[Agda] Termination checking

[Francesco Mazzoli]

Danke!

Francesco

On 8 November 2014 20:16, Andreas Abel <abela at chalmers.se> wrote:
> Here you go:
>
> https://github.com/agda/agda/commit/bde295096843265fd5386c8bba1b9104ac1e7c22
>
>
> On 08.11.2014 15:05, Andreas Abel wrote:
>>
>> Agda.Termination.TermCheck:
>>
>> -- TODO: isSubTerm should compute a size difference (Order)
>> isSubTerm :: Term -> DeBruijnPat -> Bool
>> isSubTerm t p = equal t p || properSubTerm t p
>>
>> Maybe a good time to address this TODO... ;-)
>>
>> On 08.11.2014 14:57, Andreas Abel wrote:
>>>
>>> The subterm checker of the termination checker is probably not working.
>>>
>>> It works if you use an explicit equality constraint in constructor ⟦_⟫_⟧.
>>>
>>>      ⟦_⟫_⟧ : ∀ {d d₁ d₂ ol l nl} {eq : d ≡ d₁ + d₂} → Subst d₁ ol l ->
>>> Subst d₂ l nl -> Subst (suc d) ol nl
>>>
>>> lookup .(suc d) v       (⟦_⟫_⟧ {d} {eq = eq} ρ σ) = lookup d v (_⟫_ {eq
>>> = eq} ρ σ)
>>>
>>> Full code attached.
>>>
>>>
>>> On 08.11.2014 14:10, Francesco Mazzoli wrote:
>>>>
>>>> mutual
>>>>    data Tm (l : ℕ) : Set where
>>>>      var   : Fin l -> Tm l
>>>>      _·_   : Tm l -> Tm l -> Tm l
>>>>      lam   : Tm (suc l) -> Tm l
>>>>      ⟦_,_⟧ : ∀ {d ol} -> Tm ol -> Subst d ol l -> Tm l
>>>>
>>>>    data Subst : (d : ℕ)(ol : ℕ)(nl : ℕ) -> Set where
>>>>      id    : ∀ {ol} -> Subst 0 ol ol
>>>>      _∷_   : ∀ {d ol nl} -> Tm nl -> Subst d ol nl -> Subst d (suc
>>>> ol) nl
>>>>      ⟦_⟫_⟧ : ∀ {d₁ d₂ ol l nl} -> Subst d₁ ol l -> Subst d₂ l nl ->
>>>> Subst (suc (d₁ + d₂)) ol nl
>>>>
>>>> _⟫_ : ∀ {d₁ d₂ ol l nl} -> Subst d₁ ol l -> Subst d₂ l nl -> Subst (d₁
>>>> + d₂) ol nl
>>>> id ⟫ σ = σ
>>>> (t ∷ ρ) ⟫ σ = ⟦ t , σ ⟧ ∷ (ρ ⟫ σ)
>>>> _⟫_ .{suc (d₁ + d₂)} {d₃} {ol} {_} {nl} (⟦_⟫_⟧ {d₁} {d₂} ρ σ) γ =
>>>>    subst (λ d → Subst d ol nl) (lm d₁ d₂ d₃) (ρ ⟫ ⟦ σ ⟫ γ ⟧)
>>>>    where
>>>>      lm : ∀ n m k -> n + suc (m + k) ≡ suc (n + m + k)
>>>>      lm zero m k = refl
>>>>      lm (suc n) m k = cong suc (lm n m k)
>>>>
>>>> lookup : ∀ {ol nl} d -> Fin ol -> Subst d ol nl -> Tm nl
>>>> lookup .0               v       id                    = var v
>>>> lookup d                zero    (t ∷ ρ)               = t
>>>> lookup d                (suc v) (t ∷ ρ)               = lookup d v ρ
>>>> lookup .(suc (d₁ + d₂)) v       (⟦_⟫_⟧ {d₁} {d₂} ρ σ) = lookup (d₁ +
>>>> d₂) v (ρ ⟫ σ)
>>>
>>>
>>>
>>>
>>>
>>>
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>>>
>>
>>
>
>
> --
> Andreas Abel  <><      Du bist der geliebte Mensch.
>
> Department of Computer Science and Engineering
> Chalmers and Gothenburg University, Sweden
>
> andreas.abel at gu.se
> http://www2.tcs.ifi.lmu.de/~abel/