| 1 | include "utilities/lists.ma". |
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| 2 | include "common/Globalenvs.ma". |
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| 3 | include "common/IO.ma". |
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| 4 | include "common/SmallstepExec.ma". |
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| 5 | include "joint/Joint.ma". |
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| 6 | include "joint/BEMem.ma". |
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| 7 | |
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| 8 | (* CSC: external functions never fail (??) and always return something of the |
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| 9 | size of one register, both in the frontend and in the backend. |
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| 10 | Is this reasonable??? In OCaml it always return a list, but in the frontend |
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| 11 | only the head is kept (or Undef if the list is empty) ??? *) |
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| 12 | |
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| 13 | definition address ≝ beval × beval. (* CSC: only pointers to XRAM or code memory *) |
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| 14 | |
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| 15 | definition eq_address: address → address → bool ≝ |
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| 16 | λaddr1,addr2. |
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| 17 | eq_beval (\fst addr1) (\fst addr2) ∧ eq_beval (\snd addr1) (\snd addr2). |
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| 18 | |
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| 19 | record sem_params: Type[1] ≝ |
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| 20 | { p:> params |
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| 21 | ; framesT: Type[0] |
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| 22 | ; regsT: Type[0] (* regs = pseudo-registers + hw registers *) |
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| 23 | |
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| 24 | ; pop_frame_: framesT → res framesT |
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| 25 | ; save_frame_: framesT → regsT → framesT |
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| 26 | ; greg_store_: generic_reg p → beval → regsT → res regsT |
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| 27 | ; greg_retrieve_: regsT → generic_reg p → res beval |
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| 28 | ; acca_store_: acc_a_reg p → beval → regsT → res regsT |
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| 29 | ; acca_retrieve_: regsT → acc_a_reg p → res beval |
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| 30 | ; accb_store_: acc_b_reg p → beval → regsT → res regsT |
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| 31 | ; accb_retrieve_: regsT → acc_b_reg p → res beval |
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| 32 | ; dpl_store_: dpl_reg p → beval → regsT → res regsT |
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| 33 | ; dpl_retrieve_: regsT → dpl_reg p → res beval |
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| 34 | ; dph_store_: dph_reg p → beval → regsT → res regsT |
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| 35 | ; dph_retrieve_: regsT → dph_reg p → res beval |
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| 36 | ; pair_reg_move_: regsT → pair_reg p → regsT |
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| 37 | |
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| 38 | ; init_locals : localsT p → regsT |
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| 39 | ; pointer_of_label: label → Σp:pointer. ptype p = Code |
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| 40 | }. |
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| 41 | |
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| 42 | definition address_of_label: sem_params → label → address. |
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| 43 | #p #l generalize in match (refl … (beval_pair_of_pointer (pointer_of_label p l))) |
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| 44 | cases (beval_pair_of_pointer (pointer_of_label p l)) in ⊢ (???% → ?) |
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| 45 | [ #res #_ @res |
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| 46 | | #msg cases (pointer_of_label p l) * * #q #com #off #E1 #E2 destruct ] |
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| 47 | qed. |
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| 48 | |
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| 49 | record state (p: sem_params): Type[0] ≝ |
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| 50 | { st_frms: framesT p |
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| 51 | ; pc: address |
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| 52 | ; sp: pointer |
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| 53 | ; carry: beval |
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| 54 | ; regs: regsT p |
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| 55 | ; m: bemem |
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| 56 | }. |
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| 57 | |
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| 58 | definition genv ≝ λglobals,pre,p. (genv_t Genv) (joint_function globals pre p). |
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| 59 | |
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| 60 | record sem_params2 (globals: list ident): Type[1] ≝ |
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| 61 | { sparams:> sem_params |
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| 62 | ; pre_sem_params:> sem_params_ sparams globals |
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| 63 | |
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| 64 | ; fetch_statement: state sparams → res (joint_statement sparams globals) |
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| 65 | ; fetch_external_args: external_function → state sparams → res (list val) |
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| 66 | ; set_result: list val → state sparams → res (state sparams) |
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| 67 | ; fetch_result: state sparams → nat → res val |
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| 68 | |
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| 69 | ; exec_extended: genv … pre_sem_params → extend_statements sparams → state sparams → IO io_out io_in (trace × (state sparams)) |
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| 70 | }. |
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| 71 | |
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| 72 | definition set_m: ∀p. bemem → state p → state p ≝ |
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| 73 | λp,m,st. mk_state p (st_frms … st) (pc … st) (sp … st) (carry … st) (regs … st) m. |
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| 74 | |
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| 75 | definition set_regs: ∀p. regsT p → state p → state p ≝ |
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| 76 | λp,regs,st. mk_state p (st_frms … st) (pc … st) (sp … st) (carry … st) regs (m … st). |
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| 77 | |
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| 78 | definition set_sp: ∀p. pointer → state p → state p ≝ |
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| 79 | λp,sp,st. mk_state … (st_frms … st) (pc … st) sp (carry … st) (regs … st) (m … st). |
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| 80 | |
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| 81 | definition set_carry: ∀p. beval → state p → state p ≝ |
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| 82 | λp,carry,st. mk_state … (st_frms … st) (pc … st) (sp … st) carry (regs … st) (m … st). |
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| 83 | |
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| 84 | definition set_pc: ∀p. address → state p → state p ≝ |
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| 85 | λp,pc,st. mk_state … (st_frms … st) pc (sp … st) (carry … st) (regs … st) (m … st). |
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| 86 | |
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| 87 | definition set_frms: ∀p. framesT p → state p → state p ≝ |
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| 88 | λp,frms,st. mk_state … frms (pc … st) (sp … st) (carry … st) (regs … st) (m … st). |
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| 89 | |
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| 90 | definition goto: ∀p:sem_params. label → state p → state p ≝ |
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| 91 | λp,l,st. set_pc … (address_of_label p l) st. |
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| 92 | |
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| 93 | definition greg_store: ∀p:sem_params. generic_reg p → beval → state p → res (state p) ≝ |
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| 94 | λp,dst,v,st. |
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| 95 | do regs ← greg_store_ … dst v (regs … st); |
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| 96 | OK ? (set_regs … regs st). |
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| 97 | |
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| 98 | definition greg_retrieve: ∀p:sem_params. state p → generic_reg p → res beval ≝ |
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| 99 | λp,st,dst.greg_retrieve_ … (regs … st) dst. |
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| 100 | |
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| 101 | definition acca_store: ∀p:sem_params. acc_a_reg p → beval → state p → res (state p) ≝ |
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| 102 | λp,dst,v,st. |
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| 103 | do regs ← acca_store_ … dst v (regs … st); |
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| 104 | OK ? (set_regs … regs st). |
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| 105 | |
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| 106 | definition acca_retrieve: ∀p:sem_params. state p → acc_a_reg p → res beval ≝ |
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| 107 | λp,st,dst.acca_retrieve_ … (regs … st) dst. |
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| 108 | |
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| 109 | definition accb_store: ∀p:sem_params. acc_b_reg p → beval → state p → res (state p) ≝ |
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| 110 | λp,dst,v,st. |
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| 111 | do regs ← accb_store_ … dst v (regs … st); |
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| 112 | OK ? (set_regs … regs st). |
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| 113 | |
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| 114 | definition accb_retrieve: ∀p:sem_params. state p → acc_b_reg p → res beval ≝ |
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| 115 | λp,st,dst.accb_retrieve_ … (regs … st) dst. |
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| 116 | |
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| 117 | definition dpl_store: ∀p:sem_params. dpl_reg p → beval → state p → res (state p) ≝ |
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| 118 | λp,dst,v,st. |
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| 119 | do regs ← dpl_store_ … dst v (regs … st); |
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| 120 | OK ? (set_regs … regs st). |
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| 121 | |
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| 122 | definition dpl_retrieve: ∀p:sem_params. state p → dpl_reg p → res beval ≝ |
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| 123 | λp,st,dst.dpl_retrieve_ … (regs … st) dst. |
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| 124 | |
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| 125 | definition dph_store: ∀p:sem_params. dph_reg p → beval → state p → res (state p) ≝ |
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| 126 | λp,dst,v,st. |
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| 127 | do regs ← dph_store_ … dst v (regs … st); |
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| 128 | OK ? (set_regs … regs st). |
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| 129 | |
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| 130 | definition dph_retrieve: ∀p:sem_params. state p → dph_reg p → res beval ≝ |
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| 131 | λp,st,dst.dph_retrieve_ … (regs … st) dst. |
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| 132 | |
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| 133 | definition pair_reg_move: ∀p:sem_params. state p → pair_reg p → state p ≝ |
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| 134 | λp,st,rs.set_regs … (pair_reg_move_ … (regs … st) rs) st. |
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| 135 | |
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| 136 | definition save_frame: ∀p:sem_params. state p → state p ≝ |
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| 137 | λp,st. set_frms … (save_frame_ ? (st_frms ? st) (regs … st)) st. |
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| 138 | |
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| 139 | (* removes the top frame from the frames list *) |
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| 140 | definition pop_frame: ∀p. state p → res (state p) ≝ |
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| 141 | λp,st. |
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| 142 | do frames ← pop_frame_ p (st_frms … st); |
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| 143 | OK ? (mk_state ? frames (pc … st) (sp … st) (carry … st) (regs … st) (m … st)). |
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| 144 | |
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| 145 | axiom FailedStore: String. |
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| 146 | |
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| 147 | definition push: ∀p. state p → beval → res (state p) ≝ |
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| 148 | λp,st,v. |
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| 149 | let sp ≝ sp … st in |
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| 150 | do m ← opt_to_res … (msg FailedStore) (bestorev (m … st) sp v); |
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| 151 | let sp ≝ shift_pointer … sp [[false;false;false;false;false;false;false;true]] in |
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| 152 | OK … (set_m … m (set_sp … sp st)). |
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| 153 | |
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| 154 | definition pop: ∀p. state p → res (state p × beval) ≝ |
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| 155 | λp,st. |
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| 156 | let sp ≝ sp ? st in |
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| 157 | let sp ≝ neg_shift_pointer ? sp [[false;false;false;false;false;false;false;true]] in |
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| 158 | let st ≝ set_sp … sp st in |
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| 159 | do v ← opt_to_res ? (msg FailedStore) (beloadv (m ? st) sp); |
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| 160 | OK ? 〈st,v〉. |
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| 161 | |
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| 162 | definition save_ra : ∀p. state p → label → res (state p) ≝ |
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| 163 | λp,st,l. |
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| 164 | let 〈addrl,addrh〉 ≝ address_of_label p l in |
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| 165 | do st ← push … st addrl; |
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| 166 | push … st addrh. |
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| 167 | |
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| 168 | definition fetch_ra : ∀p.state p → res (state p × address) ≝ |
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| 169 | λp,st. |
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| 170 | do 〈st,addrh〉 ← pop … st; |
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| 171 | do 〈st,addrl〉 ← pop … st; |
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| 172 | OK ? 〈st, 〈addrl,addrh〉〉. |
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| 173 | |
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| 174 | axiom MissingSymbol : String. |
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| 175 | axiom FailedLoad : String. |
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| 176 | axiom BadFunction : String. |
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| 177 | |
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| 178 | (*CSC: move elsewhere *) |
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| 179 | definition pi1: ∀A.∀P:A → Prop. (Σx:A. P x) → A ≝ |
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| 180 | λA,P,c. match c with [ dp w _ ⇒ w ]. |
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| 181 | coercion pi1: ∀A.∀P:A → Prop.∀p:(Σx:A. P x).A ≝ pi1 on _p:Σx:?.? to ?. |
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| 182 | |
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| 183 | definition eval_statement : ∀globals: list ident.∀p:sem_params2 globals. genv … (pre_sem_params … p) → state p → IO io_out io_in (trace × (state p)) ≝ |
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| 184 | λglobals,p. λge,st. |
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| 185 | ! s ← fetch_statement globals p st; |
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| 186 | match s with |
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| 187 | [ joint_st_goto l ⇒ ret ? 〈E0, goto … l st〉 |
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| 188 | | joint_st_sequential seq l ⇒ |
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| 189 | match seq with |
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| 190 | [ joint_instr_cost_label cl ⇒ ret ? 〈Echarge cl, goto … l st〉 |
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| 191 | | joint_instr_comment c ⇒ ret ? 〈E0, goto … l st〉 |
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| 192 | | joint_instr_int dest v ⇒ |
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| 193 | ! st ← greg_store … dest (BVByte v) st; |
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| 194 | ret ? 〈E0, goto … l st〉 |
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| 195 | | joint_instr_load dst addrl addrh ⇒ |
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| 196 | ! vaddrh ← dph_retrieve … st addrh; |
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| 197 | ! vaddrl ← dpl_retrieve … st addrl; |
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| 198 | ! vaddr ← pointer_of_bevals [vaddrl;vaddrh]; |
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| 199 | ! v ← opt_to_res … (msg FailedLoad) (beloadv (m … st) vaddr); |
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| 200 | ! st ← acca_store … dst v st; |
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| 201 | ret ? 〈E0, goto … l st〉 |
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| 202 | | joint_instr_store addrl addrh src ⇒ |
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| 203 | ! vaddrh ← dph_retrieve … st addrh; |
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| 204 | ! vaddrl ← dpl_retrieve … st addrl; |
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| 205 | ! vaddr ← pointer_of_bevals [vaddrl;vaddrh]; |
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| 206 | ! v ← acca_retrieve … st src; |
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| 207 | ! m' ← opt_to_res … (msg FailedStore) (bestorev (m … st) vaddr v); |
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| 208 | ret ? 〈E0, goto … l (set_m … m' st)〉 |
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| 209 | | joint_instr_cond src ltrue ⇒ |
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| 210 | ! v ← acca_retrieve … st src; |
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| 211 | ! b ← bool_of_beval v; |
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| 212 | ret ? 〈E0, goto … (if b then ltrue else l) st〉 |
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| 213 | | joint_instr_address ident prf ldest hdest ⇒ |
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| 214 | ! addr ← opt_to_res ? [MSG MissingSymbol; CTX … ident] (find_symbol ?? ge ident); |
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| 215 | ! 〈laddr,haddr〉 ← beval_pair_of_pointer (mk_pointer (block_region addr) addr ? zero_offset); |
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| 216 | ! st ← dpl_store … ldest laddr st; |
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| 217 | ! st ← dph_store … hdest haddr st; |
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| 218 | ret ? 〈E0, goto … l st〉 |
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| 219 | | joint_instr_op1 op acc_a ⇒ |
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| 220 | ! v ← acca_retrieve … st acc_a; |
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| 221 | ! v ← Byte_of_val v; |
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| 222 | let v' ≝ BVByte (op1 eval op v) in |
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| 223 | ! st ← acca_store … acc_a v' st; |
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| 224 | ret ? 〈E0, goto … l st〉 |
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| 225 | | joint_instr_op2 op acc_a src ⇒ |
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| 226 | ! v1 ← acca_retrieve … st acc_a; |
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| 227 | ! v1 ← Byte_of_val v1; |
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| 228 | ! v2 ← greg_retrieve … st src; |
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| 229 | ! v2 ← Byte_of_val v2; |
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| 230 | ! carry ← bool_of_beval (carry … st); |
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| 231 | let 〈v',carry〉 ≝ op2 eval carry op v1 v2 in |
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| 232 | let v' ≝ BVByte v' in |
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| 233 | let carry ≝ beval_of_bool carry in |
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| 234 | ! st ← acca_store … acc_a v' st; |
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| 235 | ret ? 〈E0, goto … l (set_carry … carry st)〉 |
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| 236 | | joint_instr_clear_carry ⇒ ret ? 〈E0, goto … l (set_carry … BVfalse st)〉 |
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| 237 | | joint_instr_set_carry ⇒ ret ? 〈E0, goto … l (set_carry … BVtrue st)〉 |
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| 238 | | joint_instr_opaccs op acc_a_reg acc_b_reg ⇒ |
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| 239 | ! v1 ← acca_retrieve … st acc_a_reg; |
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| 240 | ! v1 ← Byte_of_val v1; |
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| 241 | ! v2 ← accb_retrieve … st acc_b_reg; |
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| 242 | ! v2 ← Byte_of_val v2; |
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| 243 | let 〈v1',v2'〉 ≝ opaccs eval op v1 v2 in |
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| 244 | let v1' ≝ BVByte v1' in |
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| 245 | let v2' ≝ BVByte v2' in |
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| 246 | ! st ← acca_store … acc_a_reg v1' st; |
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| 247 | ! st ← accb_store … acc_b_reg v2' st; |
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| 248 | ret ? 〈E0, goto … l st〉 |
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| 249 | | joint_instr_pop dst ⇒ |
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| 250 | ! 〈st,v〉 ← pop … st; |
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| 251 | ! st ← acca_store … dst v st; |
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| 252 | ret ? 〈E0, goto … l st〉 |
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| 253 | | joint_instr_push src ⇒ |
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| 254 | ! v ← acca_retrieve … st src; |
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| 255 | ! st ← push … st v; |
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| 256 | ret ? 〈E0, goto … l st〉 |
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| 257 | | joint_instr_move dst_src ⇒ |
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| 258 | ret ? 〈E0, goto … l (pair_reg_move … st dst_src)〉 |
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| 259 | | joint_instr_call_id id argsno ⇒ |
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| 260 | ! b ← opt_to_res … [MSG MissingSymbol; CTX ? id] (find_symbol ?? ge id); |
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| 261 | ! fd ← opt_to_res … [MSG BadFunction; CTX ? id] (find_funct_ptr ?? ge b); |
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| 262 | match fd with |
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| 263 | [ Internal fn ⇒ |
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| 264 | ! st ← save_ra … st l; |
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| 265 | let st ≝ save_frame … st in |
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| 266 | let regs ≝ init_locals p (joint_if_locals … fn) in |
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| 267 | let l' ≝ joint_if_entry … fn in |
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| 268 | ret ? 〈 E0, goto … l' (set_regs … regs st)〉 |
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| 269 | | External fn ⇒ |
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| 270 | ! params ← fetch_external_args … fn st; |
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| 271 | ! evargs ← check_eventval_list params (sig_args (ef_sig fn)); |
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| 272 | ! evres ← do_io (ef_id fn) evargs (proj_sig_res (ef_sig fn)); |
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| 273 | (* CSC: XXX bug here; I think I should split it into Byte-long |
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| 274 | components; instead I am making a singleton out of it *) |
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| 275 | let vs ≝ [mk_val ? evres] in |
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| 276 | ! st ← set_result … vs st; |
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| 277 | ret ? 〈Eextcall (ef_id fn) evargs (mk_eventval ? evres), goto … l st〉 |
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| 278 | ]] |
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| 279 | | joint_st_return ⇒ |
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| 280 | ! st ← pop_frame … st; |
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| 281 | ! 〈st,pch〉 ← pop … st; |
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| 282 | ! 〈st,pcl〉 ← pop … st; |
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| 283 | ret ? 〈E0,set_pc … 〈pcl,pch〉 st〉 |
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| 284 | | joint_st_extension c ⇒ exec_extended … p ge c st ]. |
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| 285 | cases addr // |
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| 286 | qed. |
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| 287 | |
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| 288 | definition is_final: ∀globals:list ident. ∀p: sem_params2 globals. address → nat → state p → option int ≝ |
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| 289 | λglobals,p,exit,registersno,st. res_to_opt … ( |
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| 290 | do s ← fetch_statement … st; |
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| 291 | match s with |
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| 292 | [ joint_st_return ⇒ |
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| 293 | do 〈st,l〉 ← fetch_ra … st; |
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| 294 | if eq_address l exit then |
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| 295 | do val ← fetch_result globals p st registersno; |
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| 296 | match val with |
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| 297 | [ Vint sz i ⇒ intsize_eq_elim ? sz I32 ? i (λi. OK ? i) (Error ? []) |
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| 298 | | _ ⇒ Error ? []] |
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| 299 | else |
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| 300 | Error ? [] |
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| 301 | | _ ⇒ Error ? []]). |
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| 302 | |
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| 303 | definition joint_exec: ∀globals:list ident. sem_params2 globals → address → nat → execstep io_out io_in ≝ |
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| 304 | λglobals,p. |
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| 305 | λexit. |
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| 306 | λregistersno. |
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| 307 | mk_execstep … (is_final globals p exit registersno) (m p) (eval_statement globals p). |
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| 308 | |
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| 309 | (* CSC: XXX the program type does not fit with the globalenv and init_mem *) |
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| 310 | axiom make_initial_state : ∀globals:list ident.∀sparams: sem_params2 globals. joint_program … (pre_sem_params … sparams) → res ((genv … (pre_sem_params … sparams)) × (state sparams)).(* ≝ |
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| 311 | λp. |
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| 312 | do ge ← globalenv Genv ?? p; |
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| 313 | do m ← init_mem Genv ?? p; |
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| 314 | let main ≝ rtl_pr_main ?? p in |
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| 315 | do b ← opt_to_res ? [MSG MissingSymbol; CTX ? main] (find_symbol ? ? ge main); |
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| 316 | do f ← opt_to_res ? [MSG BadFunction; CTX ? main] (find_funct_ptr ? ? ge b); |
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| 317 | OK ? 〈ge,Callstate f (nil ?) [ ] (nil ?) m〉. |
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| 318 | *) |
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| 319 | |
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| 320 | definition joint_fullexec : |
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| 321 | ∀globals:list ident. ∀sparams:sem_params2 globals. joint_program globals sparams (pre_sem_params … sparams) → fullexec io_out io_in ≝ |
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| 322 | λglobals,p,program. |
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| 323 | let exit ≝ ? in |
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| 324 | let registersno ≝ ? in |
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| 325 | mk_fullexec ?? (joint_exec ? p exit registersno) ? (make_initial_state … p). |
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