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scoped_belongsto.agda
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-- scope sensitive belongs | |
-- Unlike ∈, it does not allow scope insensitive proof of belongs | |
_∈s_ : (Name × Pointer) → Env → Set | |
(n , p) ∈s [] = ⊥ | |
(n , p) ∈s ((n' , p') ∷ ρ') with n ==n n' | p ==n p' | |
... | false | _ = ( n , p ) ∈s ρ' | |
... | _ | false = ⊥ | |
... | true | true = ⊤ | |
private | |
env : Env | |
env = (y , 5) ∷ (x , 1) ∷ (z , 0) ∷(x , 0 ) ∷ [] | |
p₁ : (x , 1) ∈s env | |
p₁ = tt | |
-- this cannot be proved (◕‿◕) | |
-- p₂ : (x , 0) ∈s env | |
-- p₂ = {!!} | |
-- IS IMPOSSIBLE?! | |
x↦n∈ρ : {x n : Nat} {ρ : Env} → (x , n) ∈s ((x , n ) ∷ ρ) | |
x↦n∈ρ {zero} {zero} = tt | |
x↦n∈ρ {suc x₁} {zero} = {!!} | |
x↦n∈ρ {zero} {suc n₁} = {!!} | |
x↦n∈ρ {suc x₁} {suc n₁} = {!!} -- x↦n∈ρ {x₁} {n₁} |
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