Introduce < for Languages.

Move around some definitions.

1 files changed, 22 insertions, 3 deletions

diff --git a/src/Cfe/Derivation/Base.agda b/src/Cfe/Derivation/Base.agda
index 1f2bb63..ce368d0 100644
--- a/src/Cfe/Derivation/Base.agda
+++ b/src/Cfe/Derivation/Base.agda
@@ -1,6 +1,6 @@
 {-# OPTIONS --without-K --safe #-}
 
-open import Relation.Binary using (Setoid)
+open import Relation.Binary using (REL; Setoid)
 
 module Cfe.Derivation.Base
   {c ℓ} (over : Setoid c ℓ)
@@ -14,12 +14,31 @@ open import Data.List
 open import Data.List.Relation.Binary.Equality.Setoid over
 open import Level using (_⊔_)
 
-infix 4 _⤇_
+infix 5 _⤇_
+infix 4 _≈_
 
 data _⤇_ : Expression 0 → List C → Set (c ⊔ ℓ) where
   Eps : ε ⤇ []
-  Char : ∀ {c y} → c ∼ y → Char c ⤇ [ y ]
+  Char : ∀ {c y} → (c∼y : c ∼ y) → Char c ⤇ [ y ]
   Cat : ∀ {e₁ e₂ l₁ l₂ l} → e₁ ⤇ l₁ → e₂ ⤇ l₂ → l₁ ++ l₂ ≋ l → e₁ ∙ e₂ ⤇ l
   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
+
+data _≈_ : ∀ {e l l′} → REL (e ⤇ l) (e ⤇ l′) (c ⊔ ℓ) where
+  Eps : Eps ≈ Eps
+  Char : ∀ {c y y′} → (c∼y : c ∼ y) → (c∼y′ : c ∼ y′) → Char c∼y ≈ Char c∼y′
+  Cat : ∀ {e₁ e₂ l l₁ l₂ l₁′ l₂′ e₁⤇l₁ e₁⤇l₁′ e₂⤇l₂ e₂⤇l₂′} →
+          (e₁⤇l₁≈e₁⤇l′ : _≈_ {e₁} {l₁} {l₁′} e₁⤇l₁ e₁⤇l₁′) →
+          (e₂⤇l₂≈e₂⤇l′ : _≈_ {e₂} {l₂} {l₂′} e₂⤇l₂ e₂⤇l₂′) →
+          (eq : l₁ ++ l₂ ≋ l) → (eq′ : l₁′ ++ l₂′ ≋ l) →
+          Cat e₁⤇l₁ e₂⤇l₂ eq ≈ Cat e₁⤇l₁′ e₂⤇l₂′ eq′
+  Veeˡ : ∀ {e₁ e₂ l l′ e₁⤇l e₁⤇l′} →
+         (e₁⤇l≈e₁⤇l′ : _≈_ {e₁} {l} {l′} e₁⤇l e₁⤇l′) →
+         Veeˡ {e₂ = e₂} e₁⤇l ≈ Veeˡ e₁⤇l′
+  Veeʳ : ∀ {e₁ e₂ l l′ e₂⤇l e₂⤇l′} →
+         (e₂⤇l≈e₂⤇l′ : _≈_ {e₂} {l} {l′} e₂⤇l e₂⤇l′) →
+         Veeʳ {e₁} e₂⤇l ≈ Veeʳ e₂⤇l′
+  Fix : ∀ {e l l′ e[μe/0]⤇l e[μe/0]⤇l′} →
+        (e[μe/0]⤇l≈e[μe/0]⤇l′ : _≈_ {e [ μ e / zero ]} {l} {l′} e[μe/0]⤇l e[μe/0]⤇l′) →
+        Fix {e} e[μe/0]⤇l ≈ Fix e[μe/0]⤇l′