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{-# LANGUAGE GADTs #-}
{-# LANGUAGE StandaloneDeriving #-}
{-# LANGUAGE UnicodeSyntax #-}
module Hkl.Lattice ( Lattice(..)
, Cubic
, Tetragonal
, Orthorhombic
, Rhombohedral
, Hexagonal
, Monoclinic
, Triclinic
) where
import Numeric.Units.Dimensional.Prelude (Length, Angle)
-- | Lattice
data Cubic
data Tetragonal
data Orthorhombic
data Rhombohedral
data Hexagonal
data Monoclinic
data Triclinic
data Lattice a where
-- ^ a = b = c, alpha = beta = gamma = 90
Cubic ∷ Length Double
→ Lattice Cubic -- ^ a = b = c, alpha = beta = gamma = 90
-- a = b != c, alpha = beta = gamma = 90
Tetragonal ∷ (Length Double) -- ^ a, b
→ (Length Double) -- ^ c
→ Lattice Tetragonal
-- ^ a != b != c, alpha = beta = gamma = 90
Orthorhombic ∷ (Length Double) -- ^ a
→ (Length Double) -- ^ b
→ (Length Double) -- ^ c
→ Lattice Orthorhombic
-- ^ a = b = c, alpha = beta = gamma != 90
Rhombohedral ∷ (Length Double) -- ^ a, b, c
→ (Angle Double) -- ^ alpha, beta, gamma
→ Lattice Rhombohedral
-- ^ a = b != c, alpha = beta = 90, gamma = 120
Hexagonal ∷ (Length Double) -- ^ a, b
→ (Length Double) -- ^ c
→ Lattice Hexagonal
-- a != b != c, alpha = gamma = 90, beta != 90
Monoclinic ∷ (Length Double) -- ^ a
→ (Length Double) -- ^ b
→ (Length Double) -- ^ c
→ (Angle Double) -- ^ beta
→ Lattice Monoclinic
-- a != b != c, alpha != beta != gamma != 90
Triclinic ∷ (Length Double)
→ (Length Double) -- ^ b
→ (Length Double) -- ^ c
→ (Angle Double) -- ^ alpha
→ (Angle Double) -- ^ beta
→ (Angle Double) -- ^ gamma
→ Lattice Triclinic
deriving instance Show (Lattice a)
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