diff options
author | Chloe Brown <chloe.brown.00@outlook.com> | 2021-01-23 20:54:21 +0000 |
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committer | Chloe Brown <chloe.brown.00@outlook.com> | 2021-01-23 20:56:00 +0000 |
commit | b49309e3c9970a0a1be73239e80c432fb56b32f9 (patch) | |
tree | 60d88b67ec2b1dc7cde4c4cef15fffab395d1957 /src/Cfe/Language | |
parent | cd8ab887cdfdf3aa8dfc66871cc27be9677945c3 (diff) |
Define languages.
Diffstat (limited to 'src/Cfe/Language')
-rw-r--r-- | src/Cfe/Language/Base.agda | 49 |
1 files changed, 49 insertions, 0 deletions
diff --git a/src/Cfe/Language/Base.agda b/src/Cfe/Language/Base.agda new file mode 100644 index 0000000..eeea11d --- /dev/null +++ b/src/Cfe/Language/Base.agda @@ -0,0 +1,49 @@ +{-# OPTIONS --without-K --safe #-} + +open import Relation.Binary + +module Cfe.Language.Base + {a ℓ} (setoid : Setoid a ℓ) + where + +open Setoid setoid renaming (Carrier to A) + +open import Data.Empty.Polymorphic +open import Data.List +open import Data.List.Relation.Binary.Equality.Setoid setoid +open import Data.Nat hiding (_≤_; _⊔_) +open import Data.Product +open import Data.Sum +open import Function +open import Level renaming (suc to lsuc) + +Language : Set (lsuc a ⊔ lsuc ℓ) +Language = List A → Set (a ⊔ ℓ) + +∅ : Language +∅ = const ⊥ + +{ε} : Language +{ε} = [] ≋_ + +{_} : A → Language +{ a } = [ a ] ≋_ + +infix 4 _∪_ +infix 4 _∙_ + +_∪_ : Language → Language → Language +(A ∪ B) l = A l ⊎ B l + +_∙_ : Language → Language → Language +(A ∙ B) l = ∃[ l₁ ] ∃[ l₂ ] (A l₁ × B l₂ × l₁ ++ l₂ ≋ l) + +iterate : (Language → Language) → ℕ → Language → Language +iterate f ℕ.zero = id +iterate f (suc n) = f ∘ iterate f n + +fix : (Language → Language) → Language +fix f l = ∃[ n ] iterate f n ∅ l + +_≤_ : Language → Language → Set (a ⊔ ℓ) +A ≤ B = ∀ l → A l → B l |