Greek Script in Agda

AgdaGreek4.agda

module AgdaGreek4 where

open import Data.Maybe renaming (nothing to ⃠)
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 Letter _
vowels = α ∷ ε ∷ η ∷ ι ∷ ο ∷ υ ∷ ω ∷ []

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

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

iota-subscript-letters : Vec Letter _
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} → v vowel → v ∈ always-short-letters → v always-short

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

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

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

data _rough : Letter → Set where
  add-rough-vowel : ∀ {v} → v vowel → v rough
  add-rough-ρ : ρ rough

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

data _⟦_⟧-breathing : Letter → Case → Set where
  add-smooth : ∀ {ℓ c} → ℓ ⟦ c ⟧-smooth → ℓ ⟦ c ⟧-breathing
  add-rough : ∀ {ℓ c} → ℓ rough → ℓ ⟦ c ⟧-breathing

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

data _accent : Letter → Set where
  add-acute : ∀ {ℓ} → ℓ vowel → ℓ accent
  add-grave : ∀ {ℓ} → ℓ vowel → ℓ accent
  add-circumflex : ∀ {ℓ} → 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 → ℓ iota-subscript → Token ℓ c
  with-diaeresis : ∀ {ℓ c} → ℓ diaeresis → Token ℓ c
  with-accent-diaeresis : ∀ {ℓ c} → ℓ accent → ℓ diaeresis → Token ℓ c
  with-accent-iota : ∀ {ℓ c} → ℓ accent → ℓ iota-subscript → Token ℓ c
  with-breathing-iota : ∀ {ℓ c} → ℓ ⟦ c ⟧-breathing → ℓ iota-subscript → Token ℓ c
  with-iota : ∀ {ℓ c} → ℓ iota-subscript → Token ℓ c
  final : ∀ {ℓ c} → ℓ ⟦ c ⟧-final → Token ℓ c

-- Constructions

α-vowel : α vowel
α-vowel = is-vowel here

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

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

α-acute : α accent
α-acute = add-acute α-vowel

α-grave : α accent
α-grave = add-grave α-vowel

α-circumflex : α accent
α-circumflex = add-circumflex α-long-vowel

α-smooth : α ⟦ lower ⟧-breathing
α-smooth = add-smooth (add-smooth-lower-vowel α-vowel)

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

α-rough : α ⟦ lower ⟧-breathing
α-rough = add-rough (add-rough-vowel α-vowel)

Α-rough : α ⟦ upper ⟧-breathing
Α-rough = add-rough (add-rough-vowel α-vowel)

α-iota-subscript : α iota-subscript
α-iota-subscript = add-iota-subscript α-vowel here

-- U+1F0x
ἀ : Token α lower
ἀ = with-breathing α-smooth
ἁ : Token α lower
ἁ = with-breathing α-rough
ἂ : Token α lower
ἂ = with-accent-breathing α-grave α-smooth
ἃ : Token α lower
ἃ = with-accent-breathing α-grave α-rough
ἄ : Token α lower
ἄ = with-accent-breathing α-acute α-smooth
ἅ : Token α lower
ἅ = with-accent-breathing α-acute α-rough
ἆ : Token α lower
ἆ = with-accent-breathing α-circumflex α-smooth
ἇ : Token α lower
ἇ = with-accent-breathing α-circumflex α-rough
Ἀ : Token α upper
Ἀ = with-breathing Α-smooth
Ἁ : Token α upper
Ἁ = with-breathing Α-rough
Ἂ : Token α upper
Ἂ = with-accent-breathing α-grave Α-smooth
Ἃ : Token α upper
Ἃ = with-accent-breathing α-grave Α-rough
Ἄ : Token α upper
Ἄ = with-accent-breathing α-acute Α-smooth
Ἅ : Token α upper
Ἅ = with-accent-breathing α-acute Α-rough
Ἆ : Token α upper
Ἆ = with-accent-breathing α-circumflex Α-smooth
Ἇ : Token α upper
Ἇ = with-accent-breathing α-circumflex Α-rough

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

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

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

-- Mapping

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

letter-to-accent : ∀ {v} → v accent → Accent
letter-to-accent (add-acute x) = acute-mark
letter-to-accent (add-grave x) = grave-mark
letter-to-accent (add-circumflex x) = 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 _ = ⃠

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

letter-to-breathing : ∀ {ℓ c} → ℓ ⟦ c ⟧-breathing → Breathing
letter-to-breathing (add-smooth x) = smooth-mark
letter-to-breathing (add-rough x) = 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 _ = ⃠

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 _ = ⃠

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 _ = ⃠

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 _ = ⃠

data Token′ : Letter → Case → Maybe Accent → Maybe Breathing
            → Maybe IotaSubscript → Maybe Diaeresis → Maybe FinalForm
            → Set where
  α : ∀ {c a b is} → Token′ α c a b is ⃠ ⃠
  β : ∀ {c} → Token′ β c ⃠ ⃠ ⃠ ⃠ ⃠
  γ : ∀ {c} → Token′ γ c ⃠ ⃠ ⃠ ⃠ ⃠
  δ : ∀ {c} → Token′ δ c ⃠ ⃠ ⃠ ⃠ ⃠
  ε : ∀ {c b} → Token′ ε c ⃠ b ⃠ ⃠ ⃠
  ε-acute : ∀ {c b} → Token′ ε c (just acute-mark) b ⃠ ⃠ ⃠
  ε-grave : ∀ {c b} → Token′ ε c (just grave-mark) b ⃠ ⃠ ⃠
  ζ : ∀ {c} → Token′ ζ c ⃠ ⃠ ⃠ ⃠ ⃠
  η : ∀ {c a b is} → Token′ η c a b is ⃠ ⃠
  θ : ∀ {c} → Token′ θ c ⃠ ⃠ ⃠ ⃠ ⃠
  ι : ∀ {a b d} → Token′ ι lower a b ⃠ d ⃠
  Ι : ∀ {a b} → Token′ ι upper a b ⃠ ⃠ ⃠
  κ : ∀ {c} → Token′ κ c ⃠ ⃠ ⃠ ⃠ ⃠
  λ′ : ∀ {c} → Token′ λ′ c ⃠ ⃠ ⃠ ⃠ ⃠
  μ : ∀ {c} → Token′ μ c ⃠ ⃠ ⃠ ⃠ ⃠
  ν : ∀ {c} → Token′ ν c ⃠ ⃠ ⃠ ⃠ ⃠
  ξ : ∀ {c} → Token′ ξ c ⃠ ⃠ ⃠ ⃠ ⃠
  π : ∀ {c} → Token′ π c ⃠ ⃠ ⃠ ⃠ ⃠
  ο : ∀ {c b} → Token′ ο c ⃠ b ⃠ ⃠ ⃠
  ο-acute : ∀ {c b} → Token′ ο c (just acute-mark) b ⃠ ⃠ ⃠
  ο-grave : ∀ {c b} → Token′ ο c (just grave-mark) b ⃠ ⃠ ⃠
  ρ : ∀ {c} → Token′ ρ c ⃠ ⃠ ⃠ ⃠ ⃠
  ρ-breathing : ∀ {b : Breathing} → Token′ ρ lower ⃠ (just b) ⃠ ⃠ ⃠
  Ρ-rough : Token′ ρ upper ⃠ (just rough-mark) ⃠ ⃠ ⃠
  σ : ∀ {c} → Token′ σ c ⃠ ⃠ ⃠ ⃠ ⃠
  ς : Token′ σ lower ⃠ ⃠ ⃠ ⃠ (just final-form)
  τ : ∀ {c} → Token′ τ c ⃠ ⃠ ⃠ ⃠ ⃠
  υ : ∀ {a b d} → Token′ υ lower a b ⃠ d ⃠
  Υ : ∀ {a} → Token′ υ lower a ⃠ ⃠ ⃠ ⃠
  Υ-rough : ∀ {a} → Token′ υ lower a (just rough-mark) ⃠ ⃠ ⃠
  φ : ∀ {c} → Token′ φ c ⃠ ⃠ ⃠ ⃠ ⃠
  χ : ∀ {c} → Token′ χ c ⃠ ⃠ ⃠ ⃠ ⃠
  ω : ∀ {c a b is} → Token′ ω c a b is ⃠ ⃠

-- Expectations
 
no-Ρ-smooth : ∀ {a is d f} → ¬ Token′ ρ upper a (just smooth-mark) is d f
no-Ρ-smooth ()
 
no-Υ-smooth : ∀ {a is d f} → ¬ Token′ υ upper a (just smooth-mark) is d f
no-Υ-smooth ()
 
no-ε-circumflex : ∀ {c b is d f} → ¬ Token′ ε c (just circumflex-mark) b is d f
no-ε-circumflex ()
 
no-ο-circumflex : ∀ {c b is d f} → ¬ Token′ ο c (just circumflex-mark) b is d f
no-ο-circumflex ()
 
no-ε-iota-subscript : ∀ {c a b d f} → ¬ Token′ ε c a b (just iota-subscript-mark) d f
no-ε-iota-subscript ()
 
no-ι-iota-subscript : ∀ {c a b d f} → ¬ Token′ ι c a b (just iota-subscript-mark) d f
no-ι-iota-subscript ()
 
no-ο-iota-subscript : ∀ {c a b d f} → ¬ Token′ ο c a b (just iota-subscript-mark) d f
no-ο-iota-subscript ()
 
no-υ-iota-subscript : ∀ {c a b d f} → ¬ Token′ υ c a b (just iota-subscript-mark) d f
no-υ-iota-subscript ()
 
no-upper-diaeresis : ∀ {ℓ a b is f} → ¬ Token′ ℓ upper a b is (just diaeresis-mark) f
no-upper-diaeresis ()
 
no-Σ-final : ∀ {a b is d} → ¬ Token′ σ upper a b is d (just final-form)
no-Σ-final ()

alpha-to-rules : ∀ {ℓ c a b is d f} → Token′ ℓ c a b is d f → Token ℓ c
alpha-to-rules {c = lower} {just acute-mark} {just smooth-mark} {just _} α = ᾄ
alpha-to-rules {c = lower} {just acute-mark} {just rough-mark} {just _} α = ᾅ
alpha-to-rules {c = lower} {just grave-mark} {just smooth-mark} {just _} α = ᾂ
alpha-to-rules {c = lower} {just grave-mark} {just rough-mark} {just _} α = ᾃ
alpha-to-rules {c = lower} {just circumflex-mark} {just smooth-mark} {just _} α = ᾆ
alpha-to-rules {c = lower} {just circumflex-mark} {just rough-mark} {just _} α = ᾇ
alpha-to-rules {c = upper} {just acute-mark} {just smooth-mark} {just _} α = ᾌ
alpha-to-rules {c = upper} {just acute-mark} {just rough-mark} {just _} α = ᾍ
alpha-to-rules {c = upper} {just grave-mark} {just smooth-mark} {just _} α = ᾊ
alpha-to-rules {c = upper} {just grave-mark} {just rough-mark} {just _} α = ᾋ
alpha-to-rules {c = upper} {just circumflex-mark} {just smooth-mark} {just _} α = ᾎ
alpha-to-rules {c = upper} {just circumflex-mark} {just rough-mark} {just _} α = ᾏ
alpha-to-rules {c = lower} {⃠} {just smooth-mark} {just _} α = ᾀ
alpha-to-rules {c = lower} {⃠} {just rough-mark} {just _} α = ᾁ
alpha-to-rules {c = upper} {⃠} {just smooth-mark} {just _} α = ᾈ
alpha-to-rules {c = upper} {⃠} {just rough-mark} {just _} α = ᾉ
alpha-to-rules {a = just acute-mark} {⃠} {just _} α = with-accent-iota α-acute α-iota-subscript
alpha-to-rules {a = just grave-mark} {⃠} {just _} α = with-accent-iota α-grave α-iota-subscript
alpha-to-rules {a = just circumflex-mark} {⃠} {just _} α = with-accent-iota α-circumflex α-iota-subscript
alpha-to-rules {is = just iota-subscript-mark} α = with-iota α-iota-subscript
alpha-to-rules {c = lower} {just acute-mark} {just smooth-mark} {⃠} α = ἄ
alpha-to-rules {c = lower} {just acute-mark} {just rough-mark} {⃠} α = ἅ
alpha-to-rules {c = lower} {just grave-mark} {just smooth-mark} {⃠} α = ἂ
alpha-to-rules {c = lower} {just grave-mark} {just rough-mark} {⃠} α = ἃ
alpha-to-rules {c = lower} {just circumflex-mark} {just smooth-mark} {⃠} α = ἆ
alpha-to-rules {c = lower} {just circumflex-mark} {just rough-mark} {⃠} α = ἇ
alpha-to-rules {c = upper} {just acute-mark} {just smooth-mark} {⃠} α = Ἄ
alpha-to-rules {c = upper} {just acute-mark} {just rough-mark} {⃠} α = Ἅ
alpha-to-rules {c = upper} {just grave-mark} {just smooth-mark} {⃠} α = Ἂ
alpha-to-rules {c = upper} {just grave-mark} {just rough-mark} {⃠} α = Ἃ
alpha-to-rules {c = upper} {just circumflex-mark} {just smooth-mark} {⃠} α = Ἆ
alpha-to-rules {c = upper} {just circumflex-mark} {just rough-mark} {⃠} α = Ἇ
alpha-to-rules {c = lower} {⃠} {just smooth-mark} {⃠} α = ἀ
alpha-to-rules {c = lower} {⃠} {just rough-mark} {⃠} α = ἁ
alpha-to-rules {c = upper} {⃠} {just smooth-mark} {⃠} α = Ἀ
alpha-to-rules {c = upper} {⃠} {just rough-mark} {⃠} α = Ἁ
alpha-to-rules {a = just acute-mark} {⃠} {⃠} α = with-accent α-acute
alpha-to-rules {a = just grave-mark} {⃠} {⃠} α = with-accent α-grave
alpha-to-rules {a = just circumflex-mark} {⃠} {⃠} α = with-accent α-circumflex
alpha-to-rules {a = ⃠} {⃠} {⃠} α = unmarked
alpha-to-rules β = {!!}
alpha-to-rules γ = {!!}
alpha-to-rules δ = {!!}
alpha-to-rules ε = {!!}
alpha-to-rules ε-acute = {!!}
alpha-to-rules ε-grave = {!!}
alpha-to-rules ζ = {!!}
alpha-to-rules η = {!!}
alpha-to-rules θ = {!!}
alpha-to-rules ι = {!!}
alpha-to-rules Ι = {!!}
alpha-to-rules κ = {!!}
alpha-to-rules λ′ = {!!}
alpha-to-rules μ = {!!}
alpha-to-rules ν = {!!}
alpha-to-rules ξ = {!!}
alpha-to-rules π = {!!}
alpha-to-rules ο = {!!}
alpha-to-rules ο-acute = {!!}
alpha-to-rules ο-grave = {!!}
alpha-to-rules ρ = {!!}
alpha-to-rules ρ-breathing = {!!}
alpha-to-rules Ρ-rough = {!!}
alpha-to-rules σ = {!!}
alpha-to-rules ς = {!!}
alpha-to-rules τ = {!!}
alpha-to-rules υ = {!!}
alpha-to-rules Υ = {!!}
alpha-to-rules Υ-rough = {!!}
alpha-to-rules φ = {!!}
alpha-to-rules χ = {!!}
alpha-to-rules ω = {!!}

ScriptRules.txt

letters: α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ σ τ υ φ χ ψ ω
upper  : Α Β Γ Δ Ε Ζ Η Θ Ι Κ Λ Μ Ν Ξ Ο Π Ρ Σ Τ Υ Φ Χ Ψ Ω
vowels: α ε η ι ο υ ω

always have case: letters

can have acute accent : vowels
can have grave accent : vowels
can have circumflex : vowels (no circumflex on ε ο)

can have breathing : vowels ρ (except upper Ρ, Υ can only have rough)
can have iota subscript: α η ω (no iota subscript: ε ι ο υ)
can have length mark: α ι υ (no length mark: ε η ο ω)
can have diaeresis : ι υ (lowercase only)
can have final form : σ (lowercase only)