diff options
Diffstat (limited to '')
| -rw-r--r-- | backends/lean/Base/Diverge/Base.lean | 37 |
1 files changed, 22 insertions, 15 deletions
diff --git a/backends/lean/Base/Diverge/Base.lean b/backends/lean/Base/Diverge/Base.lean index 9458c926..e40432bd 100644 --- a/backends/lean/Base/Diverge/Base.lean +++ b/backends/lean/Base/Diverge/Base.lean @@ -21,7 +21,7 @@ namespace Lemmas else f ⟨ m, by simp_all [Nat.lt_iff_le_and_ne] ⟩ ∧ for_all_fin_aux f (m + 1) (by simp_all [Arith.add_one_le_iff_le_ne]) - termination_by for_all_fin_aux n _ m h => n - m + termination_by n - m decreasing_by simp_wf apply Nat.sub_add_lt_sub <;> try simp @@ -240,8 +240,8 @@ namespace Fix simp [fix] -- By property of the least upper bound revert Hd Hl - -- TODO: there is no conversion to select the head of a function! - conv => lhs; apply congr_fun; apply congr_fun; apply congr_fun; simp [fix_fuel_P, div?] + conv => lhs; rw [fix_fuel_P] + simp [div?] cases fix_fuel (least (fix_fuel_P f x)) f x <;> simp have Hmono := fix_fuel_mono Hmono Hineq x simp [result_rel] at Hmono @@ -255,7 +255,7 @@ namespace Fix intros x n Hf have Hfmono := fix_fuel_fix_mono Hmono n x -- TODO: there is no conversion to select the head of a function! - conv => apply congr_fun; simp [fix_fuel_P] + rw [fix_fuel_P] simp [fix_fuel_P] at Hf revert Hf Hfmono simp [div?, result_rel, fix] @@ -268,9 +268,7 @@ namespace Fix fix f x = f (fix f) x := by have Hl := fix_fuel_P_least Hmono He -- TODO: better control of simplification - conv at Hl => - apply congr_fun - simp [fix_fuel_P] + rw [fix_fuel_P] at Hl; simp at Hl -- The least upper bound is > 0 have ⟨ n, Hsucc ⟩ : ∃ n, least (fix_fuel_P f x) = Nat.succ n := by revert Hl @@ -618,12 +616,16 @@ namespace FixI @[simp] theorem is_valid_p_same (k : ((i:id) → (x:a i) → Result (b i x)) → (i:id) → (x:a i) → Result (b i x)) (x : Result c) : is_valid_p k (λ _ => x) := by - simp [is_valid_p, k_to_gen, e_to_gen] + simp [is_valid_p] + unfold k_to_gen e_to_gen + simp @[simp] theorem is_valid_p_rec (k : ((i:id) → (x:a i) → Result (b i x)) → (i:id) → (x:a i) → Result (b i x)) (i : id) (x : a i) : is_valid_p k (λ k => k i x) := by - simp [is_valid_p, k_to_gen, e_to_gen, kk_to_gen, kk_of_gen] + simp [is_valid_p] + unfold k_to_gen e_to_gen kk_to_gen kk_of_gen + simp theorem is_valid_p_ite (k : ((i:id) → (x:a i) → Result (b i x)) → (i:id) → (x:a i) → Result (b i x)) @@ -826,12 +828,16 @@ namespace FixII @[simp] theorem is_valid_p_same (k : ((i:id) → (t:ty i) → a i t → Result (b i t)) → (i:id) → (t:ty i) → a i t → Result (b i t)) (x : Result c) : is_valid_p k (λ _ => x) := by - simp [is_valid_p, k_to_gen, e_to_gen] + simp [is_valid_p] + unfold k_to_gen e_to_gen + simp @[simp] theorem is_valid_p_rec (k : ((i:id) → (t:ty i) → a i t → Result (b i t)) → (i:id) → (t:ty i) → a i t → Result (b i t)) (i : id) (t : ty i) (x : a i t) : is_valid_p k (λ k => k i t x) := by - simp [is_valid_p, k_to_gen, e_to_gen, kk_to_gen, kk_of_gen] + simp [is_valid_p] + unfold k_to_gen e_to_gen kk_to_gen kk_of_gen + simp theorem is_valid_p_ite (k : ((i:id) → (t:ty i) → a i t → Result (b i t)) → (i:id) → (t:ty i) → a i t → Result (b i t)) @@ -1531,10 +1537,11 @@ namespace Ex9 intro k a x simp only [id_body] split <;> try simp - apply is_valid_p_bind <;> try simp [*] - -- We have to show that `map k tl` is valid - -- Remark: `map_is_valid` doesn't work here, we need the specialized version - apply map_is_valid_simple + . apply is_valid_p_same + . apply is_valid_p_bind <;> try simp [*] + -- We have to show that `map k tl` is valid + -- Remark: `map_is_valid` doesn't work here, we need the specialized version + apply map_is_valid_simple def body (k : (i : Fin 1) → (t : ty i) → (x : input_ty i t) → Result (output_ty i t)) (i: Fin 1) : (t : ty i) → (x : input_ty i t) → Result (output_ty i t) := get_fun bodies i k |