progress progress #3

progress progress #3

open import Nat
open import Prelude
open import List
open import core
open import contexts
open import lemmas-consistency
open import canonical-boxed-forms

module progress where
  -- this is a little bit of syntactic sugar to avoid many layer nested Inl
  -- and Inrs that you would get from the more literal transcription of the
  -- consequent of progress as:
  --
  -- d boxedval + d indet + d casterr[ Δ ] + Σ[ d' ∈ dhexp ] (d ↦ d')
  data ok : (d : dhexp) (Δ : hctx) → Set where
    S : ∀{d Δ} → Σ[ d' ∈ dhexp ] (d ↦ d') → ok d Δ
    E : ∀{d Δ} → d casterr → ok d Δ
    I : ∀{d Δ} → d indet → ok d Δ
    V : ∀{d Δ} → d boxedval → ok d Δ

  progress : {Δ : hctx} {d : dhexp} {τ : htyp} →
             Δ , ∅ ⊢ d :: τ →
             ok d Δ
  -- constants
  progress TAConst = V (BVVal VConst)

  -- variables
  progress (TAVar x₁) = abort (somenotnone (! x₁))

  -- lambdas
  progress (TALam wt) = V (BVVal VLam)

  -- applications
  progress (TAAp wt1 wt2)
    with progress wt1 | progress wt2
    -- if the left steps, the whole thing steps
  progress (TAAp wt1 wt2) | S (_ , Step x y z) | _ = S (_ , Step (FHAp1 x) y (FHAp1 z))
    -- if the left is an error, the whole thing is an error
  progress (TAAp wt1 wt2) | E x | _ = E (CECong (FHAp1 FHOuter) x)
    -- if the left is indeterminate, inspect the right
  progress (TAAp wt1 wt2) | I i | S (_ , Step x y z) = S (_ , Step (FHAp2 (FIndet i) x) y (FHAp2 (FIndet i) z))
  progress (TAAp wt1 wt2) | I x | E x₁ = E (CECong (FHAp2 (FIndet x) FHOuter) x₁)
  progress (TAAp wt1 wt2) | I x | I x₁ = I (IAp {!!} x (FIndet x₁)) -- cyrus
    where
    lem : ∀{ Δ d1 τ τ'} → Δ , ∅ ⊢ d1 :: (τ ==> τ') →
                          d1 indet →
                          ((τ1 τ2 τ3 τ4 : htyp) (d1' : dhexp) → d1 ≠ (d1' ⟨ τ1 ==> τ2 ⇒ τ3 ==> τ4 ⟩))
    lem (TACast wt TCRefl) (ICastArr x₃ ind) τ1 τ2 .τ1 .τ2 d refl = x₃ refl
    lem (TACast wt (TCArr x₂ x₃)) (ICastArr x₄ ind) τ1 τ2 τ3 τ' d refl = {!!}
  progress (TAAp wt1 wt2) | I x | V x₁ = I (IAp {!!} x (FBoxed x₁)) -- cyrus
    -- if the left is a boxed value, inspect the right
  progress (TAAp wt1 wt2) | V v | S (_ , Step x y z) = S (_ , Step (FHAp2 (FBoxed v) x) y (FHAp2 (FBoxed v) z))
  progress (TAAp wt1 wt2) | V v | E e = E (CECong (FHAp2 (FBoxed v) FHOuter) e)
  progress (TAAp wt1 wt2) | V v | I i = I (IAp {!!} {!!} (FIndet i)) -- cyrus (issue from above, and also i think missing a rule for indet applications)
  progress (TAAp wt1 wt2) | V v | V v₂ = {!!} -- {!canonical-boxed-forms-arr wt1 x !}

  -- empty holes
  progress (TAEHole x x₁) = I IEHole

  -- nonempty holes
  progress (TANEHole xin wt x₁)
    with progress wt
  ... | S (_ , Step x y z) = S (_ , Step (FHNEHole x) y (FHNEHole z))
  ... | E x = E (CECong (FHNEHole FHOuter) x)
  ... | I x = I (INEHole (FIndet x))
  ... | V x = I (INEHole (FBoxed x))

  -- casts
  progress (TACast wt con)
    with progress wt
  ... | S (_ , Step x y z) = S (_ , Step (FHCast x) y (FHCast z))
  ... | E x = E (CECong (FHCast FHOuter) x)
  ... | I x = I {!!}
  ... | V x = V {!!}

open import Nat
open import Prelude
open import List
open import core
open import contexts
open import lemmas-consistency

module progress where
  -- this is a little bit of syntactic sugar to avoid many layer nested Inl
  -- and Inrs that you would get from the more literal transcription of the
  -- consequent of progress as:
  --
  -- d boxedval + d indet + d casterr[ Δ ] + Σ[ d' ∈ dhexp ] (d ↦ d')
  data ok : (d : dhexp) (Δ : hctx) → Set where
    S : ∀{d Δ} → Σ[ d' ∈ dhexp ] (d ↦ d') → ok d Δ
    E : ∀{d Δ} → d casterr → ok d Δ
    I : ∀{d Δ} → d indet → ok d Δ
    V : ∀{d Δ} → d boxedval → ok d Δ

  progress : {Δ : hctx} {d : dhexp} {τ : htyp} →
             Δ , ∅ ⊢ d :: τ →
             ok d Δ
  -- constants
  progress TAConst = V (BVVal VConst)

  -- variables
  progress (TAVar x₁) = abort (somenotnone (! x₁))

  -- lambdas
  progress (TALam wt) = V (BVVal VLam)

  -- applications
  progress (TAAp wt1 wt2)
    with progress wt1 | progress wt2
  progress (TAAp wt1 wt2) | S x | ih2 = {!!}
  progress (TAAp wt1 wt2) | E x | _ = E (CECong (FHAp1 FHOuter) x)
  progress (TAAp wt1 wt2) | I x | ih2 = {!!}
  progress (TAAp wt1 wt2) | V x | ih2 = {!!}

  -- empty holes
  progress (TAEHole x x₁) = I IEHole

  -- nonempty holes
  progress (TANEHole xin wt x₁)
    with progress wt
  ... | S (d' , Step x y z) = S (_ , Step {!!} {!!} {!!})
  ... | E x = E (CECong (FHNEHole FHOuter) x)
  ... | I x = I (INEHole (FIndet x))
  ... | V x = I (INEHole (FBoxed x))

  -- casts
  progress (TACast wt y)
    with progress wt
  ... | S x = {!!}
  ... | E x = E (CECong (FHCast FHOuter) x)
  ... | I x = {!x!}
  ... | V x = {!!}

  -- -- applications
  -- progress (TAAp D1 x D2)
  --   with progress D1 | progress D2
  --   -- left applicand value
  -- progress (TAAp TAConst () D2) | V VConst | _
  -- progress (TAAp {d2 = d2} D1 MAArr D2) | V (VLam {x = x} {d = d}) | V x₁ = S ([ d2 / x ] d , Step (FHAp1 (FVal VLam) {!!}) (ITLam (FVal x₁)) {!!} )
  -- progress (TAAp {d2 = d2} D1 MAArr D2) | V (VLam {x = x} {d = d}) | I x₁ = S ([ d2 / x ] d , Step (FHAp1 (FVal VLam) {!!}) (ITLam (FIndet x₁)) {!!} )
  --   -- errors propagate
  -- progress (TAAp D1 x₂ D2) | V x | E x₁ = E (EAp2 (FVal x) x₁)
  -- progress (TAAp D1 x₂ D2) | I x | E x₁ = E (EAp2 (FIndet x) x₁)
  -- progress (TAAp D1 x₂ D2) | E x | E x₁ = E (EAp1 x) -- NB: could have picked the other one here, too; this is a source of non-determinism
  -- progress (TAAp D1 x₂ D2) | S x | E x₁ = S {!!}
  -- progress (TAAp D1 x₂ D2) | E x | _    = E (EAp1 x)
  --   -- indeterminates
  -- progress (TAAp D1 x₂ D2) | I i | V v = I (IAp i  (FVal v))
  -- progress (TAAp D1 x₂ D2) | I x | I x₁ = I (IAp x (FIndet x₁))
  --   -- either applicand steps
  -- progress (TAAp D1 x₃ D2) | S (d1' , Step x x₁ x₂)  | _ = S (_ , Step (FHAp2 x) x₁ (FHAp2 x₂))
  -- progress (TAAp D1 x₄ D2) | _ | S (d2' , Step x₁ x₂ x₃) = S (_ , Step (FHAp1 {!!} x₁) x₂ (FHAp1 {!!} x₃))

  -- -- non-empty holes
  -- progress (TANEHole x D x₁)
  --   with progress D
  -- progress (TANEHole x₁ D x₂) | V v = I (INEHole (FVal v))
  -- progress (TANEHole x₁ D x₂) | I x = I (INEHole (FIndet x))
  -- progress (TANEHole x₁ D x₂) | E x = E (ENEHole x)
  -- progress (TANEHole x₃ D x₄) | S (_ , Step x x₁ x₂) = S (_ , Step (FHNEHole x) x₁ (FHNEHole x₂))

  -- -- casts
  -- progress (TACast D x)
  --   with progress D
  -- progress (TACast TAConst con) | V VConst = S (c , Step (FHCastFinal (FVal VConst)) (ITCast (FVal VConst) TAConst con) (FHFinal (FVal VConst)))
  -- progress (TACast D m)  | V VLam = S (_ , Step (FHCastFinal (FVal VLam)) (ITCast (FVal VLam) D m) (FHFinal (FVal VLam)))
  -- progress (TACast D x₁) | I x = I (ICast x)
  -- progress (TACast D x₁) | E x = E (ECastProp x)
  -- progress (TACast D x₃) | S (d , Step x x₁ x₂) = S (_ , Step (FHCast x) x₁ (FHCast x₂))


Rename diff to diff-base.

Rename diff to diff-base.

I want to move code between Parametric.Syntax.Term and
Atlas.Syntax.Term, but I have to unify the naming conventions first.

Old-commit-hash: 73a829a379ce12d2c01dbaf184ae2d380ad9abb1

import Parametric.Syntax.Type as Type
import Parametric.Syntax.Term as Term
import Parametric.Change.Type as ChangeType

module Parametric.Change.Term
    {Base : Set}
    (Constant : Term.Structure Base)
    (ΔBase : ChangeType.Structure Base)
  where

-- Terms that operate on changes

open Type.Structure Base
open Term.Structure Base Constant
open ChangeType.Structure Base ΔBase

open import Data.Product

DiffStructure : Set
DiffStructure = ∀ {ι Γ} → Term Γ (base ι ⇒ base ι ⇒ base (ΔBase ι))

ApplyStructure : Set
ApplyStructure = ∀ {ι Γ} → Term Γ (ΔType (base ι) ⇒ base ι ⇒ base ι)

module Structure where

  -- g ⊝ f  = λ x . λ Δx . g (x ⊕ Δx) ⊝ f x
  -- f ⊕ Δf = λ x . f x ⊕ Δf x (x ⊝ x)

  lift-diff-apply :
    DiffStructure →
    ApplyStructure →
    ∀ {τ Γ} →
      Term Γ (τ ⇒ τ ⇒ ΔType τ) × Term Γ (ΔType τ ⇒ τ ⇒ τ)

  lift-diff-apply diff-base apply {base ι} = diff-base , apply
  lift-diff-apply diff-base apply {σ ⇒ τ} =
    let
      -- for diff
      g  = var (that (that (that this)))
      f  = var (that (that this))
      x  = var (that this)
      Δx = var this
      -- for apply
      Δh = var (that (that this))
      h  = var (that this)
      y  = var this
      -- syntactic sugars
      diffσ  = λ {Γ} → proj₁ (lift-diff-apply diff-base apply {σ} {Γ})
      diffτ  = λ {Γ} → proj₁ (lift-diff-apply diff-base apply {τ} {Γ})
      applyσ = λ {Γ} → proj₂ (lift-diff-apply diff-base apply {σ} {Γ})
      applyτ = λ {Γ} → proj₂ (lift-diff-apply diff-base apply {τ} {Γ})
      _⊝σ_ = λ s t  → app (app diffσ s) t
      _⊝τ_ = λ s t  → app (app diffτ s) t
      _⊕σ_ = λ t Δt → app (app applyσ Δt) t
      _⊕τ_ = λ t Δt → app (app applyτ Δt) t
    in
      abs (abs (abs (abs (app f (x ⊕σ Δx) ⊝τ app g x))))
      ,
      abs (abs (abs (app h y ⊕τ app (app Δh y) (y ⊝σ y))))

  lift-diff :
    DiffStructure →
    ApplyStructure →
    ∀ {τ Γ} → Term Γ (τ ⇒ τ ⇒ ΔType τ)

  lift-diff diff-base apply = λ {τ Γ} →
    proj₁ (lift-diff-apply diff-base apply {τ} {Γ})

  lift-apply :
    DiffStructure →
    ApplyStructure →
    ∀ {τ Γ} → Term Γ (ΔType τ ⇒ τ ⇒ τ)

  lift-apply diff-base apply = λ {τ Γ} →
    proj₂ (lift-diff-apply diff-base apply {τ} {Γ})

import Parametric.Syntax.Type as Type
import Parametric.Syntax.Term as Term
import Parametric.Change.Type as ChangeType

module Parametric.Change.Term
    {Base : Set}
    (Constant : Term.Structure Base)
    (ΔBase : ChangeType.Structure Base)
  where

-- Terms that operate on changes

open Type.Structure Base
open Term.Structure Base Constant
open ChangeType.Structure Base ΔBase

open import Data.Product

DiffStructure : Set
DiffStructure = ∀ {ι Γ} → Term Γ (base ι ⇒ base ι ⇒ base (ΔBase ι))

ApplyStructure : Set
ApplyStructure = ∀ {ι Γ} → Term Γ (ΔType (base ι) ⇒ base ι ⇒ base ι)

module Structure where

  -- g ⊝ f  = λ x . λ Δx . g (x ⊕ Δx) ⊝ f x
  -- f ⊕ Δf = λ x . f x ⊕ Δf x (x ⊝ x)

  lift-diff-apply :
    DiffStructure →
    ApplyStructure →
    ∀ {τ Γ} →
      Term Γ (τ ⇒ τ ⇒ ΔType τ) × Term Γ (ΔType τ ⇒ τ ⇒ τ)

  lift-diff-apply diff apply {base ι} = diff , apply
  lift-diff-apply diff apply {σ ⇒ τ} =
    let
      -- for diff
      g  = var (that (that (that this)))
      f  = var (that (that this))
      x  = var (that this)
      Δx = var this
      -- for apply
      Δh = var (that (that this))
      h  = var (that this)
      y  = var this
      -- syntactic sugars
      diffσ  = λ {Γ} → proj₁ (lift-diff-apply diff apply {σ} {Γ})
      diffτ  = λ {Γ} → proj₁ (lift-diff-apply diff apply {τ} {Γ})
      applyσ = λ {Γ} → proj₂ (lift-diff-apply diff apply {σ} {Γ})
      applyτ = λ {Γ} → proj₂ (lift-diff-apply diff apply {τ} {Γ})
      _⊝σ_ = λ s t  → app (app diffσ s) t
      _⊝τ_ = λ s t  → app (app diffτ s) t
      _⊕σ_ = λ t Δt → app (app applyσ Δt) t
      _⊕τ_ = λ t Δt → app (app applyτ Δt) t
    in
      abs (abs (abs (abs (app f (x ⊕σ Δx) ⊝τ app g x))))
      ,
      abs (abs (abs (app h y ⊕τ app (app Δh y) (y ⊝σ y))))

  lift-diff :
    DiffStructure →
    ApplyStructure →
    ∀ {τ Γ} → Term Γ (τ ⇒ τ ⇒ ΔType τ)

  lift-diff diff apply = λ {τ Γ} →
    proj₁ (lift-diff-apply diff apply {τ} {Γ})

  lift-apply :
    DiffStructure →
    ApplyStructure →
    ∀ {τ Γ} → Term Γ (ΔType τ ⇒ τ ⇒ τ)

  lift-apply diff apply = λ {τ Γ} →
    proj₂ (lift-diff-apply diff apply {τ} {Γ})


Finish Greek Unicode 0370-03FF (partial).

module Text.Greek.Script where

open import Data.Maybe
open import Data.Vec
open import Relation.Nullary using (¬_)
open import Relation.Binary.PropositionalEquality using (_≢_)

data Case : Set where
  lower upper : Case

data Letter : Set where
  α′ β′ γ′ δ′ ε′ ζ′ η′ θ′ ι′ κ′ λ′ μ′ ν′ ξ′ ο′ π′ ρ′ σ′ τ′ υ′ φ′ χ′ ψ′ ω′ : Letter

vowels : Vec _ _
vowels = α′ ∷ ε′ ∷ η′ ∷ ι′ ∷ ο′ ∷ υ′ ∷ ω′ ∷ []

always-short-letters : Vec _ _
always-short-letters = ε′ ∷ ο′ ∷ []

diaeresis-letters : Vec _ _
diaeresis-letters = ι′ ∷ υ′ ∷ []

iota-subscript-letters : Vec _ _
iota-subscript-letters = α′ ∷ η′ ∷ ω′ ∷ []

data _vowel : Letter → Set where
  is-vowel : ∀ {v} → v ∈ vowels → v vowel

data _always-short : Letter → Set where
  is-always-short : ∀ {v} → ⦃ p : v vowel ⦄ → v ∈ always-short-letters → v always-short

data _diaeresis : Letter → Set where
  add-diaeresis : ∀ {v} → ⦃ p : v vowel ⦄ → v ∈ diaeresis-letters → v diaeresis

data _⟦_⟧-final : Letter → Case → Set where
  make-final : σ′ ⟦ lower ⟧-final

data _⟦_⟧-smooth : Letter → Case → Set where
  add-smooth-lower-vowel : ∀ {v} → ⦃ p : v vowel ⦄ → v ⟦ lower ⟧-smooth
  add-smooth-ρ : ρ′ ⟦ lower ⟧-smooth
  add-smooth-upper-vowel-not-Υ : ∀ {v} → ⦃ p : v vowel ⦄ → v ≢ υ′ → v ⟦ upper ⟧-smooth

data _with-rough : Letter → Set where
  add-rough-vowel : ∀ {v} → ⦃ p : v vowel ⦄ → v with-rough
  add-rough-ρ : ρ′ with-rough

data _iota-subscript : Letter → Set where
  add-iota-subscript : ∀ {v} → ⦃ p : v vowel ⦄ → v ∈ iota-subscript-letters → v iota-subscript

data _⟦_⟧-breathing : Letter → Case → Set where
  smooth : ∀ {ℓ c} → ⦃ p : ℓ ⟦ c ⟧-smooth ⦄ → ℓ ⟦ c ⟧-breathing
  rough : ∀ {ℓ c} → ⦃ p : ℓ with-rough ⦄ → ℓ ⟦ c ⟧-breathing

data _long-vowel : Letter → Set where
  make-long-vowel : ∀ {v} → ⦃ p : v vowel ⦄ → ¬ v always-short → v long-vowel

data _accent : Letter → Set where
  acute : ∀ {ℓ} → ⦃ p : ℓ vowel ⦄ → ℓ accent
  grave : ∀ {ℓ} → ⦃ p : ℓ vowel ⦄ → ℓ accent
  circumflex : ∀ {ℓ} → ⦃ p : ℓ long-vowel ⦄ → ℓ accent

data Token : Letter → Case → Set where
  unmarked : ∀ {ℓ c} → Token ℓ c
  with-accent : ∀ {ℓ c} → ℓ accent → Token ℓ c
  with-breathing : ∀ {ℓ c} → ℓ ⟦ c ⟧-breathing → Token ℓ c
  with-accent-breathing : ∀ {ℓ c} → ℓ accent → ℓ ⟦ c ⟧-breathing → Token ℓ c
  with-accent-breathing-iota : ∀ {ℓ c} → ℓ accent → ℓ ⟦ c ⟧-breathing → ⦃ p : ℓ iota-subscript ⦄ → Token ℓ c
  with-diaeresis : ∀ {ℓ c} → ⦃ p : ℓ diaeresis ⦄ → Token ℓ c
  with-accent-diaeresis : ∀ {ℓ c} → ℓ accent → ⦃ p : ℓ diaeresis ⦄ → Token ℓ c
  with-accent-iota : ∀ {ℓ c} → ℓ accent → ⦃ p : ℓ iota-subscript ⦄ → Token ℓ c
  with-breathing-iota : ∀ {ℓ c} → ℓ ⟦ c ⟧-breathing → ⦃ p : ℓ iota-subscript ⦄ → Token ℓ c
  with-iota : ∀ {ℓ c} → ⦃ p : ℓ iota-subscript ⦄ → Token ℓ c
  final : ∀ {ℓ c} → ⦃ p : ℓ ⟦ c ⟧-final ⦄ → Token ℓ c

-- Constructions

-- Α α
instance α-vowel : α′ vowel
α-vowel = is-vowel here

¬α-always-short : ¬ α′ always-short
¬α-always-short (is-always-short (there (there ())))

instance α-long-vowel : α′ long-vowel
α-long-vowel = make-long-vowel ¬α-always-short

instance α-smooth : α′ ⟦ lower ⟧-smooth
α-smooth = add-smooth-lower-vowel

instance Α-smooth : α′ ⟦ upper ⟧-smooth
Α-smooth = add-smooth-upper-vowel-not-Υ (λ ())

instance α-rough : α′ with-rough
α-rough = add-rough-vowel

instance α-iota-subscript : α′ iota-subscript
α-iota-subscript = add-iota-subscript here

-- Ε ε
instance ε-vowel : ε′ vowel
ε-vowel = is-vowel (there here)

ε-always-short : ε′ always-short
ε-always-short = is-always-short here

instance ε-smooth : ε′ ⟦ lower ⟧-smooth
ε-smooth = add-smooth-lower-vowel

instance Ε-smooth : ε′ ⟦ upper ⟧-smooth
Ε-smooth = add-smooth-upper-vowel-not-Υ (λ ())

instance ε-rough : ε′ with-rough
ε-rough = add-rough-vowel

-- Η η
instance η-vowel : η′ vowel
η-vowel = is-vowel (there (there here))

¬η-always-short : ¬ η′ always-short
¬η-always-short (is-always-short (there (there ())))

instance η-long-vowel : η′ long-vowel
η-long-vowel = make-long-vowel ¬η-always-short

instance η-smooth : η′ ⟦ lower ⟧-smooth
η-smooth = add-smooth-lower-vowel

instance Η-smooth : η′ ⟦ upper ⟧-smooth
Η-smooth = add-smooth-upper-vowel-not-Υ (λ ())

instance η-rough : η′ with-rough
η-rough = add-rough-vowel

instance η-iota-subscript : η′ iota-subscript
η-iota-subscript = add-iota-subscript (there here)

-- Ι ι

instance ι-vowel : ι′ vowel
ι-vowel = is-vowel (there (there (there here)))

¬ι-always-short : ¬ ι′ always-short
¬ι-always-short (is-always-short (there (there ())))

instance ι-long-vowel : ι′ long-vowel
ι-long-vowel = make-long-vowel ¬ι-always-short

instance ι-smooth : ι′ ⟦ lower ⟧-smooth
ι-smooth = add-smooth-lower-vowel

instance Ι-smooth : ι′ ⟦ upper ⟧-smooth
Ι-smooth = add-smooth-upper-vowel-not-Υ (λ ())

instance ι-rough : ι′ with-rough
ι-rough = add-rough-vowel

instance ι-diaeresis : ι′ diaeresis
ι-diaeresis = add-diaeresis here

-- Ο ο
instance ο-vowel : ο′ vowel
ο-vowel = is-vowel (there (there (there (there here))))

ο-always-short : ο′ always-short
ο-always-short = is-always-short (there here)

instance ο-smooth : ο′ ⟦ lower ⟧-smooth
ο-smooth = add-smooth-lower-vowel

instance Ο-smooth : ο′ ⟦ upper ⟧-smooth
Ο-smooth = add-smooth-upper-vowel-not-Υ (λ ())

instance ο-rough : ο′ with-rough
ο-rough = add-rough-vowel

-- Ρ ρ
instance ρ-smooth : ρ′ ⟦ lower ⟧-smooth
ρ-smooth = add-smooth-ρ

instance ρ-rough : ρ′ with-rough
ρ-rough = add-rough-ρ

-- Σ σ
instance σ-final : σ′ ⟦ lower ⟧-final
σ-final = make-final

-- Υ υ
instance υ-vowel : υ′ vowel
υ-vowel = is-vowel (there (there (there (there (there here)))))

¬υ-always-short : ¬ υ′ always-short
¬υ-always-short (is-always-short (there (there ())))

instance υ-long-vowel : υ′ long-vowel
υ-long-vowel = make-long-vowel ¬υ-always-short

instance υ-smooth : υ′ ⟦ lower ⟧-smooth
υ-smooth = add-smooth-lower-vowel

instance υ-rough : υ′ with-rough
υ-rough = add-rough-vowel

instance υ-diaeresis : υ′ diaeresis
υ-diaeresis = add-diaeresis (there here)

-- Ω ω
instance ω-vowel : ω′ vowel
ω-vowel = is-vowel (there (there (there (there (there (there here))))))

¬ω-always-short : ¬ ω′ always-short
¬ω-always-short (is-always-short (there (there ())))

instance ω-long-vowel : ω′ long-vowel
ω-long-vowel = make-long-vowel ¬ω-always-short

instance ω-smooth : ω′ ⟦ lower ⟧-smooth
ω-smooth = add-smooth-lower-vowel

instance Ω-smooth : ω′ ⟦ upper ⟧-smooth
Ω-smooth = add-smooth-upper-vowel-not-Υ (λ ())

instance ω-rough : ω′ with-rough
ω-rough = add-rough-vowel

instance ω-iota-subscript : ω′ iota-subscript
ω-iota-subscript = add-iota-subscript (there (there here))

-- Unicode
-- U+0390 - U+03CE
ΐ : Token ι′ lower -- U+0390 GREEK SMALL LETTER IOTA WITH DIALYTIKA AND TONOS
ΐ = with-accent-diaeresis acute
Α : Token α′ upper -- U+0391 GREEK CAPITAL LETTER ALPHA
Α = unmarked
Β : Token β′ upper -- U+0392 GREEK CAPITAL LETTER BETA
Β = unmarked
Γ : Token γ′ upper -- U+0393 GREEK CAPITAL LETTER GAMMA
Γ = unmarked
Δ : Token δ′ upper -- U+0394 GREEK CAPITAL LETTER DELTA
Δ = unmarked
Ε : Token ε′ upper -- U+0395 GREEK CAPITAL LETTER EPSILON
Ε = unmarked
Ζ : Token ζ′ upper -- U+0396 GREEK CAPITAL LETTER ZETA
Ζ = unmarked
Η : Token η′ upper -- U+0397 GREEK CAPITAL LETTER ETA
Η = unmarked
Θ : Token θ′ upper -- U+0398 GREEK CAPITAL LETTER THETA
Θ = unmarked
Ι : Token ι′ upper -- U+0399 GREEK CAPITAL LETTER IOTA
Ι = unmarked
Κ : Token κ′ upper -- U+039A GREEK CAPITAL LETTER KAPPA
Κ = unmarked
Λ : Token λ′ upper -- U+039B GREEK CAPITAL LETTER LAMDA
Λ = unmarked
Μ : Token μ′ upper -- U+039C GREEK CAPITAL LETTER MU
Μ = unmarked
Ν : Token ν′ upper -- U+039D GREEK CAPITAL LETTER NU
Ν = unmarked
Ξ : Token ξ′ upper -- U+039E GREEK CAPITAL LETTER XI
Ξ = unmarked
Ο : Token ο′ upper -- U+039F GREEK CAPITAL LETTER OMICRON
Ο = unmarked
Π : Token π′ upper -- U+03A0 GREEK CAPITAL LETTER PI
Π = unmarked
Ρ : Token ρ′ upper -- U+03A1 GREEK CAPITAL LETTER RHO
Ρ = unmarked
                  -- U+03A2 <reserved>
Σ : Token σ′ upper -- U+03A3 GREEK CAPITAL LETTER SIGMA
Σ = unmarked
Τ : Token τ′ upper -- U+03A4 GREEK CAPITAL LETTER TAU
Τ = unmarked
Υ : Token υ′ upper -- U+03A5 GREEK CAPITAL LETTER UPSILON
Υ = unmarked
Φ : Token φ′ upper -- U+03A6 GREEK CAPITAL LETTER PHI
Φ = unmarked
Χ : Token χ′ upper -- U+03A7 GREEK CAPITAL LETTER CHI
Χ = unmarked
Ψ : Token ψ′ upper -- U+03A8 GREEK CAPITAL LETTER PSI
Ψ = unmarked
Ω : Token ω′ upper -- U+03A9 GREEK CAPITAL LETTER OMEGA
Ω = unmarked
Ϊ : Token ι′ upper -- U+03AA GREEK CAPITAL LETTER IOTA WITH DIALYTIKA
Ϊ = with-diaeresis
Ϋ : Token υ′ upper -- U+03AB GREEK CAPITAL LETTER UPSILON WITH DIALYTIKA
Ϋ = with-diaeresis
ά : Token α′ lower -- U+03AC GREEK SMALL LETTER ALPHA WITH TONOS
ά = with-accent acute
έ : Token ε′ lower -- U+03AD GREEK SMALL LETTER EPSILON WITH TONOS
έ = with-accent acute
ή : Token η′ lower -- U+03AE GREEK SMALL LETTER ETA WITH TONOS
ή = with-accent acute
ί : Token ι′ lower -- U+03AF GREEK SMALL LETTER IOTA WITH TONOS
ί = with-accent acute
ΰ : Token υ′ lower -- U+03B0 GREEK SMALL LETTER UPSILON WITH DIALYTIKA AND TONOS
ΰ = with-accent-diaeresis acute
α : Token α′ lower -- U+03B1 GREEK SMALL LETTER ALPHA
α = unmarked
β : Token β′ lower -- U+03B2 GREEK SMALL LETTER BETA
β = unmarked
γ : Token γ′ lower -- U+03B3 GREEK SMALL LETTER GAMMA
γ = unmarked
δ : Token δ′ lower -- U+03B4 GREEK SMALL LETTER DELTA
δ = unmarked
ε : Token ε′ lower -- U+03B5 GREEK SMALL LETTER EPSILON
ε = unmarked
ζ : Token ζ′ lower -- U+03B6 GREEK SMALL LETTER ZETA
ζ = unmarked
η : Token η′ lower -- U+03B7 GREEK SMALL LETTER ETA
η = unmarked
θ : Token θ′ lower -- U+03B8 GREEK SMALL LETTER THETA
θ = unmarked
ι : Token ι′ lower -- U+03B9 GREEK SMALL LETTER IOTA
ι = unmarked
κ : Token κ′ lower -- U+03BA GREEK SMALL LETTER KAPPA
κ = unmarked
∙λ : Token λ′ lower -- U+03BB GREEK SMALL LETTER LAMDA
∙λ = unmarked
μ : Token μ′ lower -- U+03BC GREEK SMALL LETTER MU
μ = unmarked
ν : Token ν′ lower -- U+03BD GREEK SMALL LETTER NU
ν = unmarked
ξ : Token ξ′ lower -- U+03BE GREEK SMALL LETTER XI
ξ = unmarked
ο : Token ο′ lower -- U+03BF GREEK SMALL LETTER OMICRON
ο = unmarked
π : Token π′ lower -- U+03C0 GREEK SMALL LETTER PI
π = unmarked
ρ : Token ρ′ lower -- U+03C1 GREEK SMALL LETTER RHO
ρ = unmarked
ς : Token σ′ lower -- U+03C2 GREEK SMALL LETTER FINAL SIGMA
ς = final
σ : Token σ′ lower -- U+03C3 GREEK SMALL LETTER SIGMA
σ = unmarked
τ : Token τ′ lower -- U+03C4 GREEK SMALL LETTER TAU
τ = unmarked
υ : Token υ′ lower -- U+03C5 GREEK SMALL LETTER UPSILON
υ = unmarked
φ : Token φ′ lower -- U+03C6 GREEK SMALL LETTER PHI
φ = unmarked
χ : Token χ′ lower -- U+03C7 GREEK SMALL LETTER CHI
χ = unmarked
ψ : Token ψ′ lower -- U+03C8 GREEK SMALL LETTER PSI
ψ = unmarked
ω : Token ω′ lower -- U+03C9 GREEK SMALL LETTER OMEGA
ω = unmarked
ϊ : Token ι′ lower -- U+03CA GREEK SMALL LETTER IOTA WITH DIALYTIKA
ϊ = with-diaeresis
ϋ : Token υ′ lower -- U+03CB GREEK SMALL LETTER UPSILON WITH DIALYTIKA
ϋ = with-diaeresis
ό : Token ο′ lower -- U+03CC GREEK SMALL LETTER OMICRON WITH TONOS
ό = with-accent acute
ύ : Token υ′ lower -- U+03CD GREEK SMALL LETTER UPSILON WITH TONOS
ύ = with-accent acute
ώ : Token ω′ lower -- U+03CE GREEK SMALL LETTER OMEGA WITH TONOS
ώ = with-accent acute

ἀ : Token α′ lower
ἀ = with-breathing smooth
ἁ : Token α′ lower
ἁ = with-breathing rough
ἂ : Token α′ lower
ἂ = with-accent-breathing grave smooth
ἃ : Token α′ lower
ἃ = with-accent-breathing grave rough
ἄ : Token α′ lower
ἄ = with-accent-breathing acute smooth
ἅ : Token α′ lower
ἅ = with-accent-breathing acute rough
ἆ : Token α′ lower
ἆ = with-accent-breathing circumflex smooth
ἇ : Token α′ lower
ἇ = with-accent-breathing circumflex rough
Ἀ : Token α′ upper
Ἀ = with-breathing smooth
Ἁ : Token α′ upper
Ἁ = with-breathing rough
Ἂ : Token α′ upper
Ἂ = with-accent-breathing grave smooth
Ἃ : Token α′ upper
Ἃ = with-accent-breathing grave rough
Ἄ : Token α′ upper
Ἄ = with-accent-breathing acute smooth
Ἅ : Token α′ upper
Ἅ = with-accent-breathing acute rough
Ἆ : Token α′ upper
Ἆ = with-accent-breathing circumflex smooth
Ἇ : Token α′ upper
Ἇ = with-accent-breathing circumflex rough

-- U+1F7x
ὰ : Token α′ lower
ὰ = with-accent grave
ά : Token α′ lower
ά = with-accent acute

-- U+1F8x
ᾀ : Token α′ lower
ᾀ = with-breathing-iota smooth
ᾁ : Token α′ lower
ᾁ = with-breathing-iota rough
ᾂ : Token α′ lower
ᾂ = with-accent-breathing-iota grave smooth
ᾃ : Token α′ lower
ᾃ = with-accent-breathing-iota grave rough
ᾄ : Token α′ lower
ᾄ = with-accent-breathing-iota acute smooth
ᾅ : Token α′ lower
ᾅ = with-accent-breathing-iota acute rough
ᾆ : Token α′ lower
ᾆ = with-accent-breathing-iota circumflex smooth
ᾇ : Token α′ lower
ᾇ = with-accent-breathing-iota circumflex rough
ᾈ : Token α′ upper
ᾈ = with-breathing-iota smooth
ᾉ : Token α′ upper
ᾉ = with-breathing-iota rough
ᾊ : Token α′ upper
ᾊ = with-accent-breathing-iota grave smooth
ᾋ : Token α′ upper
ᾋ = with-accent-breathing-iota grave rough
ᾌ : Token α′ upper
ᾌ = with-accent-breathing-iota acute smooth
ᾍ : Token α′ upper
ᾍ = with-accent-breathing-iota acute rough
ᾎ : Token α′ upper
ᾎ = with-accent-breathing-iota circumflex smooth
ᾏ : Token α′ upper
ᾏ = with-accent-breathing-iota circumflex rough

-- U+1FBx
-- ᾰ
-- ᾱ
ᾲ : Token α′ lower
ᾲ = with-accent-iota grave
ᾳ : Token α′ lower
ᾳ = with-iota
ᾴ : Token α′ lower
ᾴ = with-accent-iota acute
ᾶ : Token α′ lower
ᾶ = with-accent circumflex
ᾷ : Token α′ lower
ᾷ = with-accent-iota circumflex
-- Ᾰ
-- Ᾱ
Ὰ : Token α′ upper
Ὰ = with-accent grave
Ά : Token α′ upper
Ά = with-accent acute
ᾼ : Token α′ upper
ᾼ = with-iota

-- Mapping

data Accent : Set where
  acute-mark grave-mark circumflex-mark : Accent

letter-to-accent : ∀ {v} → v accent → Accent
letter-to-accent acute = acute-mark
letter-to-accent grave = grave-mark
letter-to-accent circumflex = circumflex-mark

get-accent : ∀ {ℓ c} → Token ℓ c → Maybe Accent
get-accent (with-accent a) = just (letter-to-accent a)
get-accent (with-accent-breathing a _) = just (letter-to-accent a)
get-accent (with-accent-breathing-iota a _) = just (letter-to-accent a)
get-accent (with-accent-diaeresis a) = just (letter-to-accent a)
get-accent (with-accent-iota a) = just (letter-to-accent a)
get-accent _ = nothing

data Breathing : Set where
  smooth-mark rough-mark : Breathing

letter-to-breathing : ∀ {ℓ c} → ℓ ⟦ c ⟧-breathing → Breathing
letter-to-breathing smooth = smooth-mark
letter-to-breathing rough = rough-mark

get-breathing : ∀ {ℓ c} → Token ℓ c → Maybe Breathing
get-breathing (with-breathing x) = just (letter-to-breathing x)
get-breathing (with-accent-breathing _ x) = just (letter-to-breathing x)
get-breathing (with-accent-breathing-iota _ x) = just (letter-to-breathing x)
get-breathing (with-breathing-iota x) = just (letter-to-breathing x)
get-breathing _ = nothing

data IotaSubscript : Set where
  iota-subscript-mark : IotaSubscript

get-iota-subscript : ∀ {ℓ c} → Token ℓ c → Maybe IotaSubscript
get-iota-subscript (with-accent-breathing-iota _ _) = just iota-subscript-mark
get-iota-subscript (with-accent-iota _) = just iota-subscript-mark
get-iota-subscript (with-breathing-iota _) = just iota-subscript-mark
get-iota-subscript _ = nothing

data Diaeresis : Set where
  diaeresis-mark : Diaeresis

get-diaeresis : ∀ {ℓ c} → Token ℓ c → Maybe Diaeresis
get-diaeresis with-diaeresis = just diaeresis-mark
get-diaeresis (with-accent-diaeresis _) = just diaeresis-mark
get-diaeresis _ = nothing

data FinalForm : Set where
  final-form : FinalForm

get-final-form : ∀ {ℓ c} → Token ℓ c → Maybe FinalForm
get-final-form final = just final-form
get-final-form _ = nothing

module Text.Greek.Script where

open import Data.Maybe
open import Data.Vec
open import Relation.Nullary using (¬_)
open import Relation.Binary.PropositionalEquality using (_≢_)

data Case : Set where
  lower upper : Case

data Letter : Set where
  α′ β′ γ′ δ′ ε′ ζ′ η′ θ′ ι′ κ′ λ′ μ′ ν′ ξ′ ο′ π′ ρ′ σ′ τ′ υ′ φ′ χ′ ψ′ ω′ : Letter

vowels : Vec _ _
vowels = α′ ∷ ε′ ∷ η′ ∷ ι′ ∷ ο′ ∷ υ′ ∷ ω′ ∷ []

always-short-letters : Vec _ _
always-short-letters = ε′ ∷ ο′ ∷ []

diaeresis-letters : Vec _ _
diaeresis-letters = ι′ ∷ υ′ ∷ []

iota-subscript-letters : Vec _ _
iota-subscript-letters = α′ ∷ η′ ∷ ω′ ∷ []

data _vowel : Letter → Set where
  is-vowel : ∀ {v} → v ∈ vowels → v vowel

data _always-short : Letter → Set where
  is-always-short : ∀ {v} → ⦃ p : v vowel ⦄ → v ∈ always-short-letters → v always-short

data _diaeresis : Letter → Set where
  add-diaeresis : ∀ {v} → ⦃ p : v vowel ⦄ → v ∈ diaeresis-letters → v diaeresis

data _⟦_⟧-final : Letter → Case → Set where
  make-final : σ′ ⟦ lower ⟧-final

data _⟦_⟧-smooth : Letter → Case → Set where
  add-smooth-lower-vowel : ∀ {v} → ⦃ p : v vowel ⦄ → v ⟦ lower ⟧-smooth
  add-smooth-ρ : ρ′ ⟦ lower ⟧-smooth
  add-smooth-upper-vowel-not-Υ : ∀ {v} → ⦃ p : v vowel ⦄ → v ≢ υ′ → v ⟦ upper ⟧-smooth

data _with-rough : Letter → Set where
  add-rough-vowel : ∀ {v} → ⦃ p : v vowel ⦄ → v with-rough
  add-rough-ρ : ρ′ with-rough

data _iota-subscript : Letter → Set where
  add-iota-subscript : ∀ {v} → ⦃ p : v vowel ⦄ → v ∈ iota-subscript-letters → v iota-subscript

data _⟦_⟧-breathing : Letter → Case → Set where
  smooth : ∀ {ℓ c} → ⦃ p : ℓ ⟦ c ⟧-smooth ⦄ → ℓ ⟦ c ⟧-breathing
  rough : ∀ {ℓ c} → ⦃ p : ℓ with-rough ⦄ → ℓ ⟦ c ⟧-breathing

data _long-vowel : Letter → Set where
  make-long-vowel : ∀ {v} → ⦃ p : v vowel ⦄ → ¬ v always-short → v long-vowel

data _accent : Letter → Set where
  acute : ∀ {ℓ} → ⦃ p : ℓ vowel ⦄ → ℓ accent
  grave : ∀ {ℓ} → ⦃ p : ℓ vowel ⦄ → ℓ accent
  circumflex : ∀ {ℓ} → ⦃ p : ℓ long-vowel ⦄ → ℓ accent

data Token : Letter → Case → Set where
  unmarked : ∀ {ℓ c} → Token ℓ c
  with-accent : ∀ {ℓ c} → ℓ accent → Token ℓ c
  with-breathing : ∀ {ℓ c} → ℓ ⟦ c ⟧-breathing → Token ℓ c
  with-accent-breathing : ∀ {ℓ c} → ℓ accent → ℓ ⟦ c ⟧-breathing → Token ℓ c
  with-accent-breathing-iota : ∀ {ℓ c} → ℓ accent → ℓ ⟦ c ⟧-breathing → ⦃ p : ℓ iota-subscript ⦄ → Token ℓ c
  with-diaeresis : ∀ {ℓ c} → ⦃ p : ℓ diaeresis ⦄ → Token ℓ c
  with-accent-diaeresis : ∀ {ℓ c} → ℓ accent → ⦃ p : ℓ diaeresis ⦄ → Token ℓ c
  with-accent-iota : ∀ {ℓ c} → ℓ accent → ⦃ p : ℓ iota-subscript ⦄ → Token ℓ c
  with-breathing-iota : ∀ {ℓ c} → ℓ ⟦ c ⟧-breathing → ⦃ p : ℓ iota-subscript ⦄ → Token ℓ c
  with-iota : ∀ {ℓ c} → ⦃ p : ℓ iota-subscript ⦄ → Token ℓ c
  final : ∀ {ℓ c} → ⦃ p : ℓ ⟦ c ⟧-final ⦄ → Token ℓ c

-- Constructions

-- Α α
instance α-vowel : α′ vowel
α-vowel = is-vowel here

¬α-always-short : ¬ α′ always-short
¬α-always-short (is-always-short (there (there ())))

instance α-long-vowel : α′ long-vowel
α-long-vowel = make-long-vowel ¬α-always-short

instance α-smooth : α′ ⟦ lower ⟧-smooth
α-smooth = add-smooth-lower-vowel

instance Α-smooth : α′ ⟦ upper ⟧-smooth
Α-smooth = add-smooth-upper-vowel-not-Υ (λ ())

instance α-rough : α′ with-rough
α-rough = add-rough-vowel

instance α-iota-subscript : α′ iota-subscript
α-iota-subscript = add-iota-subscript here

-- Ε ε
instance ε-vowel : ε′ vowel
ε-vowel = is-vowel (there here)

ε-always-short : ε′ always-short
ε-always-short = is-always-short here

instance ε-smooth : ε′ ⟦ lower ⟧-smooth
ε-smooth = add-smooth-lower-vowel

instance Ε-smooth : ε′ ⟦ upper ⟧-smooth
Ε-smooth = add-smooth-upper-vowel-not-Υ (λ ())

instance ε-rough : ε′ with-rough
ε-rough = add-rough-vowel

-- Η η
instance η-vowel : η′ vowel
η-vowel = is-vowel (there (there here))

¬η-always-short : ¬ η′ always-short
¬η-always-short (is-always-short (there (there ())))

instance η-long-vowel : η′ long-vowel
η-long-vowel = make-long-vowel ¬η-always-short

instance η-smooth : η′ ⟦ lower ⟧-smooth
η-smooth = add-smooth-lower-vowel

instance Η-smooth : η′ ⟦ upper ⟧-smooth
Η-smooth = add-smooth-upper-vowel-not-Υ (λ ())

instance η-rough : η′ with-rough
η-rough = add-rough-vowel

η-iota-subscript : η′ iota-subscript
η-iota-subscript = add-iota-subscript (there here)

-- Ι ι

instance ι-vowel : ι′ vowel
ι-vowel = is-vowel (there (there (there here)))

¬ι-always-short : ¬ ι′ always-short
¬ι-always-short (is-always-short (there (there ())))

instance ι-long-vowel : ι′ long-vowel
ι-long-vowel = make-long-vowel ¬ι-always-short

ι-not-υ : ι′ ≢ υ′
ι-not-υ ()

instance ι-smooth : ι′ ⟦ lower ⟧-smooth
ι-smooth = add-smooth-lower-vowel

instance Ι-smooth : ι′ ⟦ upper ⟧-smooth
Ι-smooth = add-smooth-upper-vowel-not-Υ (λ ())

instance ι-rough : ι′ with-rough
ι-rough = add-rough-vowel

-- Ο ο

-- Unicode
-- U+0390 - U+03CE
ΐ : Token ι′ lower -- U+0390 GREEK SMALL LETTER IOTA WITH DIALYTIKA AND TONOS
ΐ = unmarked
Α : Token α′ upper -- U+0391 GREEK CAPITAL LETTER ALPHA
Α = unmarked
Β : Token β′ upper -- U+0392 GREEK CAPITAL LETTER BETA
Β = unmarked
Γ : Token γ′ upper -- U+0393 GREEK CAPITAL LETTER GAMMA
Γ = unmarked
Δ : Token δ′ upper -- U+0394 GREEK CAPITAL LETTER DELTA
Δ = unmarked
Ε : Token ε′ upper -- U+0395 GREEK CAPITAL LETTER EPSILON
Ε = unmarked
Ζ : Token ζ′ upper -- U+0396 GREEK CAPITAL LETTER ZETA
Ζ = unmarked
Η : Token η′ upper -- U+0397 GREEK CAPITAL LETTER ETA
Η = unmarked
Θ : Token θ′ upper -- U+0398 GREEK CAPITAL LETTER THETA
Θ = unmarked
Ι : Token ι′ upper -- U+0399 GREEK CAPITAL LETTER IOTA
Ι = unmarked
Κ : Token κ′ upper -- U+039A GREEK CAPITAL LETTER KAPPA
Κ = unmarked
Λ : Token λ′ upper -- U+039B GREEK CAPITAL LETTER LAMDA
Λ = unmarked
Μ : Token μ′ upper -- U+039C GREEK CAPITAL LETTER MU
Μ = unmarked
Ν : Token ν′ upper -- U+039D GREEK CAPITAL LETTER NU
Ν = unmarked
Ξ : Token ξ′ upper -- U+039E GREEK CAPITAL LETTER XI
Ξ = unmarked
Ο : Token ο′ upper -- U+039F GREEK CAPITAL LETTER OMICRON
Ο = unmarked
Π : Token π′ upper -- U+03A0 GREEK CAPITAL LETTER PI
Π = unmarked
Ρ : Token ρ′ upper -- U+03A1 GREEK CAPITAL LETTER RHO
Ρ = unmarked
                  -- U+03A2 <reserved>
Σ : Token σ′ upper -- U+03A3 GREEK CAPITAL LETTER SIGMA
Σ = unmarked
Τ : Token τ′ upper -- U+03A4 GREEK CAPITAL LETTER TAU
Τ = unmarked
Υ : Token υ′ upper -- U+03A5 GREEK CAPITAL LETTER UPSILON
Υ = unmarked
Φ : Token φ′ upper -- U+03A6 GREEK CAPITAL LETTER PHI
Φ = unmarked
Χ : Token χ′ upper -- U+03A7 GREEK CAPITAL LETTER CHI
Χ = unmarked
Ψ : Token ψ′ upper -- U+03A8 GREEK CAPITAL LETTER PSI
Ψ = unmarked
Ω : Token ω′ upper -- U+03A9 GREEK CAPITAL LETTER OMEGA
Ω = unmarked
Ϊ : Token ι′ upper -- U+03AA GREEK CAPITAL LETTER IOTA WITH DIALYTIKA
Ϊ = unmarked
Ϋ : Token υ′ upper -- U+03AB GREEK CAPITAL LETTER UPSILON WITH DIALYTIKA
Ϋ = unmarked
ά : Token α′ lower -- U+03AC GREEK SMALL LETTER ALPHA WITH TONOS
ά = unmarked
έ : Token ε′ lower -- U+03AD GREEK SMALL LETTER EPSILON WITH TONOS
έ = unmarked
ή : Token η′ lower -- U+03AE GREEK SMALL LETTER ETA WITH TONOS
ή = unmarked
ί : Token ι′ lower -- U+03AF GREEK SMALL LETTER IOTA WITH TONOS
ί = unmarked
ΰ : Token υ′ lower -- U+03B0 GREEK SMALL LETTER UPSILON WITH DIALYTIKA AND TONOS
ΰ = unmarked
α : Token α′ lower -- U+03B1 GREEK SMALL LETTER ALPHA
α = unmarked
β : Token β′ lower -- U+03B2 GREEK SMALL LETTER BETA
β = unmarked
γ : Token γ′ lower -- U+03B3 GREEK SMALL LETTER GAMMA
γ = unmarked
δ : Token δ′ lower -- U+03B4 GREEK SMALL LETTER DELTA
δ = unmarked
ε : Token ε′ lower -- U+03B5 GREEK SMALL LETTER EPSILON
ε = unmarked
ζ : Token ζ′ lower -- U+03B6 GREEK SMALL LETTER ZETA
ζ = unmarked
η : Token η′ lower -- U+03B7 GREEK SMALL LETTER ETA
η = unmarked
θ : Token θ′ lower -- U+03B8 GREEK SMALL LETTER THETA
θ = unmarked
ι : Token ι′ lower -- U+03B9 GREEK SMALL LETTER IOTA
ι = unmarked
κ : Token κ′ lower -- U+03BA GREEK SMALL LETTER KAPPA
κ = unmarked
∙λ : Token λ′ lower -- U+03BB GREEK SMALL LETTER LAMDA
∙λ = unmarked
μ : Token μ′ lower -- U+03BC GREEK SMALL LETTER MU
μ = unmarked
ν : Token ν′ lower -- U+03BD GREEK SMALL LETTER NU
ν = unmarked
ξ : Token ξ′ lower -- U+03BE GREEK SMALL LETTER XI
ξ = unmarked
ο : Token ο′ lower -- U+03BF GREEK SMALL LETTER OMICRON
ο = unmarked
π : Token π′ lower -- U+03C0 GREEK SMALL LETTER PI
π = unmarked
ρ : Token ρ′ lower -- U+03C1 GREEK SMALL LETTER RHO
ρ = unmarked
ς : Token σ′ lower -- U+03C2 GREEK SMALL LETTER FINAL SIGMA
ς = unmarked
σ : Token σ′ lower -- U+03C3 GREEK SMALL LETTER SIGMA
σ = unmarked
τ : Token τ′ lower -- U+03C4 GREEK SMALL LETTER TAU
τ = unmarked
υ : Token υ′ lower -- U+03C5 GREEK SMALL LETTER UPSILON
υ = unmarked
φ : Token φ′ lower -- U+03C6 GREEK SMALL LETTER PHI
φ = unmarked
χ : Token χ′ lower -- U+03C7 GREEK SMALL LETTER CHI
χ = unmarked
ψ : Token ψ′ lower -- U+03C8 GREEK SMALL LETTER PSI
ψ = unmarked
ω : Token ω′ lower -- U+03C9 GREEK SMALL LETTER OMEGA
ω = unmarked
ϊ : Token ι′ lower -- U+03CA GREEK SMALL LETTER IOTA WITH DIALYTIKA
ϊ = unmarked
ϋ : Token υ′ lower -- U+03CB GREEK SMALL LETTER UPSILON WITH DIALYTIKA
ϋ = unmarked
ό : Token ο′ lower -- U+03CC GREEK SMALL LETTER OMICRON WITH TONOS
ό = unmarked
ύ : Token υ′ lower -- U+03CD GREEK SMALL LETTER UPSILON WITH TONOS
ύ = unmarked
ώ : Token ω′ lower -- U+03CE GREEK SMALL LETTER OMEGA WITH TONOS
ώ = unmarked

ἀ : Token α′ lower
ἀ = with-breathing smooth
ἁ : Token α′ lower
ἁ = with-breathing rough
ἂ : Token α′ lower
ἂ = with-accent-breathing grave smooth
ἃ : Token α′ lower
ἃ = with-accent-breathing grave rough
ἄ : Token α′ lower
ἄ = with-accent-breathing acute smooth
ἅ : Token α′ lower
ἅ = with-accent-breathing acute rough
ἆ : Token α′ lower
ἆ = with-accent-breathing circumflex smooth
ἇ : Token α′ lower
ἇ = with-accent-breathing circumflex rough
Ἀ : Token α′ upper
Ἀ = with-breathing smooth
Ἁ : Token α′ upper
Ἁ = with-breathing rough
Ἂ : Token α′ upper
Ἂ = with-accent-breathing grave smooth
Ἃ : Token α′ upper
Ἃ = with-accent-breathing grave rough
Ἄ : Token α′ upper
Ἄ = with-accent-breathing acute smooth
Ἅ : Token α′ upper
Ἅ = with-accent-breathing acute rough
Ἆ : Token α′ upper
Ἆ = with-accent-breathing circumflex smooth
Ἇ : Token α′ upper
Ἇ = with-accent-breathing circumflex rough

-- U+1F7x
ὰ : Token α′ lower
ὰ = with-accent grave
ά : Token α′ lower
ά = with-accent acute

-- U+1F8x
ᾀ : Token α′ lower
ᾀ = with-breathing-iota smooth
ᾁ : Token α′ lower
ᾁ = with-breathing-iota rough
ᾂ : Token α′ lower
ᾂ = with-accent-breathing-iota grave smooth
ᾃ : Token α′ lower
ᾃ = with-accent-breathing-iota grave rough
ᾄ : Token α′ lower
ᾄ = with-accent-breathing-iota acute smooth
ᾅ : Token α′ lower
ᾅ = with-accent-breathing-iota acute rough
ᾆ : Token α′ lower
ᾆ = with-accent-breathing-iota circumflex smooth
ᾇ : Token α′ lower
ᾇ = with-accent-breathing-iota circumflex rough
ᾈ : Token α′ upper
ᾈ = with-breathing-iota smooth
ᾉ : Token α′ upper
ᾉ = with-breathing-iota rough
ᾊ : Token α′ upper
ᾊ = with-accent-breathing-iota grave smooth
ᾋ : Token α′ upper
ᾋ = with-accent-breathing-iota grave rough
ᾌ : Token α′ upper
ᾌ = with-accent-breathing-iota acute smooth
ᾍ : Token α′ upper
ᾍ = with-accent-breathing-iota acute rough
ᾎ : Token α′ upper
ᾎ = with-accent-breathing-iota circumflex smooth
ᾏ : Token α′ upper
ᾏ = with-accent-breathing-iota circumflex rough

-- U+1FBx
-- ᾰ
-- ᾱ
ᾲ : Token α′ lower
ᾲ = with-accent-iota grave
ᾳ : Token α′ lower
ᾳ = with-iota
ᾴ : Token α′ lower
ᾴ = with-accent-iota acute
ᾶ : Token α′ lower
ᾶ = with-accent circumflex
ᾷ : Token α′ lower
ᾷ = with-accent-iota circumflex
-- Ᾰ
-- Ᾱ
Ὰ : Token α′ upper
Ὰ = with-accent grave
Ά : Token α′ upper
Ά = with-accent acute
ᾼ : Token α′ upper
ᾼ = with-iota

-- Mapping

data Accent : Set where
  acute-mark grave-mark circumflex-mark : Accent

letter-to-accent : ∀ {v} → v accent → Accent
letter-to-accent acute = acute-mark
letter-to-accent grave = grave-mark
letter-to-accent circumflex = circumflex-mark

get-accent : ∀ {ℓ c} → Token ℓ c → Maybe Accent
get-accent (with-accent a) = just (letter-to-accent a)
get-accent (with-accent-breathing a _) = just (letter-to-accent a)
get-accent (with-accent-breathing-iota a _) = just (letter-to-accent a)
get-accent (with-accent-diaeresis a) = just (letter-to-accent a)
get-accent (with-accent-iota a) = just (letter-to-accent a)
get-accent _ = nothing

data Breathing : Set where
  smooth-mark rough-mark : Breathing

letter-to-breathing : ∀ {ℓ c} → ℓ ⟦ c ⟧-breathing → Breathing
letter-to-breathing smooth = smooth-mark
letter-to-breathing rough = rough-mark

get-breathing : ∀ {ℓ c} → Token ℓ c → Maybe Breathing
get-breathing (with-breathing x) = just (letter-to-breathing x)
get-breathing (with-accent-breathing _ x) = just (letter-to-breathing x)
get-breathing (with-accent-breathing-iota _ x) = just (letter-to-breathing x)
get-breathing (with-breathing-iota x) = just (letter-to-breathing x)
get-breathing _ = nothing

data IotaSubscript : Set where
  iota-subscript-mark : IotaSubscript

get-iota-subscript : ∀ {ℓ c} → Token ℓ c → Maybe IotaSubscript
get-iota-subscript (with-accent-breathing-iota _ _) = just iota-subscript-mark
get-iota-subscript (with-accent-iota _) = just iota-subscript-mark
get-iota-subscript (with-breathing-iota _) = just iota-subscript-mark
get-iota-subscript _ = nothing

data Diaeresis : Set where
  diaeresis-mark : Diaeresis

get-diaeresis : ∀ {ℓ c} → Token ℓ c → Maybe Diaeresis
get-diaeresis with-diaeresis = just diaeresis-mark
get-diaeresis (with-accent-diaeresis _) = just diaeresis-mark
get-diaeresis _ = nothing

data FinalForm : Set where
  final-form : FinalForm

get-final-form : ∀ {ℓ c} → Token ℓ c → Maybe FinalForm
get-final-form final = just final-form
get-final-form _ = nothing


Add the remainder of polytonic Greek Unicode.

module Text.Greek.Script where

open import Data.Maybe
open import Data.Vec
open import Relation.Nullary using (¬_)
open import Relation.Binary.PropositionalEquality using (_≢_)

data Case : Set where
  lower upper : Case

data Letter : Set where
  α′ β′ γ′ δ′ ε′ ζ′ η′ θ′ ι′ κ′ λ′ μ′ ν′ ξ′ ο′ π′ ρ′ σ′ τ′ υ′ φ′ χ′ ψ′ ω′ : Letter

vowels : Vec _ _
vowels = α′ ∷ ε′ ∷ η′ ∷ ι′ ∷ ο′ ∷ υ′ ∷ ω′ ∷ []

always-short-letters : Vec _ _
always-short-letters = ε′ ∷ ο′ ∷ []

diaeresis-letters : Vec _ _
diaeresis-letters = ι′ ∷ υ′ ∷ []

iota-subscript-letters : Vec _ _
iota-subscript-letters = α′ ∷ η′ ∷ ω′ ∷ []

data _vowel : Letter → Set where
  is-vowel : ∀ {v} → v ∈ vowels → v vowel

data _always-short : Letter → Set where
  is-always-short : ∀ {v} → ⦃ p : v vowel ⦄ → v ∈ always-short-letters → v always-short

data _diaeresis : Letter → Set where
  add-diaeresis : ∀ {v} → ⦃ p : v vowel ⦄ → v ∈ diaeresis-letters → v diaeresis

data _⟦_⟧-final : Letter → Case → Set where
  make-final : σ′ ⟦ lower ⟧-final

data _⟦_⟧-smooth : Letter → Case → Set where
  add-smooth-lower-vowel : ∀ {v} → ⦃ p : v vowel ⦄ → v ⟦ lower ⟧-smooth
  add-smooth-ρ : ρ′ ⟦ lower ⟧-smooth
  add-smooth-upper-vowel-not-Υ : ∀ {v} → ⦃ p : v vowel ⦄ → v ≢ υ′ → v ⟦ upper ⟧-smooth

data _with-rough : Letter → Set where
  add-rough-vowel : ∀ {v} → ⦃ p : v vowel ⦄ → v with-rough
  add-rough-ρ : ρ′ with-rough

data _iota-subscript : Letter → Set where
  add-iota-subscript : ∀ {v} → ⦃ p : v vowel ⦄ → v ∈ iota-subscript-letters → v iota-subscript

data _⟦_⟧-breathing : Letter → Case → Set where
  smooth : ∀ {ℓ c} → ⦃ p : ℓ ⟦ c ⟧-smooth ⦄ → ℓ ⟦ c ⟧-breathing
  rough : ∀ {ℓ c} → ⦃ p : ℓ with-rough ⦄ → ℓ ⟦ c ⟧-breathing

data _long-vowel : Letter → Set where
  make-long-vowel : ∀ {v} → ⦃ p : v vowel ⦄ → ¬ v always-short → v long-vowel

data _accent : Letter → Set where
  acute : ∀ {ℓ} → ⦃ p : ℓ vowel ⦄ → ℓ accent
  grave : ∀ {ℓ} → ⦃ p : ℓ vowel ⦄ → ℓ accent
  circumflex : ∀ {ℓ} → ⦃ p : ℓ long-vowel ⦄ → ℓ accent

data Token : Letter → Case → Set where
  unmarked : ∀ {ℓ c} → Token ℓ c
  with-accent : ∀ {ℓ c} → ℓ accent → Token ℓ c
  with-breathing : ∀ {ℓ c} → ℓ ⟦ c ⟧-breathing → Token ℓ c
  with-accent-breathing : ∀ {ℓ c} → ℓ accent → ℓ ⟦ c ⟧-breathing → Token ℓ c
  with-accent-breathing-iota : ∀ {ℓ c} → ℓ accent → ℓ ⟦ c ⟧-breathing → ⦃ p : ℓ iota-subscript ⦄ → Token ℓ c
  with-diaeresis : ∀ {ℓ c} → ⦃ p : ℓ diaeresis ⦄ → Token ℓ c
  with-accent-diaeresis : ∀ {ℓ c} → ℓ accent → ⦃ p : ℓ diaeresis ⦄ → Token ℓ c
  with-accent-iota : ∀ {ℓ c} → ℓ accent → ⦃ p : ℓ iota-subscript ⦄ → Token ℓ c
  with-breathing-iota : ∀ {ℓ c} → ℓ ⟦ c ⟧-breathing → ⦃ p : ℓ iota-subscript ⦄ → Token ℓ c
  with-iota : ∀ {ℓ c} → ⦃ p : ℓ iota-subscript ⦄ → Token ℓ c
  final : ∀ {ℓ c} → ⦃ p : ℓ ⟦ c ⟧-final ⦄ → Token ℓ c

-- Constructions

-- Α α
instance α-vowel : α′ vowel
α-vowel = is-vowel here

¬α-always-short : ¬ α′ always-short
¬α-always-short (is-always-short (there (there ())))

instance α-long-vowel : α′ long-vowel
α-long-vowel = make-long-vowel ¬α-always-short

instance α-smooth : α′ ⟦ lower ⟧-smooth
α-smooth = add-smooth-lower-vowel

instance Α-smooth : α′ ⟦ upper ⟧-smooth
Α-smooth = add-smooth-upper-vowel-not-Υ (λ ())

instance α-rough : α′ with-rough
α-rough = add-rough-vowel

instance α-iota-subscript : α′ iota-subscript
α-iota-subscript = add-iota-subscript here

-- Ε ε
instance ε-vowel : ε′ vowel
ε-vowel = is-vowel (there here)

ε-always-short : ε′ always-short
ε-always-short = is-always-short here

instance ε-smooth : ε′ ⟦ lower ⟧-smooth
ε-smooth = add-smooth-lower-vowel

instance Ε-smooth : ε′ ⟦ upper ⟧-smooth
Ε-smooth = add-smooth-upper-vowel-not-Υ (λ ())

instance ε-rough : ε′ with-rough
ε-rough = add-rough-vowel

-- Η η
instance η-vowel : η′ vowel
η-vowel = is-vowel (there (there here))

¬η-always-short : ¬ η′ always-short
¬η-always-short (is-always-short (there (there ())))

instance η-long-vowel : η′ long-vowel
η-long-vowel = make-long-vowel ¬η-always-short

instance η-smooth : η′ ⟦ lower ⟧-smooth
η-smooth = add-smooth-lower-vowel

instance Η-smooth : η′ ⟦ upper ⟧-smooth
Η-smooth = add-smooth-upper-vowel-not-Υ (λ ())

instance η-rough : η′ with-rough
η-rough = add-rough-vowel

instance η-iota-subscript : η′ iota-subscript
η-iota-subscript = add-iota-subscript (there here)

-- Ι ι

instance ι-vowel : ι′ vowel
ι-vowel = is-vowel (there (there (there here)))

¬ι-always-short : ¬ ι′ always-short
¬ι-always-short (is-always-short (there (there ())))

instance ι-long-vowel : ι′ long-vowel
ι-long-vowel = make-long-vowel ¬ι-always-short

instance ι-smooth : ι′ ⟦ lower ⟧-smooth
ι-smooth = add-smooth-lower-vowel

instance Ι-smooth : ι′ ⟦ upper ⟧-smooth
Ι-smooth = add-smooth-upper-vowel-not-Υ (λ ())

instance ι-rough : ι′ with-rough
ι-rough = add-rough-vowel

instance ι-diaeresis : ι′ diaeresis
ι-diaeresis = add-diaeresis here

-- Ο ο
instance ο-vowel : ο′ vowel
ο-vowel = is-vowel (there (there (there (there here))))

ο-always-short : ο′ always-short
ο-always-short = is-always-short (there here)

instance ο-smooth : ο′ ⟦ lower ⟧-smooth
ο-smooth = add-smooth-lower-vowel

instance Ο-smooth : ο′ ⟦ upper ⟧-smooth
Ο-smooth = add-smooth-upper-vowel-not-Υ (λ ())

instance ο-rough : ο′ with-rough
ο-rough = add-rough-vowel

-- Ρ ρ
instance ρ-smooth : ρ′ ⟦ lower ⟧-smooth
ρ-smooth = add-smooth-ρ

instance ρ-rough : ρ′ with-rough
ρ-rough = add-rough-ρ

-- Σ σ
instance σ-final : σ′ ⟦ lower ⟧-final
σ-final = make-final

-- Υ υ
instance υ-vowel : υ′ vowel
υ-vowel = is-vowel (there (there (there (there (there here)))))

¬υ-always-short : ¬ υ′ always-short
¬υ-always-short (is-always-short (there (there ())))

instance υ-long-vowel : υ′ long-vowel
υ-long-vowel = make-long-vowel ¬υ-always-short

instance υ-smooth : υ′ ⟦ lower ⟧-smooth
υ-smooth = add-smooth-lower-vowel

instance υ-rough : υ′ with-rough
υ-rough = add-rough-vowel

instance υ-diaeresis : υ′ diaeresis
υ-diaeresis = add-diaeresis (there here)

-- Ω ω
instance ω-vowel : ω′ vowel
ω-vowel = is-vowel (there (there (there (there (there (there here))))))

¬ω-always-short : ¬ ω′ always-short
¬ω-always-short (is-always-short (there (there ())))

instance ω-long-vowel : ω′ long-vowel
ω-long-vowel = make-long-vowel ¬ω-always-short

instance ω-smooth : ω′ ⟦ lower ⟧-smooth
ω-smooth = add-smooth-lower-vowel

instance Ω-smooth : ω′ ⟦ upper ⟧-smooth
Ω-smooth = add-smooth-upper-vowel-not-Υ (λ ())

instance ω-rough : ω′ with-rough
ω-rough = add-rough-vowel

instance ω-iota-subscript : ω′ iota-subscript
ω-iota-subscript = add-iota-subscript (there (there here))

-- Unicode
-- U+0390 - U+03CE
ΐ : Token ι′ lower -- U+0390 GREEK SMALL LETTER IOTA WITH DIALYTIKA AND TONOS
ΐ = with-accent-diaeresis acute
Α : Token α′ upper -- U+0391 GREEK CAPITAL LETTER ALPHA
Α = unmarked
Β : Token β′ upper -- U+0392 GREEK CAPITAL LETTER BETA
Β = unmarked
Γ : Token γ′ upper -- U+0393 GREEK CAPITAL LETTER GAMMA
Γ = unmarked
Δ : Token δ′ upper -- U+0394 GREEK CAPITAL LETTER DELTA
Δ = unmarked
Ε : Token ε′ upper -- U+0395 GREEK CAPITAL LETTER EPSILON
Ε = unmarked
Ζ : Token ζ′ upper -- U+0396 GREEK CAPITAL LETTER ZETA
Ζ = unmarked
Η : Token η′ upper -- U+0397 GREEK CAPITAL LETTER ETA
Η = unmarked
Θ : Token θ′ upper -- U+0398 GREEK CAPITAL LETTER THETA
Θ = unmarked
Ι : Token ι′ upper -- U+0399 GREEK CAPITAL LETTER IOTA
Ι = unmarked
Κ : Token κ′ upper -- U+039A GREEK CAPITAL LETTER KAPPA
Κ = unmarked
Λ : Token λ′ upper -- U+039B GREEK CAPITAL LETTER LAMDA
Λ = unmarked
Μ : Token μ′ upper -- U+039C GREEK CAPITAL LETTER MU
Μ = unmarked
Ν : Token ν′ upper -- U+039D GREEK CAPITAL LETTER NU
Ν = unmarked
Ξ : Token ξ′ upper -- U+039E GREEK CAPITAL LETTER XI
Ξ = unmarked
Ο : Token ο′ upper -- U+039F GREEK CAPITAL LETTER OMICRON
Ο = unmarked
Π : Token π′ upper -- U+03A0 GREEK CAPITAL LETTER PI
Π = unmarked
Ρ : Token ρ′ upper -- U+03A1 GREEK CAPITAL LETTER RHO
Ρ = unmarked
                  -- U+03A2 <reserved>
Σ : Token σ′ upper -- U+03A3 GREEK CAPITAL LETTER SIGMA
Σ = unmarked
Τ : Token τ′ upper -- U+03A4 GREEK CAPITAL LETTER TAU
Τ = unmarked
Υ : Token υ′ upper -- U+03A5 GREEK CAPITAL LETTER UPSILON
Υ = unmarked
Φ : Token φ′ upper -- U+03A6 GREEK CAPITAL LETTER PHI
Φ = unmarked
Χ : Token χ′ upper -- U+03A7 GREEK CAPITAL LETTER CHI
Χ = unmarked
Ψ : Token ψ′ upper -- U+03A8 GREEK CAPITAL LETTER PSI
Ψ = unmarked
Ω : Token ω′ upper -- U+03A9 GREEK CAPITAL LETTER OMEGA
Ω = unmarked
Ϊ : Token ι′ upper -- U+03AA GREEK CAPITAL LETTER IOTA WITH DIALYTIKA
Ϊ = with-diaeresis
Ϋ : Token υ′ upper -- U+03AB GREEK CAPITAL LETTER UPSILON WITH DIALYTIKA
Ϋ = with-diaeresis
ά : Token α′ lower -- U+03AC GREEK SMALL LETTER ALPHA WITH TONOS
ά = with-accent acute
έ : Token ε′ lower -- U+03AD GREEK SMALL LETTER EPSILON WITH TONOS
έ = with-accent acute
ή : Token η′ lower -- U+03AE GREEK SMALL LETTER ETA WITH TONOS
ή = with-accent acute
ί : Token ι′ lower -- U+03AF GREEK SMALL LETTER IOTA WITH TONOS
ί = with-accent acute
ΰ : Token υ′ lower -- U+03B0 GREEK SMALL LETTER UPSILON WITH DIALYTIKA AND TONOS
ΰ = with-accent-diaeresis acute
α : Token α′ lower -- U+03B1 GREEK SMALL LETTER ALPHA
α = unmarked
β : Token β′ lower -- U+03B2 GREEK SMALL LETTER BETA
β = unmarked
γ : Token γ′ lower -- U+03B3 GREEK SMALL LETTER GAMMA
γ = unmarked
δ : Token δ′ lower -- U+03B4 GREEK SMALL LETTER DELTA
δ = unmarked
ε : Token ε′ lower -- U+03B5 GREEK SMALL LETTER EPSILON
ε = unmarked
ζ : Token ζ′ lower -- U+03B6 GREEK SMALL LETTER ZETA
ζ = unmarked
η : Token η′ lower -- U+03B7 GREEK SMALL LETTER ETA
η = unmarked
θ : Token θ′ lower -- U+03B8 GREEK SMALL LETTER THETA
θ = unmarked
ι : Token ι′ lower -- U+03B9 GREEK SMALL LETTER IOTA
ι = unmarked
κ : Token κ′ lower -- U+03BA GREEK SMALL LETTER KAPPA
κ = unmarked
∙λ : Token λ′ lower -- U+03BB GREEK SMALL LETTER LAMDA
∙λ = unmarked
μ : Token μ′ lower -- U+03BC GREEK SMALL LETTER MU
μ = unmarked
ν : Token ν′ lower -- U+03BD GREEK SMALL LETTER NU
ν = unmarked
ξ : Token ξ′ lower -- U+03BE GREEK SMALL LETTER XI
ξ = unmarked
ο : Token ο′ lower -- U+03BF GREEK SMALL LETTER OMICRON
ο = unmarked
π : Token π′ lower -- U+03C0 GREEK SMALL LETTER PI
π = unmarked
ρ : Token ρ′ lower -- U+03C1 GREEK SMALL LETTER RHO
ρ = unmarked
ς : Token σ′ lower -- U+03C2 GREEK SMALL LETTER FINAL SIGMA
ς = final
σ : Token σ′ lower -- U+03C3 GREEK SMALL LETTER SIGMA
σ = unmarked
τ : Token τ′ lower -- U+03C4 GREEK SMALL LETTER TAU
τ = unmarked
υ : Token υ′ lower -- U+03C5 GREEK SMALL LETTER UPSILON
υ = unmarked
φ : Token φ′ lower -- U+03C6 GREEK SMALL LETTER PHI
φ = unmarked
χ : Token χ′ lower -- U+03C7 GREEK SMALL LETTER CHI
χ = unmarked
ψ : Token ψ′ lower -- U+03C8 GREEK SMALL LETTER PSI
ψ = unmarked
ω : Token ω′ lower -- U+03C9 GREEK SMALL LETTER OMEGA
ω = unmarked
ϊ : Token ι′ lower -- U+03CA GREEK SMALL LETTER IOTA WITH DIALYTIKA
ϊ = with-diaeresis
ϋ : Token υ′ lower -- U+03CB GREEK SMALL LETTER UPSILON WITH DIALYTIKA
ϋ = with-diaeresis
ό : Token ο′ lower -- U+03CC GREEK SMALL LETTER OMICRON WITH TONOS
ό = with-accent acute
ύ : Token υ′ lower -- U+03CD GREEK SMALL LETTER UPSILON WITH TONOS
ύ = with-accent acute
ώ : Token ω′ lower -- U+03CE GREEK SMALL LETTER OMEGA WITH TONOS
ώ = with-accent acute

-- U+1F00 - U+1FFF
ἀ : Token α′ lower -- U+1F00  ἀ GREEK SMALL LETTER ALPHA WITH PSILI
ἀ = with-breathing smooth
ἁ : Token α′ lower -- U+1F01  ἁ GREEK SMALL LETTER ALPHA WITH DASIA
ἁ = with-breathing rough
ἂ : Token α′ lower -- U+1F02  ἂ GREEK SMALL LETTER ALPHA WITH PSILI AND VARIA
ἂ = with-accent-breathing grave smooth
ἃ : Token α′ lower -- U+1F03  ἃ GREEK SMALL LETTER ALPHA WITH DASIA AND VARIA
ἃ = with-accent-breathing grave rough
ἄ : Token α′ lower -- U+1F04  ἄ GREEK SMALL LETTER ALPHA WITH PSILI AND OXIA
ἄ = with-accent-breathing acute smooth
ἅ : Token α′ lower -- U+1F05  ἅ GREEK SMALL LETTER ALPHA WITH DASIA AND OXIA
ἅ = with-accent-breathing acute rough
ἆ : Token α′ lower -- U+1F06  ἆ GREEK SMALL LETTER ALPHA WITH PSILI AND PERISPOMENI
ἆ = with-accent-breathing circumflex smooth
ἇ : Token α′ lower -- U+1F07  ἇ GREEK SMALL LETTER ALPHA WITH DASIA AND PERISPOMENI
ἇ = with-accent-breathing circumflex rough
Ἀ : Token α′ upper -- U+1F08  Ἀ GREEK CAPITAL LETTER ALPHA WITH PSILI
Ἀ = with-breathing smooth
Ἁ : Token α′ upper -- U+1F09  Ἁ GREEK CAPITAL LETTER ALPHA WITH DASIA
Ἁ = with-breathing rough
Ἂ : Token α′ upper -- U+1F0A  Ἂ GREEK CAPITAL LETTER ALPHA WITH PSILI AND VARIA
Ἂ = with-accent-breathing grave smooth
Ἃ : Token α′ upper -- U+1F0B  Ἃ GREEK CAPITAL LETTER ALPHA WITH DASIA AND VARIA
Ἃ = with-accent-breathing grave rough
Ἄ : Token α′ upper -- U+1F0C  Ἄ GREEK CAPITAL LETTER ALPHA WITH PSILI AND OXIA
Ἄ = with-accent-breathing acute smooth
Ἅ : Token α′ upper -- U+1F0D  Ἅ GREEK CAPITAL LETTER ALPHA WITH DASIA AND OXIA
Ἅ = with-accent-breathing acute rough
Ἆ : Token α′ upper -- U+1F0E  Ἆ GREEK CAPITAL LETTER ALPHA WITH PSILI AND PERISPOMENI
Ἆ = with-accent-breathing circumflex smooth
Ἇ : Token α′ upper -- U+1F0F  Ἇ GREEK CAPITAL LETTER ALPHA WITH DASIA AND PERISPOMENI
Ἇ = with-accent-breathing circumflex rough
ἐ : Token ε′ lower -- U+1F10  ἐ GREEK SMALL LETTER EPSILON WITH PSILI
ἐ = with-breathing smooth
ἑ : Token ε′ lower -- U+1F11  ἑ GREEK SMALL LETTER EPSILON WITH DASIA
ἑ = with-breathing rough
ἒ : Token ε′ lower -- U+1F12  ἒ GREEK SMALL LETTER EPSILON WITH PSILI AND VARIA
ἒ = with-accent-breathing grave smooth
ἓ : Token ε′ lower -- U+1F13  ἓ GREEK SMALL LETTER EPSILON WITH DASIA AND VARIA
ἓ = with-accent-breathing grave rough
ἔ : Token ε′ lower -- U+1F14  ἔ GREEK SMALL LETTER EPSILON WITH PSILI AND OXIA
ἔ = with-accent-breathing acute smooth
ἕ : Token ε′ lower -- U+1F15  ἕ GREEK SMALL LETTER EPSILON WITH DASIA AND OXIA
ἕ = with-accent-breathing acute rough
-- U+1F16
-- U+1F17
Ἐ : Token ε′ upper -- U+1F18  Ἐ GREEK CAPITAL LETTER EPSILON WITH PSILI
Ἐ = with-breathing smooth
Ἑ : Token ε′ upper -- U+1F19  Ἑ GREEK CAPITAL LETTER EPSILON WITH DASIA
Ἑ = with-breathing rough
Ἒ : Token ε′ upper -- U+1F1A  Ἒ GREEK CAPITAL LETTER EPSILON WITH PSILI AND VARIA
Ἒ = with-accent-breathing grave smooth
Ἓ : Token ε′ upper -- U+1F1B  Ἓ GREEK CAPITAL LETTER EPSILON WITH DASIA AND VARIA
Ἓ = with-accent-breathing grave rough
Ἔ : Token ε′ upper -- U+1F1C  Ἔ GREEK CAPITAL LETTER EPSILON WITH PSILI AND OXIA
Ἔ = with-accent-breathing acute smooth
Ἕ : Token ε′ upper -- U+1F1D  Ἕ GREEK CAPITAL LETTER EPSILON WITH DASIA AND OXIA
Ἕ = with-accent-breathing acute rough
-- U+1F1E
-- U+1F1F
ἠ : Token η′ lower -- U+1F20  ἠ GREEK SMALL LETTER ETA WITH PSILI
ἠ = with-breathing smooth
ἡ : Token η′ lower -- U+1F21  ἡ GREEK SMALL LETTER ETA WITH DASIA
ἡ = with-breathing rough
ἢ : Token η′ lower -- U+1F22  ἢ GREEK SMALL LETTER ETA WITH PSILI AND VARIA
ἢ = with-accent-breathing grave smooth
ἣ : Token η′ lower -- U+1F23  ἣ GREEK SMALL LETTER ETA WITH DASIA AND VARIA
ἣ = with-accent-breathing grave rough
ἤ : Token η′ lower -- U+1F24  ἤ GREEK SMALL LETTER ETA WITH PSILI AND OXIA
ἤ = with-accent-breathing acute smooth
ἥ : Token η′ lower -- U+1F25  ἥ GREEK SMALL LETTER ETA WITH DASIA AND OXIA
ἥ = with-accent-breathing acute rough
ἦ : Token η′ lower -- U+1F26  ἦ GREEK SMALL LETTER ETA WITH PSILI AND PERISPOMENI
ἦ = with-accent-breathing circumflex smooth
ἧ : Token η′ lower -- U+1F27  ἧ GREEK SMALL LETTER ETA WITH DASIA AND PERISPOMENI
ἧ = with-accent-breathing circumflex rough
Ἠ : Token η′ upper -- U+1F28  Ἠ GREEK CAPITAL LETTER ETA WITH PSILI
Ἠ = with-breathing smooth
Ἡ : Token η′ upper -- U+1F29  Ἡ GREEK CAPITAL LETTER ETA WITH DASIA
Ἡ = with-breathing rough
Ἢ : Token η′ upper -- U+1F2A  Ἢ GREEK CAPITAL LETTER ETA WITH PSILI AND VARIA
Ἢ = with-accent-breathing grave smooth
Ἣ : Token η′ upper -- U+1F2B  Ἣ GREEK CAPITAL LETTER ETA WITH DASIA AND VARIA
Ἣ = with-accent-breathing grave rough
Ἤ : Token η′ upper -- U+1F2C  Ἤ GREEK CAPITAL LETTER ETA WITH PSILI AND OXIA
Ἤ = with-accent-breathing acute smooth
Ἥ : Token η′ upper -- U+1F2D  Ἥ GREEK CAPITAL LETTER ETA WITH DASIA AND OXIA
Ἥ = with-accent-breathing acute rough
Ἦ : Token η′ upper -- U+1F2E  Ἦ GREEK CAPITAL LETTER ETA WITH PSILI AND PERISPOMENI
Ἦ = with-accent-breathing circumflex smooth
Ἧ : Token η′ upper -- U+1F2F  Ἧ GREEK CAPITAL LETTER ETA WITH DASIA AND PERISPOMENI
Ἧ = with-accent-breathing circumflex rough
ἰ : Token ι′ lower -- U+1F30  ἰ GREEK SMALL LETTER IOTA WITH PSILI
ἰ = with-breathing smooth
ἱ : Token ι′ lower -- U+1F31  ἱ GREEK SMALL LETTER IOTA WITH DASIA
ἱ = with-breathing rough
ἲ : Token ι′ lower -- U+1F32  ἲ GREEK SMALL LETTER IOTA WITH PSILI AND VARIA
ἲ = with-accent-breathing grave smooth
ἳ : Token ι′ lower -- U+1F33  ἳ GREEK SMALL LETTER IOTA WITH DASIA AND VARIA
ἳ = with-accent-breathing grave rough
ἴ : Token ι′ lower -- U+1F34  ἴ GREEK SMALL LETTER IOTA WITH PSILI AND OXIA
ἴ = with-accent-breathing acute smooth
ἵ : Token ι′ lower -- U+1F35  ἵ GREEK SMALL LETTER IOTA WITH DASIA AND OXIA
ἵ = with-accent-breathing acute rough
ἶ : Token ι′ lower -- U+1F36  ἶ GREEK SMALL LETTER IOTA WITH PSILI AND PERISPOMENI
ἶ = with-accent-breathing circumflex smooth
ἷ : Token ι′ lower -- U+1F37  ἷ GREEK SMALL LETTER IOTA WITH DASIA AND PERISPOMENI
ἷ = with-accent-breathing circumflex rough
Ἰ : Token ι′ upper -- U+1F38  Ἰ GREEK CAPITAL LETTER IOTA WITH PSILI
Ἰ = with-breathing smooth
Ἱ : Token ι′ upper -- U+1F39  Ἱ GREEK CAPITAL LETTER IOTA WITH DASIA
Ἱ = with-breathing rough
Ἲ : Token ι′ upper -- U+1F3A  Ἲ GREEK CAPITAL LETTER IOTA WITH PSILI AND VARIA
Ἲ = with-accent-breathing grave smooth
Ἳ : Token ι′ upper -- U+1F3B  Ἳ GREEK CAPITAL LETTER IOTA WITH DASIA AND VARIA
Ἳ = with-accent-breathing grave rough
Ἴ : Token ι′ upper -- U+1F3C  Ἴ GREEK CAPITAL LETTER IOTA WITH PSILI AND OXIA
Ἴ = with-accent-breathing acute smooth
Ἵ : Token ι′ upper -- U+1F3D  Ἵ GREEK CAPITAL LETTER IOTA WITH DASIA AND OXIA
Ἵ = with-accent-breathing acute rough
Ἶ : Token ι′ upper -- U+1F3E  Ἶ GREEK CAPITAL LETTER IOTA WITH PSILI AND PERISPOMENI
Ἶ = with-accent-breathing circumflex smooth
Ἷ : Token ι′ upper -- U+1F3F  Ἷ GREEK CAPITAL LETTER IOTA WITH DASIA AND PERISPOMENI
Ἷ = with-accent-breathing circumflex rough
ὀ : Token ο′ lower -- U+1F40  ὀ GREEK SMALL LETTER OMICRON WITH PSILI
ὀ = with-breathing smooth
ὁ : Token ο′ lower -- U+1F41  ὁ GREEK SMALL LETTER OMICRON WITH DASIA
ὁ = with-breathing rough
ὂ : Token ο′ lower -- U+1F42  ὂ GREEK SMALL LETTER OMICRON WITH PSILI AND VARIA
ὂ = with-accent-breathing grave smooth
ὃ : Token ο′ lower -- U+1F43  ὃ GREEK SMALL LETTER OMICRON WITH DASIA AND VARIA
ὃ = with-accent-breathing grave rough
ὄ : Token ο′ lower -- U+1F44  ὄ GREEK SMALL LETTER OMICRON WITH PSILI AND OXIA
ὄ = with-accent-breathing acute smooth
ὅ : Token ο′ lower -- U+1F45  ὅ GREEK SMALL LETTER OMICRON WITH DASIA AND OXIA
ὅ = with-accent-breathing acute rough
-- U+1F46
-- U+1F47
Ὀ : Token ο′ upper -- U+1F48  Ὀ GREEK CAPITAL LETTER OMICRON WITH PSILI
Ὀ = with-breathing smooth
Ὁ : Token ο′ upper -- U+1F49  Ὁ GREEK CAPITAL LETTER OMICRON WITH DASIA
Ὁ = with-breathing rough
Ὂ : Token ο′ upper -- U+1F4A  Ὂ GREEK CAPITAL LETTER OMICRON WITH PSILI AND VARIA
Ὂ = with-accent-breathing grave smooth
Ὃ : Token ο′ upper -- U+1F4B  Ὃ GREEK CAPITAL LETTER OMICRON WITH DASIA AND VARIA
Ὃ = with-accent-breathing grave rough
Ὄ : Token ο′ upper -- U+1F4C  Ὄ GREEK CAPITAL LETTER OMICRON WITH PSILI AND OXIA
Ὄ = with-accent-breathing acute smooth
Ὅ : Token ο′ upper -- U+1F4D  Ὅ GREEK CAPITAL LETTER OMICRON WITH DASIA AND OXIA
Ὅ = with-accent-breathing acute rough
-- U+1F4E
-- U+1F4F
ὐ : Token υ′ lower -- U+1F50  ὐ GREEK SMALL LETTER UPSILON WITH PSILI
ὐ = with-breathing smooth
ὑ : Token υ′ lower -- U+1F51  ὑ GREEK SMALL LETTER UPSILON WITH DASIA
ὑ = with-breathing rough
ὒ : Token υ′ lower -- U+1F52  ὒ GREEK SMALL LETTER UPSILON WITH PSILI AND VARIA
ὒ = with-accent-breathing grave smooth
ὓ : Token υ′ lower -- U+1F53  ὓ GREEK SMALL LETTER UPSILON WITH DASIA AND VARIA
ὓ = with-accent-breathing grave rough
ὔ : Token υ′ lower -- U+1F54  ὔ GREEK SMALL LETTER UPSILON WITH PSILI AND OXIA
ὔ = with-accent-breathing acute smooth
ὕ : Token υ′ lower -- U+1F55  ὕ GREEK SMALL LETTER UPSILON WITH DASIA AND OXIA
ὕ = with-accent-breathing acute rough
ὖ : Token υ′ lower -- U+1F56  ὖ GREEK SMALL LETTER UPSILON WITH PSILI AND PERISPOMENI
ὖ = with-accent-breathing circumflex smooth
ὗ : Token υ′ lower -- U+1F57  ὗ GREEK SMALL LETTER UPSILON WITH DASIA AND PERISPOMENI
ὗ = with-accent-breathing circumflex rough
-- U+1F58
Ὑ : Token υ′ upper -- U+1F59  Ὑ GREEK CAPITAL LETTER UPSILON WITH DASIA
Ὑ = with-breathing rough
-- U+1F5A
Ὓ : Token υ′ upper -- U+1F5B  Ὓ GREEK CAPITAL LETTER UPSILON WITH DASIA AND VARIA
Ὓ = with-accent-breathing grave rough
-- U+1F5C
Ὕ : Token υ′ upper -- U+1F5D  Ὕ GREEK CAPITAL LETTER UPSILON WITH DASIA AND OXIA
Ὕ = with-accent-breathing acute rough
-- U+1F5E
Ὗ : Token υ′ upper -- U+1F5F  Ὗ GREEK CAPITAL LETTER UPSILON WITH DASIA AND PERISPOMENI
Ὗ = with-accent-breathing circumflex rough
ὠ : Token ω′ lower -- U+1F60  ὠ GREEK SMALL LETTER OMEGA WITH PSILI
ὠ = with-breathing smooth
ὡ : Token ω′ lower -- U+1F61  ὡ GREEK SMALL LETTER OMEGA WITH DASIA
ὡ = with-breathing rough
ὢ : Token ω′ lower -- U+1F62  ὢ GREEK SMALL LETTER OMEGA WITH PSILI AND VARIA
ὢ = with-accent-breathing grave smooth
ὣ : Token ω′ lower -- U+1F63  ὣ GREEK SMALL LETTER OMEGA WITH DASIA AND VARIA
ὣ = with-accent-breathing grave rough
ὤ : Token ω′ lower -- U+1F64  ὤ GREEK SMALL LETTER OMEGA WITH PSILI AND OXIA
ὤ = with-accent-breathing acute smooth
ὥ : Token ω′ lower -- U+1F65  ὥ GREEK SMALL LETTER OMEGA WITH DASIA AND OXIA
ὥ = with-accent-breathing acute rough
ὦ : Token ω′ lower -- U+1F66  ὦ GREEK SMALL LETTER OMEGA WITH PSILI AND PERISPOMENI
ὦ = with-accent-breathing circumflex smooth
ὧ : Token ω′ lower -- U+1F67  ὧ GREEK SMALL LETTER OMEGA WITH DASIA AND PERISPOMENI
ὧ = with-accent-breathing circumflex rough
Ὠ : Token ω′ upper -- U+1F68  Ὠ GREEK CAPITAL LETTER OMEGA WITH PSILI
Ὠ = with-breathing smooth
Ὡ : Token ω′ upper -- U+1F69  Ὡ GREEK CAPITAL LETTER OMEGA WITH DASIA
Ὡ = with-breathing rough
Ὢ : Token ω′ upper -- U+1F6A  Ὢ GREEK CAPITAL LETTER OMEGA WITH PSILI AND VARIA
Ὢ = with-accent-breathing grave smooth
Ὣ : Token ω′ upper -- U+1F6B  Ὣ GREEK CAPITAL LETTER OMEGA WITH DASIA AND VARIA
Ὣ = with-accent-breathing grave rough
Ὤ : Token ω′ upper -- U+1F6C  Ὤ GREEK CAPITAL LETTER OMEGA WITH PSILI AND OXIA
Ὤ = with-accent-breathing acute smooth
Ὥ : Token ω′ upper -- U+1F6D  Ὥ GREEK CAPITAL LETTER OMEGA WITH DASIA AND OXIA
Ὥ = with-accent-breathing acute rough
Ὦ : Token ω′ upper -- U+1F6E  Ὦ GREEK CAPITAL LETTER OMEGA WITH PSILI AND PERISPOMENI
Ὦ = with-accent-breathing circumflex smooth
Ὧ : Token ω′ upper -- U+1F6F  Ὧ GREEK CAPITAL LETTER OMEGA WITH DASIA AND PERISPOMENI
Ὧ = with-accent-breathing circumflex rough
ὰ : Token α′ lower -- U+1F70  ὰ GREEK SMALL LETTER ALPHA WITH VARIA
ὰ = with-accent grave
ά : Token α′ lower -- U+1F71  ά GREEK SMALL LETTER ALPHA WITH OXIA
ά = with-accent acute
ὲ : Token ε′ lower -- U+1F72  ὲ GREEK SMALL LETTER EPSILON WITH VARIA
ὲ = with-accent grave
έ : Token ε′ lower -- U+1F73  έ GREEK SMALL LETTER EPSILON WITH OXIA
έ = with-accent acute
ὴ : Token η′ lower -- U+1F74  ὴ GREEK SMALL LETTER ETA WITH VARIA
ὴ = with-accent grave
ή : Token η′ lower -- U+1F75  ή GREEK SMALL LETTER ETA WITH OXIA
ή = with-accent acute
ὶ : Token ι′ lower -- U+1F76  ὶ GREEK SMALL LETTER IOTA WITH VARIA
ὶ = with-accent grave
ί : Token ι′ lower -- U+1F77  ί GREEK SMALL LETTER IOTA WITH OXIA
ί = with-accent acute
ὸ : Token ο′ lower -- U+1F78  ὸ GREEK SMALL LETTER OMICRON WITH VARIA
ὸ = with-accent grave
ό : Token ο′ lower -- U+1F79  ό GREEK SMALL LETTER OMICRON WITH OXIA
ό = with-accent acute
ὺ : Token υ′ lower -- U+1F7A  ὺ GREEK SMALL LETTER UPSILON WITH VARIA
ὺ = with-accent grave
ύ : Token υ′ lower -- U+1F7B  ύ GREEK SMALL LETTER UPSILON WITH OXIA
ύ = with-accent acute
ὼ : Token ω′ lower -- U+1F7C  ὼ GREEK SMALL LETTER OMEGA WITH VARIA
ὼ = with-accent grave
ώ : Token ω′ lower -- U+1F7D  ώ GREEK SMALL LETTER OMEGA WITH OXIA
ώ = with-accent acute
-- U+1F7E
-- U+1F7F
ᾀ : Token α′ lower -- U+1F80  ᾀ GREEK SMALL LETTER ALPHA WITH PSILI AND YPOGEGRAMMENI
ᾀ = with-breathing-iota smooth
ᾁ : Token α′ lower -- U+1F81  ᾁ GREEK SMALL LETTER ALPHA WITH DASIA AND YPOGEGRAMMENI
ᾁ = with-breathing-iota rough
ᾂ : Token α′ lower -- U+1F82  ᾂ GREEK SMALL LETTER ALPHA WITH PSILI AND VARIA AND YPOGEGRAMMENI
ᾂ = with-accent-breathing-iota grave smooth
ᾃ : Token α′ lower -- U+1F83  ᾃ GREEK SMALL LETTER ALPHA WITH DASIA AND VARIA AND YPOGEGRAMMENI
ᾃ = with-accent-breathing grave rough
ᾄ : Token α′ lower -- U+1F84  ᾄ GREEK SMALL LETTER ALPHA WITH PSILI AND OXIA AND YPOGEGRAMMENI
ᾄ = with-accent-breathing-iota acute smooth
ᾅ : Token α′ lower -- U+1F85  ᾅ GREEK SMALL LETTER ALPHA WITH DASIA AND OXIA AND YPOGEGRAMMENI
ᾅ = with-accent-breathing-iota acute rough
ᾆ : Token α′ lower -- U+1F86  ᾆ GREEK SMALL LETTER ALPHA WITH PSILI AND PERISPOMENI AND YPOGEGRAMMENI
ᾆ = with-accent-breathing-iota circumflex smooth
ᾇ : Token α′ lower -- U+1F87  ᾇ GREEK SMALL LETTER ALPHA WITH DASIA AND PERISPOMENI AND YPOGEGRAMMENI
ᾇ = with-accent-breathing-iota circumflex rough
ᾈ : Token α′ upper -- U+1F88  ᾈ GREEK CAPITAL LETTER ALPHA WITH PSILI AND PROSGEGRAMMENI
ᾈ = with-breathing-iota smooth
ᾉ : Token α′ upper -- U+1F89  ᾉ GREEK CAPITAL LETTER ALPHA WITH DASIA AND PROSGEGRAMMENI
ᾉ = with-breathing-iota rough
ᾊ : Token α′ upper -- U+1F8A  ᾊ GREEK CAPITAL LETTER ALPHA WITH PSILI AND VARIA AND PROSGEGRAMMENI
ᾊ = with-accent-breathing-iota grave smooth
ᾋ : Token α′ upper -- U+1F8B  ᾋ GREEK CAPITAL LETTER ALPHA WITH DASIA AND VARIA AND PROSGEGRAMMENI
ᾋ = with-accent-breathing-iota grave rough
ᾌ : Token α′ upper -- U+1F8C  ᾌ GREEK CAPITAL LETTER ALPHA WITH PSILI AND OXIA AND PROSGEGRAMMENI
ᾌ = with-accent-breathing-iota acute smooth
ᾍ : Token α′ upper -- U+1F8D  ᾍ GREEK CAPITAL LETTER ALPHA WITH DASIA AND OXIA AND PROSGEGRAMMENI
ᾍ = with-accent-breathing-iota acute rough
ᾎ : Token α′ upper -- U+1F8E  ᾎ GREEK CAPITAL LETTER ALPHA WITH PSILI AND PERISPOMENI AND PROSGEGRAMMENI
ᾎ = with-accent-breathing-iota circumflex smooth
ᾏ : Token α′ upper -- U+1F8F  ᾏ GREEK CAPITAL LETTER ALPHA WITH DASIA AND PERISPOMENI AND PROSGEGRAMMENI
ᾏ = with-accent-breathing-iota circumflex rough
ᾐ : Token η′ lower -- U+1F90  ᾐ GREEK SMALL LETTER ETA WITH PSILI AND YPOGEGRAMMENI
ᾐ = with-breathing-iota smooth
ᾑ : Token η′ lower -- U+1F91  ᾑ GREEK SMALL LETTER ETA WITH DASIA AND YPOGEGRAMMENI
ᾑ = with-breathing-iota rough
ᾒ : Token η′ lower -- U+1F92  ᾒ GREEK SMALL LETTER ETA WITH PSILI AND VARIA AND YPOGEGRAMMENI
ᾒ = with-accent-breathing-iota grave smooth
ᾓ : Token η′ lower -- U+1F93  ᾓ GREEK SMALL LETTER ETA WITH DASIA AND VARIA AND YPOGEGRAMMENI
ᾓ = with-accent-breathing-iota grave rough
ᾔ : Token η′ lower -- U+1F94  ᾔ GREEK SMALL LETTER ETA WITH PSILI AND OXIA AND YPOGEGRAMMENI
ᾔ = with-accent-breathing-iota acute smooth
ᾕ : Token η′ lower -- U+1F95  ᾕ GREEK SMALL LETTER ETA WITH DASIA AND OXIA AND YPOGEGRAMMENI
ᾕ = with-accent-breathing-iota acute rough
ᾖ : Token η′ lower -- U+1F96  ᾖ GREEK SMALL LETTER ETA WITH PSILI AND PERISPOMENI AND YPOGEGRAMMENI
ᾖ = with-accent-breathing-iota circumflex smooth
ᾗ : Token η′ lower -- U+1F97  ᾗ GREEK SMALL LETTER ETA WITH DASIA AND PERISPOMENI AND YPOGEGRAMMENI
ᾗ = with-accent-breathing-iota circumflex rough
ᾘ : Token η′ upper -- U+1F98  ᾘ GREEK CAPITAL LETTER ETA WITH PSILI AND PROSGEGRAMMENI
ᾘ = with-breathing-iota smooth
ᾙ : Token η′ upper -- U+1F99  ᾙ GREEK CAPITAL LETTER ETA WITH DASIA AND PROSGEGRAMMENI
ᾙ = with-breathing-iota rough
ᾚ : Token η′ upper -- U+1F9A  ᾚ GREEK CAPITAL LETTER ETA WITH PSILI AND VARIA AND PROSGEGRAMMENI
ᾚ = with-accent-breathing-iota grave smooth
ᾛ : Token η′ upper -- U+1F9B  ᾛ GREEK CAPITAL LETTER ETA WITH DASIA AND VARIA AND PROSGEGRAMMENI
ᾛ = with-accent-breathing-iota grave rough
ᾜ : Token η′ upper -- U+1F9C  ᾜ GREEK CAPITAL LETTER ETA WITH PSILI AND OXIA AND PROSGEGRAMMENI
ᾜ = with-accent-breathing-iota acute smooth
ᾝ : Token η′ upper -- U+1F9D  ᾝ GREEK CAPITAL LETTER ETA WITH DASIA AND OXIA AND PROSGEGRAMMENI
ᾝ = with-accent-breathing-iota acute rough
ᾞ : Token η′ upper -- U+1F9E  ᾞ GREEK CAPITAL LETTER ETA WITH PSILI AND PERISPOMENI AND PROSGEGRAMMENI
ᾞ = with-accent-breathing-iota circumflex smooth
ᾟ : Token η′ upper -- U+1F9F  ᾟ GREEK CAPITAL LETTER ETA WITH DASIA AND PERISPOMENI AND PROSGEGRAMMENI
ᾟ = with-accent-breathing-iota circumflex rough
ᾠ : Token ω′ lower -- U+1FA0  ᾠ GREEK SMALL LETTER OMEGA WITH PSILI AND YPOGEGRAMMENI
ᾠ = with-breathing-iota smooth
ᾡ : Token ω′ lower -- U+1FA1  ᾡ GREEK SMALL LETTER OMEGA WITH DASIA AND YPOGEGRAMMENI
ᾡ = with-breathing-iota rough
ᾢ : Token ω′ lower -- U+1FA2  ᾢ GREEK SMALL LETTER OMEGA WITH PSILI AND VARIA AND YPOGEGRAMMENI
ᾢ = with-accent-breathing-iota grave smooth
ᾣ : Token ω′ lower -- U+1FA3  ᾣ GREEK SMALL LETTER OMEGA WITH DASIA AND VARIA AND YPOGEGRAMMENI
ᾣ = with-accent-breathing-iota grave rough
ᾤ : Token ω′ lower -- U+1FA4  ᾤ GREEK SMALL LETTER OMEGA WITH PSILI AND OXIA AND YPOGEGRAMMENI
ᾤ = with-accent-breathing-iota acute smooth
ᾥ : Token ω′ lower -- U+1FA5  ᾥ GREEK SMALL LETTER OMEGA WITH DASIA AND OXIA AND YPOGEGRAMMENI
ᾥ = with-accent-breathing-iota acute rough
ᾦ : Token ω′ lower -- U+1FA6  ᾦ GREEK SMALL LETTER OMEGA WITH PSILI AND PERISPOMENI AND YPOGEGRAMMENI
ᾦ = with-accent-breathing-iota circumflex smooth
ᾧ : Token ω′ lower -- U+1FA7  ᾧ GREEK SMALL LETTER OMEGA WITH DASIA AND PERISPOMENI AND YPOGEGRAMMENI
ᾧ = with-accent-breathing-iota circumflex rough
ᾨ : Token ω′ upper -- U+1FA8  ᾨ GREEK CAPITAL LETTER OMEGA WITH PSILI AND PROSGEGRAMMENI
ᾨ = with-breathing-iota smooth
ᾩ : Token ω′ upper -- U+1FA9  ᾩ GREEK CAPITAL LETTER OMEGA WITH DASIA AND PROSGEGRAMMENI
ᾩ = with-breathing-iota rough
ᾪ : Token ω′ upper -- U+1FAA  ᾪ GREEK CAPITAL LETTER OMEGA WITH PSILI AND VARIA AND PROSGEGRAMMENI
ᾪ = with-accent-breathing-iota grave smooth
ᾫ : Token ω′ upper -- U+1FAB  ᾫ GREEK CAPITAL LETTER OMEGA WITH DASIA AND VARIA AND PROSGEGRAMMENI
ᾫ = with-accent-breathing-iota grave rough
ᾬ : Token ω′ upper -- U+1FAC  ᾬ GREEK CAPITAL LETTER OMEGA WITH PSILI AND OXIA AND PROSGEGRAMMENI
ᾬ = with-accent-breathing-iota acute smooth
ᾭ : Token ω′ upper -- U+1FAD  ᾭ GREEK CAPITAL LETTER OMEGA WITH DASIA AND OXIA AND PROSGEGRAMMENI
ᾭ = with-accent-breathing-iota acute rough
ᾮ : Token ω′ upper -- U+1FAE  ᾮ GREEK CAPITAL LETTER OMEGA WITH PSILI AND PERISPOMENI AND PROSGEGRAMMENI
ᾮ = with-accent-breathing-iota circumflex smooth
ᾯ : Token ω′ upper -- U+1FAF  ᾯ GREEK CAPITAL LETTER OMEGA WITH DASIA AND PERISPOMENI AND PROSGEGRAMMENI
ᾯ = with-accent-breathing-iota circumflex rough
-- U+1FB0 ᾰ GREEK SMALL LETTER ALPHA WITH VRACHY
-- U+1FB1 ᾱ GREEK SMALL LETTER ALPHA WITH MACRON
ᾲ : Token α′ lower -- U+1FB2  ᾲ GREEK SMALL LETTER ALPHA WITH VARIA AND YPOGEGRAMMENI
ᾲ = with-accent-iota grave
ᾳ : Token α′ lower -- U+1FB3  ᾳ GREEK SMALL LETTER ALPHA WITH YPOGEGRAMMENI
ᾳ = with-iota
ᾴ : Token α′ lower -- U+1FB4  ᾴ GREEK SMALL LETTER ALPHA WITH OXIA AND YPOGEGRAMMENI
ᾴ = with-accent-iota acute
-- U+1FB5
ᾶ : Token α′ lower -- U+1FB6  ᾶ GREEK SMALL LETTER ALPHA WITH PERISPOMENI
ᾶ = with-accent-iota circumflex
ᾷ : Token α′ lower -- U+1FB7  ᾷ GREEK SMALL LETTER ALPHA WITH PERISPOMENI AND YPOGEGRAMMENI
ᾷ = with-accent-iota circumflex
-- U+1FB8 Ᾰ GREEK CAPITAL LETTER ALPHA WITH VRACHY
-- U+1FB9 Ᾱ GREEK CAPITAL LETTER ALPHA WITH MACRON
Ὰ : Token α′ upper -- U+1FBA  Ὰ GREEK CAPITAL LETTER ALPHA WITH VARIA
Ὰ = with-accent grave
Ά : Token α′ upper -- U+1FBB  Ά GREEK CAPITAL LETTER ALPHA WITH OXIA
Ά = with-accent acute
ᾼ : Token α′ upper -- U+1FBC  ᾼ GREEK CAPITAL LETTER ALPHA WITH PROSGEGRAMMENI
ᾼ = with-iota
-- U+1FBD  ᾽  GREEK KORONIS
-- U+1FBE  ι  GREEK PROSGEGRAMMENI
-- U+1FBF  ᾿  GREEK PSILI
-- U+1FC0  ῀  GREEK PERISPOMENI
-- U+1FC1  ῁  GREEK DIALYTIKA AND PERISPOMENI
ῂ : Token η′ lower -- U+1FC2  ῂ GREEK SMALL LETTER ETA WITH VARIA AND YPOGEGRAMMENI accent circumflex
ῂ = with-accent-iota grave
ῃ : Token η′ lower -- U+1FC3  ῃ GREEK SMALL LETTER ETA WITH YPOGEGRAMMENI
ῃ = with-iota
ῄ : Token η′ lower -- U+1FC4  ῄ GREEK SMALL LETTER ETA WITH OXIA AND YPOGEGRAMMENI
ῄ = with-accent-iota acute
-- U+1FC5
ῆ : Token η′ lower -- U+1FC6  ῆ GREEK SMALL LETTER ETA WITH PERISPOMENI
ῆ = with-accent circumflex
ῇ : Token η′ lower -- U+1FC7  ῇ GREEK SMALL LETTER ETA WITH PERISPOMENI AND YPOGEGRAMMENI
ῇ = with-accent-iota circumflex
Ὲ : Token ε′ upper -- U+1FC8  Ὲ GREEK CAPITAL LETTER EPSILON WITH VARIA
Ὲ = with-accent grave
Έ : Token ε′ upper -- U+1FC9  Έ GREEK CAPITAL LETTER EPSILON WITH OXIA
Έ = with-accent acute
Ὴ : Token η′ upper -- U+1FCA  Ὴ GREEK CAPITAL LETTER ETA WITH VARIA
Ὴ = with-accent grave
Ή : Token η′ upper -- U+1FCB  Ή GREEK CAPITAL LETTER ETA WITH OXIA
Ή = with-accent acute
ῌ : Token η′ upper -- U+1FCC  ῌ GREEK CAPITAL LETTER ETA WITH PROSGEGRAMMENI
ῌ = with-iota
-- U+1FCD  ῍ GREEK PSILI AND VARIA
-- U+1FCE  ῎ GREEK PSILI AND OXIA
-- U+1FCF  ῏ GREEK PSILI AND PERISPOMENI
-- U+1FD0  ῐ GREEK SMALL LETTER IOTA WITH VRACHY
-- U+1FD1  ῑ GREEK SMALL LETTER IOTA WITH MACRON
ῒ : Token ι′ lower -- U+1FD2  ῒ GREEK SMALL LETTER IOTA WITH DIALYTIKA AND VARIA
ῒ = with-accent-diaeresis grave
ΐ : Token ι′ lower -- U+1FD3  ΐ GREEK SMALL LETTER IOTA WITH DIALYTIKA AND OXIA
ΐ = with-accent-diaeresis acute
-- U+1FD4
-- U+1FD5
ῖ : Token ι′ lower -- U+1FD6  ῖ GREEK SMALL LETTER IOTA WITH PERISPOMENI
ῖ = with-accent circumflex
ῗ : Token ι′ lower -- U+1FD7  ῗ GREEK SMALL LETTER IOTA WITH DIALYTIKA AND PERISPOMENI
ῗ = with-accent-diaeresis circumflex
-- U+1FD8 Ῐ GREEK CAPITAL LETTER IOTA WITH VRACHY
-- U+1FD9 Ῑ GREEK CAPITAL LETTER IOTA WITH MACRON
Ὶ : Token ι′ upper -- U+1FDA  Ὶ GREEK CAPITAL LETTER IOTA WITH VARIA
Ὶ = with-accent grave
Ί : Token ι′ upper -- U+1FDB  Ί GREEK CAPITAL LETTER IOTA WITH OXIA
Ί = with-accent acute
-- U+1FDC
-- U+1FDD  ῝ GREEK DASIA AND VARIA
-- U+1FDE  ῞ GREEK DASIA AND OXIA
-- U+1FDF  ῟ GREEK DASIA AND PERISPOMENI
-- U+1FE0 ῠ GREEK SMALL LETTER UPSILON WITH VRACHY
-- U+1FE1 ῡ GREEK SMALL LETTER UPSILON WITH MACRON
ῢ : Token υ′ lower -- U+1FE2  ῢ GREEK SMALL LETTER UPSILON WITH DIALYTIKA AND VARIA
ῢ = with-accent-diaeresis grave
ΰ : Token υ′ lower -- U+1FE3  ΰ GREEK SMALL LETTER UPSILON WITH DIALYTIKA AND OXIA
ΰ = with-accent-diaeresis acute
ῤ : Token ρ′ lower -- U+1FE4 ῤ GREEK SMALL LETTER RHO WITH PSILI
ῤ = with-breathing smooth
ῥ : Token ρ′ lower -- U+1FE5 ῥ GREEK SMALL LETTER RHO WITH DASIA
ῥ = with-breathing rough
ῦ : Token υ′ lower -- U+1FE6  ῦ GREEK SMALL LETTER UPSILON WITH PERISPOMENI
ῦ = with-accent circumflex
ῧ : Token υ′ lower -- U+1FE7  ῧ GREEK SMALL LETTER UPSILON WITH DIALYTIKA AND PERISPOMENI
ῧ = with-accent-diaeresis circumflex
-- U+1FE8 Ῠ GREEK CAPITAL LETTER UPSILON WITH VRACHY
-- U+1FE9 Ῡ GREEK CAPITAL LETTER UPSILON WITH MACRON
Ὺ : Token υ′ upper -- U+1FEA  Ὺ GREEK CAPITAL LETTER UPSILON WITH VARIA
Ὺ = with-accent grave
Ύ : Token υ′ upper -- U+1FEB  Ύ GREEK CAPITAL LETTER UPSILON WITH OXIA
Ύ = with-accent acute
Ῥ : Token ρ′ upper -- U+1FEC Ῥ GREEK CAPITAL LETTER RHO WITH DASIA
Ῥ = with-breathing rough
-- U+1FED  ῭ GREEK DIALYTIKA AND VARIA
-- U+1FEE  ΅ GREEK DIALYTIKA AND OXIA
-- U+1FEF  ` GREEK VARIA
-- U+1FF0
-- U+1FF1
ῲ : Token ω′ lower -- U+1FF2  ῲ GREEK SMALL LETTER OMEGA WITH VARIA AND YPOGEGRAMMENI
ῲ = with-accent-iota grave
ῳ : Token ω′ lower -- U+1FF3  ῳ GREEK SMALL LETTER OMEGA WITH YPOGEGRAMMENI
ῳ = with-iota
ῴ : Token ω′ lower -- U+1FF4  ῴ GREEK SMALL LETTER OMEGA WITH OXIA AND YPOGEGRAMMENI
ῴ = with-accent-iota acute
-- U+1FF5
ῶ : Token ω′ lower -- U+1FF6  ῶ GREEK SMALL LETTER OMEGA WITH PERISPOMENI
ῶ = with-accent circumflex
ῷ : Token ω′ lower -- U+1FF7  ῷ GREEK SMALL LETTER OMEGA WITH PERISPOMENI AND YPOGEGRAMMENI
ῷ = with-accent-iota circumflex
Ὸ : Token ο′ upper -- U+1FF8  Ὸ GREEK CAPITAL LETTER OMICRON WITH VARIA
Ὸ = with-accent grave
Ό : Token ο′ upper -- U+1FF9  Ό GREEK CAPITAL LETTER OMICRON WITH OXIA
Ό = with-accent acute
Ὼ : Token ω′ upper -- U+1FFA  Ὼ GREEK CAPITAL LETTER OMEGA WITH VARIA
Ὼ = with-accent grave
Ώ : Token ω′ upper -- U+1FFB  Ώ GREEK CAPITAL LETTER OMEGA WITH OXIA
Ώ = with-accent acute
ῼ : Token ω′ upper -- U+1FFC  ῼ GREEK CAPITAL LETTER OMEGA WITH PROSGEGRAMMENI
ῼ = with-iota
-- U+1FFD  ´ GREEK OXIA
-- U+1FFE  ῾ GREEK DASIA
-- U+1FFF

-- Mapping

data Accent : Set where
  acute-mark grave-mark circumflex-mark : Accent

letter-to-accent : ∀ {v} → v accent → Accent
letter-to-accent acute = acute-mark
letter-to-accent grave = grave-mark
letter-to-accent circumflex = circumflex-mark

get-accent : ∀ {ℓ c} → Token ℓ c → Maybe Accent
get-accent (with-accent a) = just (letter-to-accent a)
get-accent (with-accent-breathing a _) = just (letter-to-accent a)
get-accent (with-accent-breathing-iota a _) = just (letter-to-accent a)
get-accent (with-accent-diaeresis a) = just (letter-to-accent a)
get-accent (with-accent-iota a) = just (letter-to-accent a)
get-accent _ = nothing

data Breathing : Set where
  smooth-mark rough-mark : Breathing

letter-to-breathing : ∀ {ℓ c} → ℓ ⟦ c ⟧-breathing → Breathing
letter-to-breathing smooth = smooth-mark
letter-to-breathing rough = rough-mark

get-breathing : ∀ {ℓ c} → Token ℓ c → Maybe Breathing
get-breathing (with-breathing x) = just (letter-to-breathing x)
get-breathing (with-accent-breathing _ x) = just (letter-to-breathing x)
get-breathing (with-accent-breathing-iota _ x) = just (letter-to-breathing x)
get-breathing (with-breathing-iota x) = just (letter-to-breathing x)
get-breathing _ = nothing

data IotaSubscript : Set where
  iota-subscript-mark : IotaSubscript

get-iota-subscript : ∀ {ℓ c} → Token ℓ c → Maybe IotaSubscript
get-iota-subscript (with-accent-breathing-iota _ _) = just iota-subscript-mark
get-iota-subscript (with-accent-iota _) = just iota-subscript-mark
get-iota-subscript (with-breathing-iota _) = just iota-subscript-mark
get-iota-subscript _ = nothing

data Diaeresis : Set where
  diaeresis-mark : Diaeresis

get-diaeresis : ∀ {ℓ c} → Token ℓ c → Maybe Diaeresis
get-diaeresis with-diaeresis = just diaeresis-mark
get-diaeresis (with-accent-diaeresis _) = just diaeresis-mark
get-diaeresis _ = nothing

data FinalForm : Set where
  final-form : FinalForm

get-final-form : ∀ {ℓ c} → Token ℓ c → Maybe FinalForm
get-final-form final = just final-form
get-final-form _ = nothing

module Text.Greek.Script where

open import Data.Maybe
open import Data.Vec
open import Relation.Nullary using (¬_)
open import Relation.Binary.PropositionalEquality using (_≢_)

data Case : Set where
  lower upper : Case

data Letter : Set where
  α′ β′ γ′ δ′ ε′ ζ′ η′ θ′ ι′ κ′ λ′ μ′ ν′ ξ′ ο′ π′ ρ′ σ′ τ′ υ′ φ′ χ′ ψ′ ω′ : Letter

vowels : Vec _ _
vowels = α′ ∷ ε′ ∷ η′ ∷ ι′ ∷ ο′ ∷ υ′ ∷ ω′ ∷ []

always-short-letters : Vec _ _
always-short-letters = ε′ ∷ ο′ ∷ []

diaeresis-letters : Vec _ _
diaeresis-letters = ι′ ∷ υ′ ∷ []

iota-subscript-letters : Vec _ _
iota-subscript-letters = α′ ∷ η′ ∷ ω′ ∷ []

data _vowel : Letter → Set where
  is-vowel : ∀ {v} → v ∈ vowels → v vowel

data _always-short : Letter → Set where
  is-always-short : ∀ {v} → ⦃ p : v vowel ⦄ → v ∈ always-short-letters → v always-short

data _diaeresis : Letter → Set where
  add-diaeresis : ∀ {v} → ⦃ p : v vowel ⦄ → v ∈ diaeresis-letters → v diaeresis

data _⟦_⟧-final : Letter → Case → Set where
  make-final : σ′ ⟦ lower ⟧-final

data _⟦_⟧-smooth : Letter → Case → Set where
  add-smooth-lower-vowel : ∀ {v} → ⦃ p : v vowel ⦄ → v ⟦ lower ⟧-smooth
  add-smooth-ρ : ρ′ ⟦ lower ⟧-smooth
  add-smooth-upper-vowel-not-Υ : ∀ {v} → ⦃ p : v vowel ⦄ → v ≢ υ′ → v ⟦ upper ⟧-smooth

data _with-rough : Letter → Set where
  add-rough-vowel : ∀ {v} → ⦃ p : v vowel ⦄ → v with-rough
  add-rough-ρ : ρ′ with-rough

data _iota-subscript : Letter → Set where
  add-iota-subscript : ∀ {v} → ⦃ p : v vowel ⦄ → v ∈ iota-subscript-letters → v iota-subscript

data _⟦_⟧-breathing : Letter → Case → Set where
  smooth : ∀ {ℓ c} → ⦃ p : ℓ ⟦ c ⟧-smooth ⦄ → ℓ ⟦ c ⟧-breathing
  rough : ∀ {ℓ c} → ⦃ p : ℓ with-rough ⦄ → ℓ ⟦ c ⟧-breathing

data _long-vowel : Letter → Set where
  make-long-vowel : ∀ {v} → ⦃ p : v vowel ⦄ → ¬ v always-short → v long-vowel

data _accent : Letter → Set where
  acute : ∀ {ℓ} → ⦃ p : ℓ vowel ⦄ → ℓ accent
  grave : ∀ {ℓ} → ⦃ p : ℓ vowel ⦄ → ℓ accent
  circumflex : ∀ {ℓ} → ⦃ p : ℓ long-vowel ⦄ → ℓ accent

data Token : Letter → Case → Set where
  unmarked : ∀ {ℓ c} → Token ℓ c
  with-accent : ∀ {ℓ c} → ℓ accent → Token ℓ c
  with-breathing : ∀ {ℓ c} → ℓ ⟦ c ⟧-breathing → Token ℓ c
  with-accent-breathing : ∀ {ℓ c} → ℓ accent → ℓ ⟦ c ⟧-breathing → Token ℓ c
  with-accent-breathing-iota : ∀ {ℓ c} → ℓ accent → ℓ ⟦ c ⟧-breathing → ⦃ p : ℓ iota-subscript ⦄ → Token ℓ c
  with-diaeresis : ∀ {ℓ c} → ⦃ p : ℓ diaeresis ⦄ → Token ℓ c
  with-accent-diaeresis : ∀ {ℓ c} → ℓ accent → ⦃ p : ℓ diaeresis ⦄ → Token ℓ c
  with-accent-iota : ∀ {ℓ c} → ℓ accent → ⦃ p : ℓ iota-subscript ⦄ → Token ℓ c
  with-breathing-iota : ∀ {ℓ c} → ℓ ⟦ c ⟧-breathing → ⦃ p : ℓ iota-subscript ⦄ → Token ℓ c
  with-iota : ∀ {ℓ c} → ⦃ p : ℓ iota-subscript ⦄ → Token ℓ c
  final : ∀ {ℓ c} → ⦃ p : ℓ ⟦ c ⟧-final ⦄ → Token ℓ c

-- Constructions

-- Α α
instance α-vowel : α′ vowel
α-vowel = is-vowel here

¬α-always-short : ¬ α′ always-short
¬α-always-short (is-always-short (there (there ())))

instance α-long-vowel : α′ long-vowel
α-long-vowel = make-long-vowel ¬α-always-short

instance α-smooth : α′ ⟦ lower ⟧-smooth
α-smooth = add-smooth-lower-vowel

instance Α-smooth : α′ ⟦ upper ⟧-smooth
Α-smooth = add-smooth-upper-vowel-not-Υ (λ ())

instance α-rough : α′ with-rough
α-rough = add-rough-vowel

instance α-iota-subscript : α′ iota-subscript
α-iota-subscript = add-iota-subscript here

-- Ε ε
instance ε-vowel : ε′ vowel
ε-vowel = is-vowel (there here)

ε-always-short : ε′ always-short
ε-always-short = is-always-short here

instance ε-smooth : ε′ ⟦ lower ⟧-smooth
ε-smooth = add-smooth-lower-vowel

instance Ε-smooth : ε′ ⟦ upper ⟧-smooth
Ε-smooth = add-smooth-upper-vowel-not-Υ (λ ())

instance ε-rough : ε′ with-rough
ε-rough = add-rough-vowel

-- Η η
instance η-vowel : η′ vowel
η-vowel = is-vowel (there (there here))

¬η-always-short : ¬ η′ always-short
¬η-always-short (is-always-short (there (there ())))

instance η-long-vowel : η′ long-vowel
η-long-vowel = make-long-vowel ¬η-always-short

instance η-smooth : η′ ⟦ lower ⟧-smooth
η-smooth = add-smooth-lower-vowel

instance Η-smooth : η′ ⟦ upper ⟧-smooth
Η-smooth = add-smooth-upper-vowel-not-Υ (λ ())

instance η-rough : η′ with-rough
η-rough = add-rough-vowel

instance η-iota-subscript : η′ iota-subscript
η-iota-subscript = add-iota-subscript (there here)

-- Ι ι

instance ι-vowel : ι′ vowel
ι-vowel = is-vowel (there (there (there here)))

¬ι-always-short : ¬ ι′ always-short
¬ι-always-short (is-always-short (there (there ())))

instance ι-long-vowel : ι′ long-vowel
ι-long-vowel = make-long-vowel ¬ι-always-short

instance ι-smooth : ι′ ⟦ lower ⟧-smooth
ι-smooth = add-smooth-lower-vowel

instance Ι-smooth : ι′ ⟦ upper ⟧-smooth
Ι-smooth = add-smooth-upper-vowel-not-Υ (λ ())

instance ι-rough : ι′ with-rough
ι-rough = add-rough-vowel

instance ι-diaeresis : ι′ diaeresis
ι-diaeresis = add-diaeresis here

-- Ο ο
instance ο-vowel : ο′ vowel
ο-vowel = is-vowel (there (there (there (there here))))

ο-always-short : ο′ always-short
ο-always-short = is-always-short (there here)

instance ο-smooth : ο′ ⟦ lower ⟧-smooth
ο-smooth = add-smooth-lower-vowel

instance Ο-smooth : ο′ ⟦ upper ⟧-smooth
Ο-smooth = add-smooth-upper-vowel-not-Υ (λ ())

instance ο-rough : ο′ with-rough
ο-rough = add-rough-vowel

-- Ρ ρ
instance ρ-smooth : ρ′ ⟦ lower ⟧-smooth
ρ-smooth = add-smooth-ρ

instance ρ-rough : ρ′ with-rough
ρ-rough = add-rough-ρ

-- Σ σ
instance σ-final : σ′ ⟦ lower ⟧-final
σ-final = make-final

-- Υ υ
instance υ-vowel : υ′ vowel
υ-vowel = is-vowel (there (there (there (there (there here)))))

¬υ-always-short : ¬ υ′ always-short
¬υ-always-short (is-always-short (there (there ())))

instance υ-long-vowel : υ′ long-vowel
υ-long-vowel = make-long-vowel ¬υ-always-short

instance υ-smooth : υ′ ⟦ lower ⟧-smooth
υ-smooth = add-smooth-lower-vowel

instance υ-rough : υ′ with-rough
υ-rough = add-rough-vowel

instance υ-diaeresis : υ′ diaeresis
υ-diaeresis = add-diaeresis (there here)

-- Ω ω
instance ω-vowel : ω′ vowel
ω-vowel = is-vowel (there (there (there (there (there (there here))))))

¬ω-always-short : ¬ ω′ always-short
¬ω-always-short (is-always-short (there (there ())))

instance ω-long-vowel : ω′ long-vowel
ω-long-vowel = make-long-vowel ¬ω-always-short

instance ω-smooth : ω′ ⟦ lower ⟧-smooth
ω-smooth = add-smooth-lower-vowel

instance Ω-smooth : ω′ ⟦ upper ⟧-smooth
Ω-smooth = add-smooth-upper-vowel-not-Υ (λ ())

instance ω-rough : ω′ with-rough
ω-rough = add-rough-vowel

instance ω-iota-subscript : ω′ iota-subscript
ω-iota-subscript = add-iota-subscript (there (there here))

-- Unicode
-- U+0390 - U+03CE
ΐ : Token ι′ lower -- U+0390 GREEK SMALL LETTER IOTA WITH DIALYTIKA AND TONOS
ΐ = with-accent-diaeresis acute
Α : Token α′ upper -- U+0391 GREEK CAPITAL LETTER ALPHA
Α = unmarked
Β : Token β′ upper -- U+0392 GREEK CAPITAL LETTER BETA
Β = unmarked
Γ : Token γ′ upper -- U+0393 GREEK CAPITAL LETTER GAMMA
Γ = unmarked
Δ : Token δ′ upper -- U+0394 GREEK CAPITAL LETTER DELTA
Δ = unmarked
Ε : Token ε′ upper -- U+0395 GREEK CAPITAL LETTER EPSILON
Ε = unmarked
Ζ : Token ζ′ upper -- U+0396 GREEK CAPITAL LETTER ZETA
Ζ = unmarked
Η : Token η′ upper -- U+0397 GREEK CAPITAL LETTER ETA
Η = unmarked
Θ : Token θ′ upper -- U+0398 GREEK CAPITAL LETTER THETA
Θ = unmarked
Ι : Token ι′ upper -- U+0399 GREEK CAPITAL LETTER IOTA
Ι = unmarked
Κ : Token κ′ upper -- U+039A GREEK CAPITAL LETTER KAPPA
Κ = unmarked
Λ : Token λ′ upper -- U+039B GREEK CAPITAL LETTER LAMDA
Λ = unmarked
Μ : Token μ′ upper -- U+039C GREEK CAPITAL LETTER MU
Μ = unmarked
Ν : Token ν′ upper -- U+039D GREEK CAPITAL LETTER NU
Ν = unmarked
Ξ : Token ξ′ upper -- U+039E GREEK CAPITAL LETTER XI
Ξ = unmarked
Ο : Token ο′ upper -- U+039F GREEK CAPITAL LETTER OMICRON
Ο = unmarked
Π : Token π′ upper -- U+03A0 GREEK CAPITAL LETTER PI
Π = unmarked
Ρ : Token ρ′ upper -- U+03A1 GREEK CAPITAL LETTER RHO
Ρ = unmarked
                  -- U+03A2 <reserved>
Σ : Token σ′ upper -- U+03A3 GREEK CAPITAL LETTER SIGMA
Σ = unmarked
Τ : Token τ′ upper -- U+03A4 GREEK CAPITAL LETTER TAU
Τ = unmarked
Υ : Token υ′ upper -- U+03A5 GREEK CAPITAL LETTER UPSILON
Υ = unmarked
Φ : Token φ′ upper -- U+03A6 GREEK CAPITAL LETTER PHI
Φ = unmarked
Χ : Token χ′ upper -- U+03A7 GREEK CAPITAL LETTER CHI
Χ = unmarked
Ψ : Token ψ′ upper -- U+03A8 GREEK CAPITAL LETTER PSI
Ψ = unmarked
Ω : Token ω′ upper -- U+03A9 GREEK CAPITAL LETTER OMEGA
Ω = unmarked
Ϊ : Token ι′ upper -- U+03AA GREEK CAPITAL LETTER IOTA WITH DIALYTIKA
Ϊ = with-diaeresis
Ϋ : Token υ′ upper -- U+03AB GREEK CAPITAL LETTER UPSILON WITH DIALYTIKA
Ϋ = with-diaeresis
ά : Token α′ lower -- U+03AC GREEK SMALL LETTER ALPHA WITH TONOS
ά = with-accent acute
έ : Token ε′ lower -- U+03AD GREEK SMALL LETTER EPSILON WITH TONOS
έ = with-accent acute
ή : Token η′ lower -- U+03AE GREEK SMALL LETTER ETA WITH TONOS
ή = with-accent acute
ί : Token ι′ lower -- U+03AF GREEK SMALL LETTER IOTA WITH TONOS
ί = with-accent acute
ΰ : Token υ′ lower -- U+03B0 GREEK SMALL LETTER UPSILON WITH DIALYTIKA AND TONOS
ΰ = with-accent-diaeresis acute
α : Token α′ lower -- U+03B1 GREEK SMALL LETTER ALPHA
α = unmarked
β : Token β′ lower -- U+03B2 GREEK SMALL LETTER BETA
β = unmarked
γ : Token γ′ lower -- U+03B3 GREEK SMALL LETTER GAMMA
γ = unmarked
δ : Token δ′ lower -- U+03B4 GREEK SMALL LETTER DELTA
δ = unmarked
ε : Token ε′ lower -- U+03B5 GREEK SMALL LETTER EPSILON
ε = unmarked
ζ : Token ζ′ lower -- U+03B6 GREEK SMALL LETTER ZETA
ζ = unmarked
η : Token η′ lower -- U+03B7 GREEK SMALL LETTER ETA
η = unmarked
θ : Token θ′ lower -- U+03B8 GREEK SMALL LETTER THETA
θ = unmarked
ι : Token ι′ lower -- U+03B9 GREEK SMALL LETTER IOTA
ι = unmarked
κ : Token κ′ lower -- U+03BA GREEK SMALL LETTER KAPPA
κ = unmarked
∙λ : Token λ′ lower -- U+03BB GREEK SMALL LETTER LAMDA
∙λ = unmarked
μ : Token μ′ lower -- U+03BC GREEK SMALL LETTER MU
μ = unmarked
ν : Token ν′ lower -- U+03BD GREEK SMALL LETTER NU
ν = unmarked
ξ : Token ξ′ lower -- U+03BE GREEK SMALL LETTER XI
ξ = unmarked
ο : Token ο′ lower -- U+03BF GREEK SMALL LETTER OMICRON
ο = unmarked
π : Token π′ lower -- U+03C0 GREEK SMALL LETTER PI
π = unmarked
ρ : Token ρ′ lower -- U+03C1 GREEK SMALL LETTER RHO
ρ = unmarked
ς : Token σ′ lower -- U+03C2 GREEK SMALL LETTER FINAL SIGMA
ς = final
σ : Token σ′ lower -- U+03C3 GREEK SMALL LETTER SIGMA
σ = unmarked
τ : Token τ′ lower -- U+03C4 GREEK SMALL LETTER TAU
τ = unmarked
υ : Token υ′ lower -- U+03C5 GREEK SMALL LETTER UPSILON
υ = unmarked
φ : Token φ′ lower -- U+03C6 GREEK SMALL LETTER PHI
φ = unmarked
χ : Token χ′ lower -- U+03C7 GREEK SMALL LETTER CHI
χ = unmarked
ψ : Token ψ′ lower -- U+03C8 GREEK SMALL LETTER PSI
ψ = unmarked
ω : Token ω′ lower -- U+03C9 GREEK SMALL LETTER OMEGA
ω = unmarked
ϊ : Token ι′ lower -- U+03CA GREEK SMALL LETTER IOTA WITH DIALYTIKA
ϊ = with-diaeresis
ϋ : Token υ′ lower -- U+03CB GREEK SMALL LETTER UPSILON WITH DIALYTIKA
ϋ = with-diaeresis
ό : Token ο′ lower -- U+03CC GREEK SMALL LETTER OMICRON WITH TONOS
ό = with-accent acute
ύ : Token υ′ lower -- U+03CD GREEK SMALL LETTER UPSILON WITH TONOS
ύ = with-accent acute
ώ : Token ω′ lower -- U+03CE GREEK SMALL LETTER OMEGA WITH TONOS
ώ = with-accent acute

ἀ : Token α′ lower
ἀ = with-breathing smooth
ἁ : Token α′ lower
ἁ = with-breathing rough
ἂ : Token α′ lower
ἂ = with-accent-breathing grave smooth
ἃ : Token α′ lower
ἃ = with-accent-breathing grave rough
ἄ : Token α′ lower
ἄ = with-accent-breathing acute smooth
ἅ : Token α′ lower
ἅ = with-accent-breathing acute rough
ἆ : Token α′ lower
ἆ = with-accent-breathing circumflex smooth
ἇ : Token α′ lower
ἇ = with-accent-breathing circumflex rough
Ἀ : Token α′ upper
Ἀ = with-breathing smooth
Ἁ : Token α′ upper
Ἁ = with-breathing rough
Ἂ : Token α′ upper
Ἂ = with-accent-breathing grave smooth
Ἃ : Token α′ upper
Ἃ = with-accent-breathing grave rough
Ἄ : Token α′ upper
Ἄ = with-accent-breathing acute smooth
Ἅ : Token α′ upper
Ἅ = with-accent-breathing acute rough
Ἆ : Token α′ upper
Ἆ = with-accent-breathing circumflex smooth
Ἇ : Token α′ upper
Ἇ = with-accent-breathing circumflex rough

-- U+1F7x
ὰ : Token α′ lower
ὰ = with-accent grave
ά : Token α′ lower
ά = with-accent acute

-- U+1F8x
ᾀ : Token α′ lower
ᾀ = with-breathing-iota smooth
ᾁ : Token α′ lower
ᾁ = with-breathing-iota rough
ᾂ : Token α′ lower
ᾂ = with-accent-breathing-iota grave smooth
ᾃ : Token α′ lower
ᾃ = with-accent-breathing-iota grave rough
ᾄ : Token α′ lower
ᾄ = with-accent-breathing-iota acute smooth
ᾅ : Token α′ lower
ᾅ = with-accent-breathing-iota acute rough
ᾆ : Token α′ lower
ᾆ = with-accent-breathing-iota circumflex smooth
ᾇ : Token α′ lower
ᾇ = with-accent-breathing-iota circumflex rough
ᾈ : Token α′ upper
ᾈ = with-breathing-iota smooth
ᾉ : Token α′ upper
ᾉ = with-breathing-iota rough
ᾊ : Token α′ upper
ᾊ = with-accent-breathing-iota grave smooth
ᾋ : Token α′ upper
ᾋ = with-accent-breathing-iota grave rough
ᾌ : Token α′ upper
ᾌ = with-accent-breathing-iota acute smooth
ᾍ : Token α′ upper
ᾍ = with-accent-breathing-iota acute rough
ᾎ : Token α′ upper
ᾎ = with-accent-breathing-iota circumflex smooth
ᾏ : Token α′ upper
ᾏ = with-accent-breathing-iota circumflex rough

-- U+1FBx
-- ᾰ
-- ᾱ
ᾲ : Token α′ lower
ᾲ = with-accent-iota grave
ᾳ : Token α′ lower
ᾳ = with-iota
ᾴ : Token α′ lower
ᾴ = with-accent-iota acute
ᾶ : Token α′ lower
ᾶ = with-accent circumflex
ᾷ : Token α′ lower
ᾷ = with-accent-iota circumflex
-- Ᾰ
-- Ᾱ
Ὰ : Token α′ upper
Ὰ = with-accent grave
Ά : Token α′ upper
Ά = with-accent acute
ᾼ : Token α′ upper
ᾼ = with-iota

-- Mapping

data Accent : Set where
  acute-mark grave-mark circumflex-mark : Accent

letter-to-accent : ∀ {v} → v accent → Accent
letter-to-accent acute = acute-mark
letter-to-accent grave = grave-mark
letter-to-accent circumflex = circumflex-mark

get-accent : ∀ {ℓ c} → Token ℓ c → Maybe Accent
get-accent (with-accent a) = just (letter-to-accent a)
get-accent (with-accent-breathing a _) = just (letter-to-accent a)
get-accent (with-accent-breathing-iota a _) = just (letter-to-accent a)
get-accent (with-accent-diaeresis a) = just (letter-to-accent a)
get-accent (with-accent-iota a) = just (letter-to-accent a)
get-accent _ = nothing

data Breathing : Set where
  smooth-mark rough-mark : Breathing

letter-to-breathing : ∀ {ℓ c} → ℓ ⟦ c ⟧-breathing → Breathing
letter-to-breathing smooth = smooth-mark
letter-to-breathing rough = rough-mark

get-breathing : ∀ {ℓ c} → Token ℓ c → Maybe Breathing
get-breathing (with-breathing x) = just (letter-to-breathing x)
get-breathing (with-accent-breathing _ x) = just (letter-to-breathing x)
get-breathing (with-accent-breathing-iota _ x) = just (letter-to-breathing x)
get-breathing (with-breathing-iota x) = just (letter-to-breathing x)
get-breathing _ = nothing

data IotaSubscript : Set where
  iota-subscript-mark : IotaSubscript

get-iota-subscript : ∀ {ℓ c} → Token ℓ c → Maybe IotaSubscript
get-iota-subscript (with-accent-breathing-iota _ _) = just iota-subscript-mark
get-iota-subscript (with-accent-iota _) = just iota-subscript-mark
get-iota-subscript (with-breathing-iota _) = just iota-subscript-mark
get-iota-subscript _ = nothing

data Diaeresis : Set where
  diaeresis-mark : Diaeresis

get-diaeresis : ∀ {ℓ c} → Token ℓ c → Maybe Diaeresis
get-diaeresis with-diaeresis = just diaeresis-mark
get-diaeresis (with-accent-diaeresis _) = just diaeresis-mark
get-diaeresis _ = nothing

data FinalForm : Set where
  final-form : FinalForm

get-final-form : ∀ {ℓ c} → Token ℓ c → Maybe FinalForm
get-final-form final = just final-form
get-final-form _ = nothing


IDesc: tagged indexed description

IDesc: tagged indexed description


Added doc.

Added doc.

Ignore-this: d943a6359f1fa72487ab808788c3bd0e

darcs-hash:20110227043610-3bd4e-0cb5a48fd55778fc07d4e4e5389bf3e2d2648b58.gz

----------------------------------------------------------------------------
-- Well-founded induction on the relation MCR
----------------------------------------------------------------------------

{-# OPTIONS --no-termination-check #-}

-- N.B This module does not contain combined proofs, but it imports
-- modules which contain combined proofs.

module FOTC.Program.McCarthy91.MCR.WellFoundedInductionATP where

open import FOTC.Base

open import FOTC.Data.Nat

open import FOTC.Program.McCarthy91.McCarthy91
open import FOTC.Program.McCarthy91.MCR
open import FOTC.Program.McCarthy91.MCR.PropertiesATP

----------------------------------------------------------------------------

-- Adapted from FOTC.Data.Nat.Induction.WellFoundedI.wfInd-LT₁.
wfInd-MCR : (P : D → Set) →
            (∀ {m} → N m → (∀ {n} → N n → MCR n m → P n) → P m) →
            ∀ {n} → N n → P n
wfInd-MCR P accH Nn = accH Nn (helper Nn)
  where
    helper : ∀ {m n} → N m → N n → MCR n m → P n
    helper Nm zN 0«m = ⊥-elim (0«x→⊥ Nm 0«m)

    -- This equation does not pass the termination check.
    helper zN (sN {n} Nn) Sn«0 = accH (sN Nn)
      (λ {n'} Nn' n'«Sn →
        let n'«0 : MCR n' zero
            n'«0 = «-trans Nn' (sN Nn) zN n'«Sn Sn«0

        in helper zN Nn' n'«0
      )

    -- Other version of the previous equation (this version neither
    -- pass the termination check).
    -- helper zN (sN {n} Nn) Sn«0 = accH (sN Nn)
    --   (λ {n'} Nn' n'«Sn →
    --     let n'«n : MCR n' n
    --         n'«n = x«Sy→x«y Nn' Nn n'«Sn

    --     in helper Nn Nn' n'«n
    --   )

    -- Other version of the previous equation (this version neither
    -- pass the termination check).
    -- helper zN Nn n«0 = accH Nn
    --   (λ {n'} Nn' n'«n →
    --     let n'«0 : MCR n' zero
    --         n'«0 = «-trans Nn' Nn zN n'«n n«0

    --     in helper zN Nn' n'«0
    --   )

    -- Other version of the previous equation (this version neither
    -- pass the termination check).
    -- helper {n = n} zN Nn n«0 =
    --   accH Nn (λ {n'} Nn' n'«n → helper Nn Nn' n'«n)

    helper (sN {m} Nm) (sN {n} Nn) Sn«Sm = helper Nm (sN Nn) Sn«m
      where
        Sn«m : MCR (succ n) m
        Sn«m = x«Sy→x«y (sN Nn) Nm Sn«Sm

----------------------------------------------------------------------------
-- Well-founded induction on the relation MCR
----------------------------------------------------------------------------

{-# OPTIONS --no-termination-check #-}

-- N.B This module does not contain combined proofs, but it imports
-- modules which contain combined proofs.

module FOTC.Program.McCarthy91.MCR.WellFoundedInductionATP where

open import FOTC.Base

open import FOTC.Data.Nat

open import FOTC.Program.McCarthy91.McCarthy91
open import FOTC.Program.McCarthy91.MCR
open import FOTC.Program.McCarthy91.MCR.PropertiesATP

----------------------------------------------------------------------------

-- Adapted from FOTC.Data.Nat.Induction.WellFoundedI.wfInd-LT₁.
wfInd-MCR : (P : D → Set) →
            (∀ {m} → N m → (∀ {n} → N n → MCR n m → P n) → P m) →
            ∀ {n} → N n → P n
wfInd-MCR P accH Nn = accH Nn (helper Nn)
  where
    helper : ∀ {m n} → N m → N n → MCR n m → P n
    helper Nm zN 0«m = ⊥-elim (0«x→⊥ Nm 0«m)

    -- This equation does not pass the termination check.
    helper zN Nn n«0 = accH Nn
      (λ {n'} Nn' n'«n →
        let n'«0 : MCR n' zero
            n'«0 = «-trans Nn' Nn zN n'«n n«0

        in helper zN Nn' n'«0
      )

    helper (sN {m} Nm) (sN {n} Nn) Sn«Sm = helper Nm (sN Nn) Sn«m
      where
        Sn«m : MCR (succ n) m
        Sn«m = x«Sy→x«y (sN Nn) Nm Sn«Sm