| 1 | (**************************************************************************) |
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| 2 | (* ___ *) |
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| 3 | (* ||M|| *) |
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| 4 | (* ||A|| A project by Andrea Asperti *) |
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| 5 | (* ||T|| *) |
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| 6 | (* ||I|| Developers: *) |
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| 7 | (* ||T|| The HELM team. *) |
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| 8 | (* ||A|| http://helm.cs.unibo.it *) |
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| 9 | (* \ / *) |
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| 10 | (* \ / This file is distributed under the terms of the *) |
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| 11 | (* v GNU General Public License Version 2 *) |
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| 12 | (* *) |
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| 13 | (**************************************************************************) |
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| 14 | |
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| 15 | include "arithmetics/nat.ma". |
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| 16 | include "basics/types.ma". |
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| 17 | include "basics/deqsets.ma". |
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| 18 | |
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| 19 | inductive FunctionName : Type[0] ≝ |
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| 20 | | a_function_id : ℕ → FunctionName. |
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| 21 | |
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| 22 | inductive CallCostLabel : Type[0] ≝ |
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| 23 | | a_call_label : ℕ → CallCostLabel. |
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| 24 | |
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| 25 | inductive ReturnPostCostLabel : Type[0] ≝ |
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| 26 | | a_return_cost_label : ℕ → ReturnPostCostLabel. |
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| 27 | |
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| 28 | inductive NonFunctionalLabel : Type[0] ≝ |
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| 29 | | a_non_functional_label : ℕ → NonFunctionalLabel. |
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| 30 | |
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| 31 | inductive CostLabel : Type[0] ≝ |
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| 32 | | a_call : CallCostLabel → CostLabel |
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| 33 | | a_return_post : ReturnPostCostLabel → CostLabel |
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| 34 | | a_non_functional_label : NonFunctionalLabel → CostLabel. |
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| 35 | |
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| 36 | coercion a_call. |
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| 37 | coercion a_return_post. |
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| 38 | coercion a_non_functional_label. |
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| 39 | |
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| 40 | definition ret_act_label_to_cost_label : |
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| 41 | (ReturnPostCostLabel + NonFunctionalLabel) → CostLabel ≝ |
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| 42 | λx.match x with [inl a ⇒ a_return_post a | inr b ⇒ a_non_functional_label b]. |
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| 43 | |
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| 44 | coercion ret_act_label_to_cost_label. |
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| 45 | |
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| 46 | inductive ActionLabel : Type[0] ≝ |
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| 47 | | call_act : FunctionName → CallCostLabel → ActionLabel |
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| 48 | | ret_act : option(ReturnPostCostLabel + NonFunctionalLabel) → ActionLabel |
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| 49 | | cost_act : NonFunctionalLabel → ActionLabel |
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| 50 | | tau_act : ActionLabel. |
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| 51 | |
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| 52 | record program_counter_type : Type[1] ≝ |
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| 53 | { pc_type : DeqSet |
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| 54 | ; succ_pc : pc_type → pc_type |
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| 55 | }. |
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| 56 | |
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| 57 | record abstract_status : Type[2] ≝ |
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| 58 | { as_status :> Type[0] |
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| 59 | ; as_execute : ActionLabel → relation as_status |
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| 60 | ; as_pc : program_counter_type |
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| 61 | ; as_pc_of : as_status → (pc_type as_pc) |
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| 62 | ; is_jump : as_status → bool |
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| 63 | }. |
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| 64 | |
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| 65 | inductive raw_trace (S : abstract_status) : S → S → Type[0] ≝ |
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| 66 | | t_base : ∀st : S.raw_trace S st st |
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| 67 | | t_ind : ∀st1,st2,st3 : S.∀l : ActionLabel. |
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| 68 | as_execute S l st1 st2 → raw_trace S st2 st3 → raw_trace S st1 st3. |
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| 69 | |
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| 70 | |
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