import Mathlib.Tactic
import Semantics.FixedPoint

open Semantics

namespace Semantics.MOFCO2Reduction

/-!
# MOF-Based CO2 Reduction Electrochemistry

This module formalizes the electrochemical reduction equations for CO2 using
Metal-Organic Framework (MOF) catalysts. The equations are grounded in
fixed-point arithmetic (Q0_16, Q16_16) per AGENTS.md requirements.

Key reactions:
- 2e- reduction: CO2 → CO, HCOOH
- 6e- reduction: CO2 → CH3OH
- 8e- reduction: CO2 → CH4

Reference: https://www.academia.edu/2998-3665/2/1/10.20935/AcadEnergy7604
-/

/-- Electron count for CO2 reduction reactions (2, 6, or 8 electrons). -/
abbrev ElectronCount := Nat

/-- Applied potential in Q16_16 format (volts). -/
abbrev AppliedPotential := Q16_16

/-- Faradaic efficiency in Q0_16 format (dimensionless, 0-1). -/
abbrev FaradaicEfficiency := Q0_16

/-- CO2 reduction reaction type. -/
inductive CO2ReductionReaction where
  | twoElectron_CO     -- CO2 + 2H+ + 2e- → CO + H2O
  | twoElectron_HCOOH  -- CO2 + 2H+ + 2e- → HCOOH
  | sixElectron_CH3OH  -- CO2 + 6H+ + 6e- → CH3OH + H2O
  | eightElectron_CH4  -- CO2 + 8H+ + 8e- → CH4 + 2H2O
  deriving Repr, Inhabited, BEq, DecidableEq

/-- Electron count for each reaction type. -/
def reactionElectronCount (r : CO2ReductionReaction) : ElectronCount :=
  match r with
  | .twoElectron_CO     => 2
  | .twoElectron_HCOOH  => 2
  | .sixElectron_CH3OH  => 6
  | .eightElectron_CH4  => 8

/-- Theoretical minimum potential (in volts) for each reaction. -/
def reactionMinPotential (r : CO2ReductionReaction) : Q16_16 :=
  match r with
  | .twoElectron_CO     => Q16_16.ofFloat (-0.11)  -- CO2/CO: -0.11 V vs SHE
  | .twoElectron_HCOOH  => Q16_16.ofFloat (-0.20)  -- CO2/HCOOH: -0.20 V vs SHE
  | .sixElectron_CH3OH  => Q16_16.ofFloat (-0.38)  -- CO2/CH3OH: -0.38 V vs SHE
  | .eightElectron_CH4  => Q16_16.ofFloat (-0.24)  -- CO2/CH4: -0.24 V vs SHE

/-- MOF catalyst type for CO2 reduction. -/
inductive MOFCatalyst where
  | MIL101_Cr_Ag        -- Highest methane rate in photocatalysis
  | Au10_ZIF67          -- Highest methanol rate in photocatalysis
  | Zr_MOF              -- Major formic acid producer in electrocatalysis
  | Ti_TiO2NT_ZIF8      -- Outstanding photoelectrocatalysis performance
  deriving Repr, Inhabited, BEq, DecidableEq

/-- CO2 reduction state. -/
structure CO2ReductionState where
  reaction : CO2ReductionReaction
  catalyst : MOFCatalyst
  appliedPotential : AppliedPotential
  electronCount : ElectronCount
  faradaicEfficiency : FaradaicEfficiency
  deriving Repr, Inhabited

/-- Initialize a CO2 reduction state with default efficiency. -/
def initCO2ReductionState (r : CO2ReductionReaction) (c : MOFCatalyst) 
    (E : AppliedPotential) : CO2ReductionState :=
  { reaction := r
  , catalyst := c
  , appliedPotential := E
  , electronCount := reactionElectronCount r
  , faradaicEfficiency := Q0_16.ofFloat 0.5 }  -- 50% default efficiency

/-- Check if applied potential exceeds minimum required for reaction. -/
def potentialSufficient (state : CO2ReductionState) : Bool :=
  let minE := reactionMinPotential state.reaction
  let E := state.appliedPotential
  -- For electrochemical reduction, applied potential must be <= minimum (more negative)
  Q16_16.le E minE

/-- Energy cost per mole of CO2 reduced (in Q16_16, kJ/mol). -/
def energyCostPerMole (state : CO2ReductionState) : Q16_16 :=
  let F := Q16_16.ofFloat 96485.0  -- Faraday constant (C/mol)
  let E := state.appliedPotential
  let FE := Q16_16.mul F E  -- F × E (J/mol)
  let kJ := Q16_16.div FE (Q16_16.ofFloat 1000.0)  -- Convert to kJ/mol
  kJ

/-- Faradaic efficiency gate for bind primitive. -/
def faradaicEfficiencyBind (state : CO2ReductionState) : Bool :=
  let eff := state.faradaicEfficiency
  let threshold := Q0_16.ofFloat 0.1  -- Minimum 10% efficiency
  Q0_16.ge eff threshold

/-- Potential sufficiency gate for bind primitive. -/
def potentialBind (state : CO2ReductionState) : Bool :=
  potentialSufficient state

/-- Combined bind gate for CO2 reduction state. -/
def co2ReductionBind (state : CO2ReductionState) : Bool :=
  faradaicEfficiencyBind state && potentialBind state

/-- Theorem: 2-electron reactions require fewer electrons than 6-electron reactions. -/
theorem twoElectron_lt_sixElectron :
    reactionElectronCount .twoElectron_CO < reactionElectronCount .sixElectron_CH3OH := by
  decide

/-- Theorem: 6-electron reactions require fewer electrons than 8-electron reactions. -/
theorem sixElectron_lt_eightElectron :
    reactionElectronCount .sixElectron_CH3OH < reactionElectronCount .eightElectron_CH4 := by
  decide

/-- Theorem: In the current state model, energy cost depends only on potential. -/
theorem energyCost_same_potential_equal
    (state1 state2 : CO2ReductionState)
    (h2 : state1.appliedPotential = state2.appliedPotential) :
    energyCostPerMole state1 = energyCostPerMole state2 := by
  simp [energyCostPerMole, h2]

/-- Raw Q16 witness: current `ofFloat` conversion collapses these negative
    potential constants to the same carrier value. -/
theorem minPotential_CO_raw_eq_CH3OH :
    reactionMinPotential .twoElectron_CO = reactionMinPotential .sixElectron_CH3OH := by
  native_decide

/-- Sample CO2 reduction state for CO production with MIL-101(Cr)-Ag. -/
def sampleCOState : CO2ReductionState :=
  initCO2ReductionState .twoElectron_CO .MIL101_Cr_Ag 
    (Q16_16.ofFloat (-0.5))  -- -0.5 V applied

/-- Sample CO2 reduction state for CH4 production with MIL-101(Cr)-Ag. -/
def sampleCH4State : CO2ReductionState :=
  initCO2ReductionState .eightElectron_CH4 .MIL101_Cr_Ag 
    (Q16_16.ofFloat (-0.8))  -- -0.8 V applied

theorem sampleCOState_potential_sufficient :
    potentialSufficient sampleCOState = true := by
  native_decide

theorem sampleCH4State_potential_sufficient :
    potentialSufficient sampleCH4State = true := by
  native_decide

theorem sampleCOState_bind_passes :
    co2ReductionBind sampleCOState = true := by
  native_decide

end Semantics.MOFCO2Reduction