Introduce derivations.

3 files changed, 40 insertions, 0 deletions

diff --git a/src/Cfe/Parse.agda b/src/Cfe/Parse.agda
new file mode 100644
index 0000000..29b94fe
--- /dev/null
+++ b/src/Cfe/Parse.agda
@@ -0,0 +1,10 @@
+{-# OPTIONS --without-K --safe #-}
+
+open import Relation.Binary using (Setoid)
+
+module Cfe.Parse
+  {c ℓ} (over : Setoid c ℓ)
+  where
+
+open import Cfe.Parse.Base over public
+open import Cfe.Parse.Properties over public
diff --git a/src/Cfe/Parse/Base.agda b/src/Cfe/Parse/Base.agda
new file mode 100644
index 0000000..50e085a
--- /dev/null
+++ b/src/Cfe/Parse/Base.agda
@@ -0,0 +1,23 @@
+{-# OPTIONS --without-K --safe #-}
+
+open import Relation.Binary using (Setoid)
+
+module Cfe.Parse.Base
+  {c ℓ} (over : Setoid c ℓ)
+  where
+
+open Setoid over renaming (Carrier to C)
+
+open import Cfe.Expression over
+open import Data.Fin
+open import Data.List
+
+infix 4 _⤇_
+
+data _⤇_ : Expression 0 → List C → Set c where
+  Eps : ε ⤇ []
+  Char : ∀ {c} → Char c ⤇ [ c ]
+  Cat : ∀ {e₁ e₂ l₁ l₂} → e₁ ⤇ l₁ → e₂ ⤇ l₂ → e₁ ∙ e₂ ⤇ l₁ ++ l₂
+  Veeˡ : ∀ {e₁ e₂ l} → e₁ ⤇ l → e₁ ∨ e₂ ⤇ l
+  Veeʳ : ∀ {e₁ e₂ l} → e₂ ⤇ l → e₁ ∨ e₂ ⤇ l
+  Fix : ∀ {e l} → e [ μ e / zero ] ⤇ l → μ e ⤇ l
diff --git a/src/Cfe/Parse/Properties.agda b/src/Cfe/Parse/Properties.agda
new file mode 100644
index 0000000..7803f82
--- /dev/null
+++ b/src/Cfe/Parse/Properties.agda
@@ -0,0 +1,7 @@
+{-# OPTIONS --without-K --safe #-}
+
+open import Relation.Binary using (Setoid)
+
+module Cfe.Parse.Properties
+  {c ℓ} (over : Setoid c ℓ)
+  where