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p4_exec_sem_arch_soundnessScript.sml
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p4_exec_sem_arch_soundnessScript.sml
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open HolKernel boolLib Parse bossLib;
val _ = new_theory "p4_exec_sem_arch_soundness";
open p4Lib;
open listTheory ottTheory p4Theory p4_auxTheory p4_exec_semTheory p4_exec_sem_frames_soundnessTheory;
(* Type argument added to avoid "Unbound type variable(s) in definition: "'a"" *)
Definition arch_exec_sound:
(arch_exec_sound arch_frame_list (type:('a itself)) =
!(actx:'a actx) aenv g_scope_list status astate'.
arch_exec actx (aenv, g_scope_list, arch_frame_list, status) = SOME astate' ==>
arch_red actx (aenv, g_scope_list, arch_frame_list, status) astate')
End
Theorem arch_exec_sound_red:
!arch_frame_list type. arch_exec_sound arch_frame_list type
Proof
Cases_on `arch_frame_list` >> (
fs [arch_exec_sound] >>
Cases_on `status` >> (
fs [arch_exec_def]
)
) >> (
rpt strip_tac >>
PairCases_on `actx` >>
rename1 `(ab_list, pblock_map, ffblock_map, input_f, output_f, copyin_pbl, copyout_pbl, apply_table_f, ext_map, func_map)` >>
PairCases_on `aenv` >>
rename1 `(aenv0, in_out_list, in_out_list', ascope)` >>
rename1 `(i, in_out_list, in_out_list', ascope)`
) >| [
Cases_on `EL i ab_list` >| [
(* input *)
fs [arch_exec_def] >>
Cases_on `input_f (in_out_list,ascope)` >> (
fs []
) >>
PairCases_on `x` >>
fs [] >>
rw [] >>
metis_tac [(valOf o find_clause_arch_red) "arch_in", clause_name_def],
(* programmable block initialisation *)
fs [arch_exec_def] >>
Cases_on `ALOOKUP pblock_map s` >> (
fs []
) >>
PairCases_on `x` >>
fs [] >>
rename1 `(x0, x_d_l, b_func_map, t_scope, pars_map, tbl_map)` >>
rename1 `(p, x_d_l, b_func_map, t_scope, pars_map, tbl_map)` >>
Cases_on `lookup_block_body s b_func_map` >> (
fs []
) >>
rename1 `lookup_block_body s b_func_map = SOME stmt` >>
fs [] >>
Cases_on `copyin_pbl (MAP FST x_d_l,MAP SND x_d_l,l,ascope)` >> (
fs []
) >>
Cases_on `oLASTN 1 g_scope_list` >> (
fs []
) >>
Cases_on `x'` >> (
fs []
) >>
Cases_on `t` >> (
fs []
) >>
Cases_on `initialise_var_stars func_map b_func_map ext_map [declare_list_in_scope (t_scope,x); h]` >> (
fs []
) >>
rw [] >>
irule ((valOf o find_clause_arch_red) "arch_pbl_init") >>
fs [clause_name_def] >>
qexistsl_tac [`ZIP (l, ZIP(MAP FST x_d_l, MAP SND x_d_l))`, `x`] >>
fs [] >>
rpt strip_tac >| [
fs [map_tri_zip12],
gs [listTheory.oEL_EQ_EL] >>
metis_tac [oLASTN_imp_LASTN],
fs [map_tri_zip12, ZIP_MAP_FST_SND],
fs [map_tri_zip12, ZIP_MAP_FST_SND]
],
(* fixed-function block *)
fs [arch_exec_def] >>
Cases_on `ALOOKUP ffblock_map s` >> (
fs []
) >>
Cases_on `x` >>
fs [] >>
Cases_on `f ascope` >> (
fs []
) >>
rw [] >>
metis_tac [(valOf o find_clause_arch_red) "arch_ffbl", clause_name_def],
(* output *)
fs [arch_exec_def] >>
Cases_on `output_f (in_out_list',ascope)` >> (
fs []
) >>
PairCases_on `x` >>
fs [] >>
rw [] >>
metis_tac [(valOf o find_clause_arch_red) "arch_out", clause_name_def]
],
fs [arch_exec_def],
fs [arch_exec_def],
Cases_on `state_fin status_running l` >| [
(* programmable block return *)
fs [state_fin_def] >>
rw [] >>
fs [arch_exec_def] >>
Cases_on `EL i ab_list` >> (
fs []
) >>
Cases_on `ALOOKUP pblock_map s` >> (
fs []
) >>
PairCases_on `x` >>
fs [state_fin_exec_def] >>
Cases_on `lookup_block_body s x2` >> (
fs []
) >>
rename1 `lookup_block_body s b_func_map = SOME stmt` >>
fs [] >>
Cases_on `copyout_pbl
(g_scope_list,ascope,MAP SND x1,MAP FST x1,
set_fin_status x0 status_running)` >> (
fs []
) >>
rw [] >>
irule ((valOf o find_clause_arch_red) "arch_pbl_ret") >>
fs [clause_name_def, state_fin_def] >>
qexists_tac `ZIP (l, ZIP (MAP FST x1, MAP SND x1))` >>
rpt strip_tac >| [
fs [map_tri_zip12],
fs [map_tri_zip12, ZIP_MAP_FST_SND],
fs [map_tri_zip12, ZIP_MAP_FST_SND]
],
(* programmable block execution *)
fs [GSYM state_fin_exec_equiv, arch_exec_def] >>
Cases_on `EL i ab_list` >> (
fs []
) >>
Cases_on `ALOOKUP pblock_map s` >> (
fs []
) >>
PairCases_on `x` >>
fs [state_fin_exec_equiv, state_fin_def] >>
Cases_on `frames_exec (apply_table_f,ext_map,func_map,x2,x4,x5)
(ascope,g_scope_list,l,status_running)` >> (
fs []
) >>
PairCases_on `x` >>
fs [] >>
rw [] >>
irule ((valOf o find_clause_arch_red) "arch_pbl_exec") >>
fs [clause_name_def] >>
(*
qexists_tac `ZIP (l', x1)` >>
rpt strip_tac >| [
fs [map_tri_zip12],
fs [map_tri_zip12],
*)
assume_tac frame_list_exec_sound_red >>
fs [frame_list_exec_sound]
(*
]
*)
],
(* programmable block return *)
subgoal `state_fin (status_returnv v) l` >- (
fs [state_fin_def]
) >>
fs [arch_exec_def] >>
Cases_on `EL i ab_list` >> (
fs []
) >>
Cases_on `ALOOKUP pblock_map s` >> (
fs []
) >>
PairCases_on `x` >>
fs [] >>
Cases_on `lookup_block_body s x2` >> (
fs []
) >>
rename1 `lookup_block_body s b_func_map = SOME stmt` >>
fs [] >>
Cases_on `copyout_pbl
(g_scope_list, ascope, MAP SND x1, MAP FST x1,
set_fin_status x0 (status_returnv v))` >> (
fs []
) >>
rw [] >>
irule ((valOf o find_clause_arch_red) "arch_pbl_ret") >>
fs [clause_name_def] >>
qexists_tac `ZIP (l', x1)` >>
fs [map_tri_zip12],
(* programmable block transition *)
fs [arch_exec_def] >>
Cases_on `EL i ab_list` >> (
fs []
) >>
Cases_on `ALOOKUP pblock_map s'` >> (
fs []
) >>
PairCases_on `x` >>
fs [state_fin_exec_equiv] >>
Cases_on `state_fin (status_trans s) l` >> (
fs []
) >| [
(* programmable block return *)
Cases_on `lookup_block_body s' x2` >> (
fs []
) >>
rename1 `lookup_block_body s' b_func_map = SOME stmt` >>
fs [] >>
Cases_on `copyout_pbl
(g_scope_list,ascope,MAP SND x1,MAP FST x1,
set_fin_status x0 (status_trans s))` >> (
fs []
) >>
rw [] >>
irule ((valOf o find_clause_arch_red) "arch_pbl_ret") >>
fs [clause_name_def] >>
qexists_tac `ZIP (l', x1)` >>
fs [map_tri_zip12],
(* parser transition *)
Cases_on `x0` >> (
fs []
) >>
Cases_on `ALOOKUP x4 s` >> (
fs []
) >>
rw [] >>
irule ((valOf o find_clause_arch_red) "arch_parser_trans") >>
fs [clause_name_def, state_fin_def] (* >>
qexists_tac `ZIP (l', x1)` >>
rpt strip_tac >| [
fs [map_tri_zip12],
fs [map_tri_zip12]
]
*)
]
]
QED
val _ = export_theory ();