Guidance on very shallow embedding VHDL in AGDA

Question

for my project in Programming Languages I am doing a very shallow and simple embedding VHDL digital circuits in agda. The aim is to write the syntax, static semantics, dynamic semantics and then write some proofs to show our understanding of the material. Up till now I have written the following code:

data Ckt : Set where

   var      : String → Ckt
   bool     : Bool → Ckt 
   empty    : Ckt
   gate     : String →  ℕ → ℕ → Ckt  -- name in out 
   series   : String →  Ckt → Ckt → Ckt -- name  ckt1 ckt2
   parallel : String →  Ckt → Ckt → Ckt --name ckt1 ckt2  

And : Ckt 
And = gate "And"  2 1    

data Ctxt : Set where
  □   : Ctxt
  _,_ : (String ×  ℕ ×  ℕ) → Ctxt → Ctxt


_≈_ : Ctxt → Ctxt → Set
□ ≈ □                               = ⊤
□ ≈ (_ , _)                         = ⊥
(_ , _) ≈ □                         = ⊥
((s₁ , (in₁ , out₂)) , Γ₁) ≈ ((s₂ , (in₃ , out₄)) , Γ₂) = True (s₁ ≟ s₂) × in₁ ≡ in₃ × out₂ ≡ out₄  × Γ₁ ≈ Γ₂


--static Semantics
data _⊢_  : (Γ : Ctxt) → (e : Ckt)  → Set where

  VarT      : ∀ {Γ s τ} → ((s , τ) ∈ Γ) → Γ ⊢ var s
  BoolT     : ∀ {Γ b} → Γ ⊢ bool b 
  EmptyT    : ∀ {Γ} → Γ ⊢ empty 
  GateT     : ∀ {Γ s i o} → (s , (i , o)) ∈ Γ  → Γ ⊢ gate s i o
  SeriesT   : ∀ {Γ s c₁ c₂} →  Γ ⊢ c₁ → Γ ⊢ c₂  → Γ ⊢ series s c₁ c₂ 
  ParallelT : ∀ {Γ s c₁ c₂} →  Γ ⊢ c₁ → Γ ⊢ c₂  → Γ ⊢ parallel s c₁ c₂

What I am stuck at is how can I convert this program so as to carry out the program execution i-e I don't know how to start writing the dynamic semantics. Also, if there is any way to improve the syntax or statics of my current program then please let me know.