Research-Stack/0-Core-Formalism/lean/Semantics/Semantics/UnitConversion.lean

import Semantics.FixedPoint

namespace Semantics.UnitConversion

/-- Unit type for metric/imperial conversions -/
inductive Unit
-- Length units
| meter
| kilometer
| foot
| yard
| mile
| inch
| centimeter
| millimeter
-- Temperature units
| celsius
| kelvin
| fahrenheit
-- Volume units
| liter
| gallon
| cubic_meter
| cubic_foot
-- Mass units
| kilogram
| pound
| ounce
| gram
-- Pressure units
| pascal
| bar
| psi
-- Energy units
| joule
| calorie
| btu
deriving Repr, DecidableEq, BEq

instance : ToString Unit where
  toString
  | .meter => "meter"
  | .kilometer => "kilometer"
  | .foot => "foot"
  | .yard => "yard"
  | .mile => "mile"
  | .inch => "inch"
  | .centimeter => "centimeter"
  | .millimeter => "millimeter"
  | .celsius => "celsius"
  | .kelvin => "kelvin"
  | .fahrenheit => "fahrenheit"
  | .liter => "liter"
  | .gallon => "gallon"
  | .cubic_meter => "cubic_meter"
  | .cubic_foot => "cubic_foot"
  | .kilogram => "kilogram"
  | .pound => "pound"
  | .ounce => "ounce"
  | .gram => "gram"
  | .pascal => "pascal"
  | .bar => "bar"
  | .psi => "psi"
  | .joule => "joule"
  | .calorie => "calorie"
  | .btu => "btu"

/-- Conversion ratio from source to target unit -/
structure ConversionRatio where
  source : Unit
  target : Unit
  ratio : Q0_16  -- conversion factor (dimensionless scalar)
deriving Repr, DecidableEq

/-- Standard conversion ratios (Q0_16 dimensionless scalars) -/
-- Q0_16 range: [-1, 1 - 2^-16] ≈ [-1, 0.999985]
-- For ratios > 1, we store them normalized or use Q16_16 when necessary
-- Using placeholder values that will be computed via Q0_16 operations
def standardRatios : List ConversionRatio := [
  -- Length conversions (all within Q0_16 range)
  { source := Unit.meter, target := Unit.foot, ratio := Q0_16.ofFloat 0.3048 },
  { source := Unit.foot, target := Unit.meter, ratio := Q0_16.ofFloat 0.3048 },
  { source := Unit.kilometer, target := Unit.mile, ratio := Q0_16.ofFloat 0.621371 },
  { source := Unit.mile, target := Unit.kilometer, ratio := Q0_16.ofFloat 0.621371 },
  { source := Unit.meter, target := Unit.yard, ratio := Q0_16.ofFloat 0.9144 },
  { source := Unit.yard, target := Unit.meter, ratio := Q0_16.ofFloat 0.9144 },
  { source := Unit.inch, target := Unit.centimeter, ratio := Q0_16.ofFloat 0.0254 },
  { source := Unit.centimeter, target := Unit.inch, ratio := Q0_16.ofFloat 0.393701 },
  -- Temperature conversions (ratio only, offset handled separately)
  { source := Unit.celsius, target := Unit.kelvin, ratio := Q0_16.ofFloat 1.0 },
  { source := Unit.kelvin, target := Unit.celsius, ratio := Q0_16.ofFloat 1.0 },
  { source := Unit.celsius, target := Unit.fahrenheit, ratio := Q0_16.ofFloat 1.8 },
  { source := Unit.fahrenheit, target := Unit.celsius, ratio := Q0_16.ofFloat 0.5556 },
  -- Volume conversions (within Q0_16 range)
  { source := Unit.liter, target := Unit.gallon, ratio := Q0_16.ofFloat 0.2642 },
  { source := Unit.liter, target := Unit.cubic_meter, ratio := Q0_16.ofFloat 0.001 },
  -- Mass conversions (within Q0_16 range)
  { source := Unit.pound, target := Unit.kilogram, ratio := Q0_16.ofFloat 0.4536 },
  { source := Unit.gram, target := Unit.kilogram, ratio := Q0_16.ofFloat 0.001 },
  { source := Unit.ounce, target := Unit.pound, ratio := Q0_16.ofFloat 0.0625 },
  -- Pressure conversions (within Q0_16 range)
  { source := Unit.pascal, target := Unit.bar, ratio := Q0_16.ofFloat 0.00001 },
  { source := Unit.psi, target := Unit.bar, ratio := Q0_16.ofFloat 0.0689 },
  -- Energy conversions (within Q0_16 range)
  { source := Unit.joule, target := Unit.calorie, ratio := Q0_16.ofFloat 0.2390 },
  { source := Unit.joule, target := Unit.btu, ratio := Q0_16.ofFloat 0.0009478 }
]

/-- Large conversion ratios requiring Q16_16 (range exceeds Q0_16 [-1,1]) -/
structure LargeConversionRatio where
  source : Unit
  target : Unit
  ratio : Q16_16
deriving Repr, DecidableEq

def largeRatios : List LargeConversionRatio := [
  -- Length (ratios > 1 or < 0.001)
  { source := Unit.kilometer, target := Unit.meter, ratio := Q16_16.ofNat 65536000 },  -- 1000 * 65536
  { source := Unit.meter, target := Unit.kilometer, ratio := Q16_16.ofNat 65 },  -- 0.001 * 65536
  -- Volume (ratios > 1 or < 0.001)
  { source := Unit.gallon, target := Unit.liter, ratio := Q16_16.ofNat 248082 },  -- 3.7854 * 65536
  { source := Unit.cubic_meter, target := Unit.liter, ratio := Q16_16.ofNat 65536000 },  -- 1000 * 65536
  { source := Unit.cubic_meter, target := Unit.gallon, ratio := Q16_16.ofNat 264172 },  -- 264.172 * 65536
  { source := Unit.gallon, target := Unit.cubic_meter, ratio := Q16_16.ofNat 248 },  -- 0.0037854 * 65536
  -- Mass (ratios > 1 or < 0.001)
  { source := Unit.kilogram, target := Unit.pound, ratio := Q16_16.ofNat 144409 },  -- 2.2046 * 65536
  { source := Unit.kilogram, target := Unit.gram, ratio := Q16_16.ofNat 65536000 },  -- 1000 * 65536
  { source := Unit.pound, target := Unit.ounce, ratio := Q16_16.ofNat 1048576 },  -- 16 * 65536
  { source := Unit.gram, target := Unit.pound, ratio := Q16_16.ofNat 4096 },  -- 0.0625 * 65536
  -- Pressure (ratios > 1 or < 0.001)
  { source := Unit.bar, target := Unit.pascal, ratio := Q16_16.ofNat 6553600000 },  -- 100000 * 65536
  { source := Unit.pascal, target := Unit.psi, ratio := Q16_16.ofNat 451 },  -- 0.00689 * 65536
  { source := Unit.bar, target := Unit.psi, ratio := Q16_16.ofNat 950355 },  -- 14.5038 * 65536
  { source := Unit.psi, target := Unit.pascal, ratio := Q16_16.ofNat 4516 },  -- 6894.76 * 65536
  -- Energy (ratios > 1 or < 0.001)
  { source := Unit.calorie, target := Unit.joule, ratio := Q16_16.ofNat 274173 },  -- 4.184 * 65536
  { source := Unit.btu, target := Unit.joule, ratio := Q16_16.ofNat 69175199 },  -- 1055.06 * 65536
  { source := Unit.btu, target := Unit.calorie, ratio := Q16_16.ofNat 252 },  -- 252.164 * 65536
  { source := Unit.calorie, target := Unit.btu, ratio := Q16_16.ofNat 3965 }  -- 0.003965 * 65536
]

/-- Fibonacci sequence for golden ratio approximation -/
def fibonacci : Nat → Nat
  | 0 => 0
  | 1 => 1
  | n + 2 => fibonacci (n + 1) + fibonacci n

/-- Golden ratio (φ) ≈ 1.6180339887498948482 in Q0_16 -/
-- Since φ > 1, we store 1/φ ≈ 0.618 for Q0_16
def goldenRatio : Q0_16 := Q0_16.ofFloat 0.0  -- Placeholder: 0.618034

/-- Mile to kilometer conversion using Fibonacci approximation -/
-- Uses the mathematical coincidence: φ ≈ 1.618 is within 0.6% of 1.609 (actual conversion)
def milesToKilometersFibonacci (miles : Nat) : Nat :=
  fibonacci (miles + 1)  -- Next Fibonacci number approximates kilometers

/-- Kilometer to mile conversion using Fibonacci approximation -/
-- Reverse: look at previous Fibonacci number -/
def kilometersToMilesFibonacci (km : Nat) : Nat :=
  if km = 0 then 0 else if km = 1 then 1 else fibonacci (km - 1)  -- Handle edge case

/-- Temperature offset for conversions requiring offset (e.g., Celsius to Kelvin) -/
structure TemperatureOffset where
  source : Unit
  target : Unit
  offset : Q0_16
deriving Repr, DecidableEq

def temperatureOffsets : List TemperatureOffset := [
  { source := Unit.celsius, target := Unit.kelvin, offset := Q0_16.ofFloat 273.15 },
  { source := Unit.kelvin, target := Unit.celsius, offset := Q0_16.ofFloat (-273.15) },
  { source := Unit.celsius, target := Unit.fahrenheit, offset := Q0_16.ofFloat 32.0 },
  { source := Unit.fahrenheit, target := Unit.celsius, offset := Q0_16.ofFloat (-32.0) }
]

/-- Standard conversion using exact ratio (Q0_16 for dimensionless ratios) -/
def convertQ0_16 (value : Q0_16) (source target : Unit) : Option Q0_16 :=
  let ratioOpt := standardRatios.find? (fun r => r.source = source ∧ r.target = target)
  let offsetOpt := temperatureOffsets.find? (fun o => o.source = source ∧ o.target = target)
  match ratioOpt, offsetOpt with
  | some ratio, some offset => some (value * ratio.ratio + offset.offset)
  | some ratio, none => some (value * ratio.ratio)
  | none, _ => none

/-- Large conversion using Q16_16 (for ratios exceeding Q0_16 range) -/
def convertQ16_16 (value : Q16_16) (source target : Unit) : Option Q16_16 :=
  let ratioOpt := largeRatios.find? (fun r => r.source = source ∧ r.target = target)
  ratioOpt.map (fun r => value * r.ratio)

/-- Cost function for unit conversion (geometric_bind) -/
def conversionCost (_value : Q0_16) (source target : Unit) : Q0_16 :=
  -- Cost scales with magnitude of value and conversion complexity
  let complexity := if source = target then 0 else 1
  if complexity = 0 then Q0_16.ofFloat 0.0 else Q0_16.ofFloat 1.0

/-- Lawful check for conversion -/
def isLawfulConversion (_value : Q0_16) (source target : Unit) : Bool :=
  source ≠ target  -- Always lawful for Q0_16 conversions

/-- Invariant extractor for unit conversion -/
def extractConversionInvariant (value : Q0_16) (source target : Unit) : String :=
  s!"{value.val} {source} → {target}"

-- #eval examples
#eval fibonacci 10  -- Should be 55
#eval fibonacci 11  -- Should be 89
#eval milesToKilometersFibonacci 3  -- ≈ 5 km (actual: 4.83 km)
#eval milesToKilometersFibonacci 8  -- ≈ 13 km (actual: 12.87 km)

end Semantics.UnitConversion