoConfidence}}}}\,        \\ \,\htmlId{682}{\htmlClass{Symbol}{\text{\_}}}\,               \end{pmatrix}$ → success (_ , Enact-NoConf)
    $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#1915}{\htmlId{737}{\htmlClass{InductiveConstructor}{\text{UpdateCommittee}}}}\,     \\ \,\htmlId{759}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Specification.Enact.Properties.html#760}{\htmlId{760}{\htmlClass{Bound}{\text{new}}}}\, , \,\href{Ledger.Conway.Specification.Enact.Properties.html#766}{\htmlId{766}{\htmlClass{Bound}{\text{rem}}}}\, , \,\href{Ledger.Conway.Specification.Enact.Properties.html#772}{\htmlId{772}{\htmlClass{Bound}{\text{q}}}}\,\,\htmlId{773}{\htmlClass{Symbol}{\text{)}}}\, \end{pmatrix}$ →
      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)"
    $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#1953}{\htmlId{1094}{\htmlClass{InductiveConstructor}{\text{NewConstitution}}}}\,     \\ \,\htmlId{1116}{\htmlClass{Symbol}{\text{\_}}}\,               \end{pmatrix}$ → success (-, Enact-NewConst)
    $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#1991}{\htmlId{1172}{\htmlClass{InductiveConstructor}{\text{TriggerHardFork}}}}\,     \\ \,\htmlId{1194}{\htmlClass{Symbol}{\text{\_}}}\,               \end{pmatrix}$ → success (-, Enact-HF)
    $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#2029}{\htmlId{1244}{\htmlClass{InductiveConstructor}{\text{ChangePParams}}}}\,       \\ \,\htmlId{1266}{\htmlClass{Symbol}{\text{\_}}}\,               \end{pmatrix}$ → success (-, Enact-PParams)
    $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#2105}{\htmlId{1321}{\htmlClass{InductiveConstructor}{\text{Info}}}}\,                \\ \,\htmlId{1343}{\htmlClass{Symbol}{\text{\_}}}\,               \end{pmatrix}$ → success (-, Enact-Info)
    $\begin{pmatrix} \,\href{Ledger.Conway.Specification.Gov.Actions.html#2067}{\htmlId{1395}{\htmlClass{InductiveConstructor}{\text{TreasuryWithdrawal}}}}\,  \\ \,\href{Ledger.Conway.Specification.Enact.Properties.html#1417}{\htmlId{1417}{\htmlClass{Bound}{\text{wdrl}}}}\,            \end{pmatrix}$ →
      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
  ... | $\begin{pmatrix} \,\htmlId{1718}{\htmlClass{DottedPattern Symbol}{\text{.}}}\,\,\href{Ledger.Conway.Specification.Gov.Actions.html#1877}{\htmlId{1719}{\htmlClass{DottedPattern InductiveConstructor}{\text{NoConfidence}}}}\,        \\ \,\htmlId{1741}{\htmlClass{Symbol}{\text{\_}}}\,               \end{pmatrix}$ | Enact-NoConf   = refl
  ... | $\begin{pmatrix} \,\htmlId{1795}{\htmlClass{DottedPattern Symbol}{\text{.}}}\,\,\href{Ledger.Conway.Specification.Gov.Actions.html#1915}{\htmlId{1796}{\htmlClass{DottedPattern InductiveConstructor}{\text{UpdateCommittee}}}}\,     \\ \,\htmlId{1818}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Specification.Enact.Properties.html#1819}{\htmlId{1819}{\htmlClass{Bound}{\text{new}}}}\, , \,\href{Ledger.Conway.Specification.Enact.Properties.html#1825}{\htmlId{1825}{\htmlClass{Bound}{\text{rem}}}}\, , \,\href{Ledger.Conway.Specification.Enact.Properties.html#1831}{\htmlId{1831}{\htmlClass{Bound}{\text{q}}}}\,\,\htmlId{1832}{\htmlClass{Symbol}{\text{)}}}\, \end{pmatrix}$ | 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
  ... | $\begin{pmatrix} \,\htmlId{2062}{\htmlClass{DottedPattern Symbol}{\text{.}}}\,\,\href{Ledger.Conway.Specification.Gov.Actions.html#1953}{\htmlId{2063}{\htmlClass{DottedPattern InductiveConstructor}{\text{NewConstitution}}}}\,     \\ \,\htmlId{2085}{\htmlClass{Symbol}{\text{\_}}}\,               \end{pmatrix}$ | Enact-NewConst = refl
  ... | $\begin{pmatrix} \,\htmlId{2139}{\htmlClass{DottedPattern Symbol}{\text{.}}}\,\,\href{Ledger.Conway.Specification.Gov.Actions.html#1991}{\htmlId{2140}{\htmlClass{DottedPattern InductiveConstructor}{\text{TriggerHardFork}}}}\,     \\ \,\htmlId{2162}{\htmlClass{Symbol}{\text{\_}}}\,               \end{pmatrix}$ | Enact-HF       = refl
  ... | $\begin{pmatrix} \,\htmlId{2216}{\htmlClass{DottedPattern Symbol}{\text{.}}}\,\,\href{Ledger.Conway.Specification.Gov.Actions.html#2029}{\htmlId{2217}{\htmlClass{DottedPattern InductiveConstructor}{\text{ChangePParams}}}}\,       \\ \,\htmlId{2239}{\htmlClass{Symbol}{\text{\_}}}\,               \end{pmatrix}$ | Enact-PParams  = refl
  ... | $\begin{pmatrix} \,\htmlId{2293}{\htmlClass{DottedPattern Symbol}{\text{.}}}\,\,\href{Ledger.Conway.Specification.Gov.Actions.html#2105}{\htmlId{2294}{\htmlClass{DottedPattern InductiveConstructor}{\text{Info}}}}\,                \\ \,\htmlId{2316}{\htmlClass{Symbol}{\text{\_}}}\,               \end{pmatrix}$ | Enact-Info     = refl
  ... | $\begin{pmatrix} \,\htmlId{2370}{\htmlClass{DottedPattern Symbol}{\text{.}}}\,\,\href{Ledger.Conway.Specification.Gov.Actions.html#2067}{\htmlId{2371}{\htmlClass{DottedPattern InductiveConstructor}{\text{TreasuryWithdrawal}}}}\,  \\ \,\href{Ledger.Conway.Specification.Enact.Properties.html#2393}{\htmlId{2393}{\htmlClass{Bound}{\text{wdrl}}}}\,            \end{pmatrix}$ | Enact-Wdrl p
    rewrite dec-yes (¿ ∑[ x ← s .withdrawals ∪⁺ wdrl ] x ≤ EnactEnv.treasury Γᵉ ¿) p .proj₂
    = refl