1 | include "LTL/LTL.ma". |
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2 | include "LIN/LIN.ma". |
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3 | include "utilities/BitVectorTrieSet.ma". |
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4 | include alias "common/Graphs.ma". |
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5 | |
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6 | definition translate_statement: ∀globals. ltl_statement globals → pre_lin_statement globals ≝ |
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7 | λglobals: list ident. |
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8 | λs: ltl_statement globals. |
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9 | match s with |
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10 | [ RETURN ⇒ RETURN ?? |
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11 | | sequential instr lbl ⇒ sequential … instr it |
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12 | | GOTO l ⇒ GOTO lin_params_ globals l |
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13 | ]. |
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14 | |
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15 | (* Invariant: l has not been visited yet the very first time the |
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16 | function is called and in the true branch of a conditional call. |
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17 | This avoid useless gotos. |
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18 | |
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19 | Note: the OCaml code contains some useful explanatory comments. *) |
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20 | let rec visit |
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21 | (globals: list ident) (g: label → option (ltl_statement globals)) |
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22 | (required: identifier_set LabelTag) (visited: identifier_set LabelTag) |
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23 | (generated: list (lin_statement globals)) (l: label) (n: nat) |
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24 | on n: identifier_set LabelTag × (list (lin_statement globals)) ≝ |
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25 | match n with |
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26 | [ O ⇒ ⊥ (* CSC: Case to be made impossible; use dummy value? *) |
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27 | | S n' ⇒ |
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28 | if mem_set … visited l then |
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29 | 〈add_set ? required l, 〈None …, GOTO … globals l〉 :: generated〉 |
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30 | else |
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31 | let visited' ≝ add_set ? visited l in |
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32 | match g l with |
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33 | [ None ⇒ ⊥ (* Case to be made impossible with more dependent types *) |
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34 | | Some statement ⇒ |
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35 | let translated_statement ≝ translate_statement globals statement in |
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36 | let generated' ≝ 〈Some … l, translated_statement〉 :: generated in |
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37 | match statement with |
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38 | [ sequential instr l2 ⇒ |
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39 | match instr with |
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40 | [ COND acc_a_reg l1 ⇒ |
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41 | let 〈required', generated''〉 ≝ |
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42 | visit globals g required visited' generated' l2 n' in |
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43 | let required'' ≝ add_set ? required' l1 in |
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44 | if mem_set … visited' l1 then |
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45 | 〈required', generated''〉 |
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46 | else |
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47 | visit globals g required'' visited' generated'' l1 n' |
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48 | | _ ⇒ visit globals g required visited' generated' l2 n'] |
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49 | | RETURN ⇒ 〈required, generated'〉 |
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50 | | GOTO l2 ⇒ visit globals g required visited' generated' l2 n']]]. |
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51 | [1,2: @daemon (*CSC: impossible cases, use more dependent types *) ] |
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52 | qed. |
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53 | |
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54 | (* CSC: The branch compression (aka tunneling) optimization is not implemented |
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55 | in Matita *) |
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56 | definition branch_compress ≝ λglobals.λa:label → option (ltl_statement globals).a. |
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57 | |
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58 | definition translate_graph: |
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59 | ∀globals. label → nat → |
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60 | (label → option (ltl_statement globals)) → codeT … (lin_params globals) |
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61 | ≝ |
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62 | λglobals,entry,labels_upper_bound,g. |
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63 | let g ≝ branch_compress ? g in |
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64 | let visited ≝ ∅ in |
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65 | let required ≝ { (entry) } in |
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66 | let 〈required', translated〉 ≝ visit globals g required visited [ ] entry labels_upper_bound in |
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67 | let reversed ≝ rev ? translated in |
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68 | map ?? |
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69 | (λs. let 〈l,x〉 ≝ s in |
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70 | match l with |
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71 | [ None ⇒ 〈None …,x〉 |
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72 | | Some l ⇒ |
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73 | 〈if mem_set … required' l then Some ? l else None ?, |
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74 | x〉]) |
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75 | reversed. |
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76 | |
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77 | definition translate_int_fun: |
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78 | ∀globals. |
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79 | joint_internal_function … (ltl_params globals) → |
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80 | joint_internal_function … (lin_params globals) |
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81 | ≝ |
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82 | λglobals,f. |
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83 | mk_joint_internal_function globals (lin_params globals) |
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84 | (joint_if_luniverse ?? f) (joint_if_runiverse ?? f) it it it (joint_if_stacksize ?? f) |
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85 | (translate_graph globals (joint_if_entry ?? f) (nat_of_pos … (next_identifier … (joint_if_luniverse … f))) |
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86 | (lookup ?? (joint_if_code … f))) |
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87 | ??. |
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88 | cases daemon (*CSC: XXXXXXXXX Dead code produced *) |
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89 | qed. |
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90 | |
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91 | definition ltl_to_lin : ltl_program → lin_program ≝ |
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92 | λp. transform_program … p (transf_fundef … (translate_int_fun …)). |
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