52 lines
2 KiB
Text
52 lines
2 KiB
Text
constant heap : Type
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constant ptr : Type
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constant val : Type
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constant pt : ptr → val → heap
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constant hunion : heap → heap → heap
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constant is_def : heap → Prop
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infix `∙`:60 := hunion
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infix `↣`:70 := pt
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/-
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constant hunion_is_assoc : is_associative heap hunion
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constant hunion_is_comm : is_commutative heap hunion
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attribute [instance] hunion_is_comm hunion_is_assoc
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axiom noalias : ∀ (h : heap) (y₁ y₂ : ptr) (w₁ w₂ : val), is_def (h ∙ y₁ ↣ w₁ ∙ y₂ ↣ w₂) → y₁ ≠ y₂
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-/
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open tactic
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meta def my_tac : tactic unit :=
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using_smt `[ { [smt]
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intros,
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smt_tactic.add_lemmas_from_facts,
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eblast
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} ]
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-- set_option profiler true
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example
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(h₁ h₂ : heap) (x₁ x₂ x₃ x₄ : ptr) (v₁ v₂ v₃ : val)
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(hcomm : ∀ x y, x ∙ y = y ∙ x)
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(hassoc : ∀ x y z, (x ∙ y) ∙ z = x ∙ (y ∙ z))
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(hnoalias : ∀ h y₁ y₂ w₁ w₂, is_def (h ∙ y₁ ↣ w₁ ∙ y₂ ↣ w₂) → y₁ ≠ y₂)
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: is_def (h₁ ∙ (x₁ ↣ v₁ ∙ x₂ ↣ v₂) ∙ h₂ ∙ (x₃ ↣ v₃)) → x₁ ≠ x₃ ∧ x₁ ≠ x₂ ∧ x₂ ≠ x₃ :=
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by my_tac -- should work
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example
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(h₁ h₂ : heap) (x₁ x₂ x₃ x₄ : ptr) (v₁ v₂ v₃ : val)
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(hcomm : ∀ x y, x ∙ y = y ∙ x)
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(hassoc : ∀ x y z, (x ∙ y) ∙ z = x ∙ (y ∙ z))
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(hnoalias : ∀ h y₁ y₂ w₁ w₂, is_def (h ∙ y₁ ↣ w₁ ∙ y₂ ↣ w₂) → y₁ ≠ y₂)
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: is_def (h₁ ∙ (x₁ ↣ v₁ ∙ x₂ ↣ v₂) ∙ h₂ ∙ (x₃ ↣ v₃)) → x₁ ≠ x₃ ∧ x₁ ≠ x₂ ∧ x₂ ≠ x₃ :=
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by try_for 100 $ my_tac -- should timeout
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example
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(h₁ h₂ : heap) (x₁ x₂ x₃ x₄ : ptr) (v₁ v₂ v₃ : val)
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(hcomm : ∀ x y, x ∙ y = y ∙ x)
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(hassoc : ∀ x y z, (x ∙ y) ∙ z = x ∙ (y ∙ z))
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(hnoalias : ∀ h y₁ y₂ w₁ w₂, is_def (h ∙ y₁ ↣ w₁ ∙ y₂ ↣ w₂) → y₁ ≠ y₂)
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: is_def (h₁ ∙ (x₁ ↣ v₁ ∙ x₂ ↣ v₂) ∙ h₂ ∙ (x₃ ↣ v₃)) → x₁ ≠ x₃ ∧ x₁ ≠ x₂ ∧ x₂ ≠ x₃ :=
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by try_for 10000 $ my_tac -- should work
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