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icing_optimisationsLib.sml
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icing_optimisationsLib.sml
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(*
Library defining HOL4 automation that builds an optimiser
correctness theorem for an optimisation plan.
*)
structure icing_optimisationsLib =
struct
open floatToRealProofsTheory icing_realIdProofsTheory source_to_source2ProofsTheory
listTheory Portable;
open preamble;
local
fun mk_single_rewriteFPexp_correct_thm th1 th2 =
let
val arglist =
th1 |> concl
|> dest_forall |> snd
|> dest_forall |> snd
|> dest_forall |> snd
|> dest_forall |> snd
|> dest_forall |> snd
|> rator |> rator |> rator |> rator |> rator |> rand;
val arg =
th2 |> concl
|> dest_forall |> snd
|> dest_forall |> snd
|> dest_forall |> snd
|> dest_forall |> snd
|> dest_forall |> snd
|> rator |> rator |> rator |> rator |> rator |> rand
|> listSyntax.dest_list |> fst |> hd (* TODO: Check length *);
in
SIMP_RULE std_ss [GSYM AND_IMP_INTRO] rewriteExp_compositional
|> SPECL [arglist,arg]
|> (fn th => MP th th1)
|> (fn th => MP th th2)
|> SIMP_RULE std_ss [APPEND]
end;
fun mk_rewriteFPexp_correct_thm_list thms correctthm =
case thms of
[] => correctthm
| th1::thms =>
mk_rewriteFPexp_correct_thm_list thms (mk_single_rewriteFPexp_correct_thm correctthm th1);
fun mk_rewriteFPexp_list_correct_thm th1 =
let
val arglist =
th1 |> concl
|> dest_forall |> snd
|> dest_forall |> snd
|> dest_forall |> snd
|> dest_forall |> snd
|> dest_forall |> snd
|> rator |> rator |> rator |> rator |> rator |> rand;
in
SPEC arglist lift_rewriteFPexp_correct_list
|> (fn th => MP th th1)
end;
val all_optimisation_proofs =
map (fn ((a,(b,c,d))) => (a,(b,c))) (DB.thy "icing_optimisationProofs");
(* Automatically prove a is_perform_rewrites_correct theorem for the given plan *)
fun mk_plan_correct_thm plan_list :(term * thm)=
case plan_list of
(* Base case: Empty plan -> No plan used in correctness theorem *)
[] => (“[]:opt_step list”, is_perform_rewrites_correct_empty_plan)
| p1 :: ps => (* Cons case *)
let
(* Recursive call *)
val (rec_plan, rec_thm) = mk_plan_correct_thm ps
(* Result plan, used for instantiation of theorems *)
val full_plan = Parse.Term ‘^p1 :: ^rec_plan’
(* Get the Datatype constructor used, can be "Label", "Expected" or "Apply" *)
val dtype_comb = rator p1
in
(* Simple case: "Label s" --> can be appended to the correctness theorem *)
if (Term.compare(dtype_comb, “source_to_source2$Label”) = EQUAL)
then
(full_plan,
MP (Q.SPECL [‘^(rand p1)’, ‘^rec_plan’] is_perform_rewrites_correct_label) rec_thm)
(* Simple case: "Expected e" --> can be appended to the correctness theorem *)
else if (Term.compare(dtype_comb, “source_to_source2$Expected”) = EQUAL)
then (full_plan,
MP (Q.SPECL [‘^(rand p1)’, ‘^rec_plan’] is_perform_rewrites_correct_expected) rec_thm)
else (* Must be an Apply (path, rws) now *)
let
val _ = if (Term.compare(dtype_comb, “source_to_source2$Apply”) <> EQUAL)
then raise Feedback.mk_HOL_ERR "" "" "Internal err, expected Apply" else ()
val (pth, rws) = rand p1 |> dest_pair
(* corr_thms = list of is_rewriteFPexp_correct theorems *)
val corr_thms:thm list = rand p1
|> dest_pair |> #2 (* extract the rewrites *)
|> listSyntax.dest_list |> #1
|> map (fn t => (t, DB.apropos_in t all_optimisation_proofs)) (* Look up correctness theorems *)
|> map (fn (t, thms) =>
(print_term t; print (" has thm :\n"); map (fn d => print_thm (#1 (#2 d))) thms; print ("\n\n"); thms))
|> map (fn datas => if (length datas <> 1)
then if (length datas = 0)
then raise Feedback.mk_HOL_ERR "" "" "Not enough matching theorems"
else raise Feedback.mk_HOL_ERR "" "" "Too many matching theorems"
else #1 (#2 (hd datas)))
(* |> (fn datas => if (length datas <> 1) then raise ERR "Too many matching theorems" ""
else datas)*)
(* Join the theorems into a single theorem about each of them*)
val all_rewrites_correct_thm = mk_rewriteFPexp_correct_thm_list corr_thms empty_rw_correct
(* lift the theorem to is_rewriteFPexp_list_correct *)
val all_rewrites_list_correct_thm = mk_rewriteFPexp_list_correct_thm all_rewrites_correct_thm
(* Extract argument list from theorem *)
val args = all_rewrites_list_correct_thm |> concl
|> dest_forall |> snd |> dest_forall |> snd
|> dest_forall |> snd |> dest_forall |> snd
|> dest_forall |> snd
|> rator |> rator |> rator |> rator |> rator |> rand
(* build a single perform_rewrites_correct theorem using modus-ponens *)
val perform_rw_correct_thm =
MP (Q.SPEC ‘^args’ is_rewriteFPexp_correct_lift_perform_rewrites)
all_rewrites_list_correct_thm
|> Q.SPEC ‘^(rand p1 |> dest_pair |> #1)’
(* finally, use the "CONS" theorem for plans to prepend the current Apply node *)
val final_perform_rw_thm =
let
val th1 = MP (Q.SPECL [‘^args’, ‘^(rand p1 |> dest_pair |> #1)’, ‘^rec_plan’]
is_perform_rewrites_correct_cons)
perform_rw_correct_thm
in
MP th1 rec_thm end
in (full_plan, final_perform_rw_thm)
end
end;
in
fun mk_stos_pass_correct_thm plan_list =
let
val (thePlan, plan_correct_perform_rewrites) = mk_plan_correct_thm plan_list;
val plan_correct_optimise_with_plan =
MP (Q.SPEC ‘^thePlan’ is_optimise_with_plan_correct_lift)
plan_correct_perform_rewrites
(* val stos_pass_correct_with_plan =
MP (Q.SPEC ‘[^thePlan]’ stos_pass_with_plans_correct)
(MP (Q.SPEC ‘^thePlan’ is_optimise_with_plan_correct_sing)
plan_correct_optimise_with_plan)
in stos_pass_correct_with_plan *)
in plan_correct_optimise_with_plan
end;
end;
(** Real-valued identity proof *)
local
fun mk_single_real_id_thm th1 th2 =
let
val arglist =
th1 |> concl
|> dest_forall |> snd
|> dest_forall |> snd
|> dest_forall |> snd
|> dest_forall |> snd
|> dest_forall |> snd
|> rator |> rator |> rator |> rator |> rator |> rand;
val arg =
th2 |> concl
|> dest_forall |> snd
|> dest_forall |> snd
|> dest_forall |> snd
|> dest_forall |> snd
|> dest_forall |> snd
|> rator |> rator |> rator |> rator |> rator |> rand
|> listSyntax.dest_list |> fst |> hd (* TODO: Check length *);
in
SIMP_RULE std_ss [GSYM AND_IMP_INTRO] real_valued_id_compositional
|> SPECL [arglist,arg]
|> (fn th => MP th th1)
|> (fn th => MP th th2)
|> SIMP_RULE std_ss [APPEND]
end;
fun mk_real_id_thm_list thms correctthm =
case thms of
[] => correctthm
| th1::thms =>
mk_real_id_thm_list thms (mk_single_real_id_thm correctthm th1);
fun mk_real_id_list_thm th1 =
let
val arglist =
th1 |> concl
|> dest_forall |> snd
|> dest_forall |> snd
|> dest_forall |> snd
|> dest_forall |> snd
|> dest_forall |> snd
|> rator |> rator |> rator |> rator |> rator |> rand;
in
SPEC arglist lift_real_id_exp_list_strong
|> (fn th => MP th th1)
end;
val all_realid_proofs =
map (fn ((a,(b,c,d))) => (a,(b,c))) (DB.thy "icing_realIdProofs");
(* Automatically prove a is_perform_rewrites_correct theorem for the given plan *)
fun mk_plan_correct_thm plan_list :(term * thm)=
case plan_list of
(* Base case: Empty plan -> No plan used in correctness theorem *)
[] => (“[]:opt_step list”, is_real_id_perform_rewrites_empty)
| p1 :: ps => (* Cons case *)
let
(* Recursive call *)
val (rec_plan, rec_thm) = mk_plan_correct_thm ps
(* Result plan, used for instantiation of theorems *)
val full_plan = Parse.Term ‘^p1 :: ^rec_plan’
(* Get the Datatype constructor used, can be "Label", "Expected" or "Apply" *)
val dtype_comb = rator p1
in
(* Simple case: "Label s" --> can be appended to the correctness theorem *)
if (Term.compare(dtype_comb, “source_to_source2$Label”) = EQUAL)
then
(full_plan,
MP (Q.SPECL [‘^(rand p1)’, ‘^rec_plan’] is_perform_rewrites_correct_label_real_id) rec_thm)
(* Simple case: "Expected e" --> can be appended to the correctness theorem *)
else if (Term.compare(dtype_comb, “source_to_source2$Expected”) = EQUAL)
then (full_plan,
MP (Q.SPECL [‘^(rand p1)’, ‘^rec_plan’] is_perform_rewrites_correct_expected_real_id) rec_thm)
else (* Must be an Apply (path, rws) now *)
let
val _ = if (Term.compare(dtype_comb, “source_to_source2$Apply”) <> EQUAL)
then raise Feedback.mk_HOL_ERR "" "" "Internal err, expected Apply" else ()
val (pth, rws) = rand p1 |> dest_pair
(* corr_thms = list of is_rewriteFPexp_correct theorems *)
val corr_thms:thm list = rand p1
|> dest_pair |> #2 (* extract the rewrites *)
|> listSyntax.dest_list |> #1
|> map (fn t => (t, DB.apropos_in t all_realid_proofs)) (* Look up correctness theorems *)
|> map (fn (t, thms) =>
(print_term t; print (":\n"); map (fn d => print_thm (#1 (#2 d))) thms; thms))
|> map (fn datas => if (length datas <> 1)
then if (length datas = 0)
then raise Feedback.mk_HOL_ERR "" "" "Not enough matching theorems"
else raise Feedback.mk_HOL_ERR "" "" "Too many matching theorems"
else #1 (#2 (hd datas)))
(* |> (fn datas => if (length datas <> 1) then raise ERR "Too many matching theorems" ""
else datas)*)
(* Join the theorems into a single theorem about each of them*)
val all_rewrites_correct_thm = mk_real_id_thm_list corr_thms empty_rw_real_id
(* lift the theorem to is_rewriteFPexp_list_correct *)
val all_rewrites_list_correct_thm = mk_real_id_list_thm all_rewrites_correct_thm
(* Extract argument list from theorem *)
val args = all_rewrites_list_correct_thm |> concl
|> dest_forall |> snd |> dest_forall |> snd
|> dest_forall |> snd |> dest_forall |> snd
|> dest_forall |> snd
|> rator |> rator |> rator |> rator |> rator |> rand
(* build a single perform_rewrites_correct theorem using modus-ponens *)
val perform_rw_correct_thm =
MP (Q.SPEC ‘^args’ is_real_id_list_perform_rewrites_lift)
all_rewrites_list_correct_thm
|> Q.SPEC ‘^(rand p1 |> dest_pair |> #1)’
(* finally, use the "CONS" theorem for plans to prepend the current Apply node *)
val final_perform_rw_thm =
let
val th1 = MP (Q.SPECL [‘^args’, ‘^(rand p1 |> dest_pair |> #1)’, ‘^rec_plan’]
is_perform_rewrites_correct_cons_real_id)
perform_rw_correct_thm
in
MP th1 rec_thm end
in (full_plan, final_perform_rw_thm)
end
end;
in
fun mk_stos_pass_real_id_thm plan_list =
let
val (thePlan, plan_correct_perform_rewrites) = mk_plan_correct_thm plan_list;
val plan_correct_optimise_with_plan =
MP (Q.SPEC ‘^thePlan’ is_real_id_perform_rewrites_optimise_with_plan_lift)
plan_correct_perform_rewrites
(* val stos_pass_correct_with_plan =
MP (Q.SPEC ‘[^thePlan]’ stos_pass_with_plans_real_id)
(MP (Q.SPEC ‘^thePlan’ is_optimise_with_plan_correct_sing_real_id)
plan_correct_optimise_with_plan)
in stos_pass_correct_with_plan *)
in plan_correct_optimise_with_plan
end;
end;
end