author | paulson <lp15@cam.ac.uk> |
Mon, 30 Nov 2020 22:00:23 +0000 | |
changeset 72797 | 402afc68f2f9 |
parent 70507 | 06a62b29085e |
child 74051 | bd575b1bd9bf |
permissions | -rw-r--r-- |
39941 | 1 |
(* Title: HOL/Tools/Meson/meson_clausify.ML |
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Author: Jia Meng, Cambridge University Computer Laboratory and NICTA |
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Author: Jasmin Blanchette, TU Muenchen |
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|
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Transformation of HOL theorems into CNF forms. |
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*) |
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||
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signature MESON_CLAUSIFY = |
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sig |
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val new_skolem_var_prefix : string |
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val new_nonskolem_var_prefix : string |
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val is_zapped_var_name : string -> bool |
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val is_quasi_lambda_free : term -> bool |
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val introduce_combinators_in_cterm : Proof.context -> cterm -> thm |
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val introduce_combinators_in_theorem : Proof.context -> thm -> thm |
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val cluster_of_zapped_var_name : string -> (int * (int * int)) * bool |
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simplifier uses proper Proof.context instead of historic type simpset;
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val ss_only : thm list -> Proof.context -> Proof.context |
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val cnf_axiom : |
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Proof.context -> bool -> bool -> int -> thm |
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-> (thm * term) option * thm list |
|
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end; |
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|
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structure Meson_Clausify : MESON_CLAUSIFY = |
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struct |
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|
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(* the extra "Meson" helps prevent clashes (FIXME) *) |
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val new_skolem_var_prefix = "MesonSK" |
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val new_nonskolem_var_prefix = "MesonV" |
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|
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fun is_zapped_var_name s = |
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exists (fn prefix => String.isPrefix prefix s) |
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[new_skolem_var_prefix, new_nonskolem_var_prefix] |
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(**** Transformation of Elimination Rules into First-Order Formulas****) |
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|
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val cfalse = Thm.cterm_of \<^theory_context>\<open>HOL\<close> \<^term>\<open>False\<close>; |
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val ctp_false = Thm.cterm_of \<^theory_context>\<open>HOL\<close> (HOLogic.mk_Trueprop \<^term>\<open>False\<close>); |
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|
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(* Converts an elim-rule into an equivalent theorem that does not have the |
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predicate variable. Leaves other theorems unchanged. We simply instantiate |
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improved Waldmeister support -- even run it by default on unit equational goals
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the conclusion variable to False. (Cf. "transform_elim_prop" in |
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perform eta-expansion of quantifier bodies in Sledgehammer translation when needed + transform elim rules later;
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"Sledgehammer_Util".) *) |
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fun transform_elim_theorem th = |
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(case Thm.concl_of th of (*conclusion variable*) |
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\<^const>\<open>Trueprop\<close> $ (Var (v as (_, \<^typ>\<open>bool\<close>))) => |
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simplified Thm.instantiate and derivatives: the LHS refers to non-certified variables -- this merely serves as index into already certified structures (or is ignored);
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Thm.instantiate ([], [(v, cfalse)]) th |
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| Var (v as (_, \<^typ>\<open>prop\<close>)) => |
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simplified Thm.instantiate and derivatives: the LHS refers to non-certified variables -- this merely serves as index into already certified structures (or is ignored);
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Thm.instantiate ([], [(v, ctp_false)]) th |
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| _ => th) |
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|
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|
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(**** SKOLEMIZATION BY INFERENCE (lcp) ****) |
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||
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fun mk_old_skolem_term_wrapper t = |
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let val T = fastype_of t in |
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Const (\<^const_name>\<open>Meson.skolem\<close>, T --> T) $ t |
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end |
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fun beta_eta_in_abs_body (Abs (s, T, t')) = Abs (s, T, beta_eta_in_abs_body t') |
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| beta_eta_in_abs_body t = Envir.beta_eta_contract t |
|
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this looks like the most appropriate place to do the beta-eta-contraction
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(*Traverse a theorem, accumulating Skolem function definitions.*) |
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fun old_skolem_defs th = |
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let |
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fun dec_sko (Const (\<^const_name>\<open>Ex\<close>, _) $ (body as Abs (_, T, p))) rhss = |
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(*Existential: declare a Skolem function, then insert into body and continue*) |
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let |
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val args = Misc_Legacy.term_frees body |
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thread original theorem along with CNF theorem, as a step toward killing the Skolem cache
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(* Forms a lambda-abstraction over the formal parameters *) |
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val rhs = |
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fold_rev (absfree o dest_Free) args |
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(HOLogic.choice_const T $ beta_eta_in_abs_body body) |
|
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|> mk_old_skolem_term_wrapper |
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val comb = list_comb (rhs, args) |
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in dec_sko (subst_bound (comb, p)) (rhs :: rhss) end |
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| dec_sko (Const (\<^const_name>\<open>All\<close>,_) $ Abs (a, T, p)) rhss = |
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(*Universal quant: insert a free variable into body and continue*) |
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let val fname = singleton (Name.variant_list (Misc_Legacy.add_term_names (p, []))) a |
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in dec_sko (subst_bound (Free(fname,T), p)) rhss end |
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| dec_sko (\<^const>\<open>conj\<close> $ p $ q) rhss = rhss |> dec_sko p |> dec_sko q |
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| dec_sko (\<^const>\<open>disj\<close> $ p $ q) rhss = rhss |> dec_sko p |> dec_sko q |
|
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| dec_sko (\<^const>\<open>Trueprop\<close> $ p) rhss = dec_sko p rhss |
|
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| dec_sko _ rhss = rhss |
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in dec_sko (Thm.prop_of th) [] end; |
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||
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(**** REPLACING ABSTRACTIONS BY COMBINATORS ****) |
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|
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fun is_quasi_lambda_free (Const (\<^const_name>\<open>Meson.skolem\<close>, _) $ _) = true |
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| is_quasi_lambda_free (t1 $ t2) = |
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is_quasi_lambda_free t1 andalso is_quasi_lambda_free t2 |
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| is_quasi_lambda_free (Abs _) = false |
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| is_quasi_lambda_free _ = true |
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fun abstract ctxt ct = |
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96 |
let |
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val Abs (_, _, body) = Thm.term_of ct |
98 |
val (x, cbody) = Thm.dest_abs NONE ct |
|
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val (A, cbodyT) = Thm.dest_funT (Thm.ctyp_of_cterm ct) |
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fun makeK () = Thm.instantiate' [SOME A, SOME cbodyT] [SOME cbody] @{thm abs_K} |
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in |
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case body of |
|
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Const _ => makeK() |
|
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| Free _ => makeK() |
|
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| Var _ => makeK() (*though Var isn't expected*) |
|
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| Bound 0 => Thm.instantiate' [SOME A] [] @{thm abs_I} (*identity: I*) |
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| rator$rand => |
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if Term.is_dependent rator then (*C or S*) |
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if Term.is_dependent rand then (*S*) |
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let val crator = Thm.lambda x (Thm.dest_fun cbody) |
111 |
val crand = Thm.lambda x (Thm.dest_arg cbody) |
|
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val (C, B) = Thm.dest_funT (Thm.dest_ctyp1 (Thm.ctyp_of_cterm crator)) |
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val abs_S' = @{thm abs_S} |
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|> instantiate'_normalize [SOME A, SOME B, SOME C] [SOME crator, SOME crand] |
|
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val (_,rhs) = Thm.dest_equals (Thm.cprop_of abs_S') |
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in |
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Thm.transitive abs_S' (Conv.binop_conv (abstract ctxt) rhs) |
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118 |
end |
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else (*C*) |
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let val crator = Thm.lambda x (Thm.dest_fun cbody) |
121 |
val crand = Thm.dest_arg cbody |
|
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val (C, B) = Thm.dest_funT (Thm.dest_ctyp1 (Thm.ctyp_of_cterm crator)) |
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val abs_C' = @{thm abs_C} |
124 |
|> instantiate'_normalize [SOME A, SOME B, SOME C] [SOME crator, SOME crand] |
|
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val (_,rhs) = Thm.dest_equals (Thm.cprop_of abs_C') |
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126 |
in |
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Thm.transitive abs_C' (Conv.fun_conv (Conv.arg_conv (abstract ctxt)) rhs) |
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128 |
end |
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else if Term.is_dependent rand then (*B or eta*) |
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if rand = Bound 0 then Thm.eta_conversion ct |
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else (*B*) |
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let val crator = Thm.dest_fun cbody |
133 |
val crand = Thm.lambda x (Thm.dest_arg cbody) |
|
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val (C, B) = Thm.dest_funT (Thm.ctyp_of_cterm crator) |
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val abs_B' = @{thm abs_B} |
136 |
|> instantiate'_normalize [SOME A, SOME B, SOME C] [SOME crator, SOME crand] |
|
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val (_,rhs) = Thm.dest_equals (Thm.cprop_of abs_B') |
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in Thm.transitive abs_B' (Conv.arg_conv (abstract ctxt) rhs) end |
139 |
else makeK () |
|
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| _ => raise Fail "abstract: Bad term" |
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end; |
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142 |
|
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(* Traverse a theorem, remplacing lambda-abstractions with combinators. *) |
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fun introduce_combinators_in_cterm ctxt ct = |
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if is_quasi_lambda_free (Thm.term_of ct) then |
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Thm.reflexive ct |
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else case Thm.term_of ct of |
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Abs _ => |
149 |
let |
|
150 |
val (cv, cta) = Thm.dest_abs NONE ct |
|
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val (v, _) = dest_Free (Thm.term_of cv) |
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val u_th = introduce_combinators_in_cterm ctxt cta |
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val cu = Thm.rhs_of u_th |
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val comb_eq = abstract ctxt (Thm.lambda cv cu) |
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in Thm.transitive (Thm.abstract_rule v cv u_th) comb_eq end |
156 |
| _ $ _ => |
|
157 |
let val (ct1, ct2) = Thm.dest_comb ct in |
|
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Thm.combination (introduce_combinators_in_cterm ctxt ct1) |
159 |
(introduce_combinators_in_cterm ctxt ct2) |
|
37349 | 160 |
end |
161 |
||
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fun introduce_combinators_in_theorem ctxt th = |
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if is_quasi_lambda_free (Thm.prop_of th) then |
37349 | 164 |
th |
24827 | 165 |
else |
37349 | 166 |
let |
167 |
val th = Drule.eta_contraction_rule th |
|
60328 | 168 |
val eqth = introduce_combinators_in_cterm ctxt (Thm.cprop_of th) |
37349 | 169 |
in Thm.equal_elim eqth th end |
170 |
handle THM (msg, _, _) => |
|
61268 | 171 |
(warning ("Error in the combinator translation of " ^ Thm.string_of_thm ctxt th ^ |
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172 |
"\nException message: " ^ msg); |
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(* A type variable of sort "{}" will make "abstraction" fail. *) |
37349 | 174 |
TrueI) |
16009 | 175 |
|
176 |
(*cterms are used throughout for efficiency*) |
|
69593 | 177 |
val cTrueprop = Thm.cterm_of \<^theory_context>\<open>HOL\<close> HOLogic.Trueprop; |
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|
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(*Given an abstraction over n variables, replace the bound variables by free |
|
180 |
ones. Return the body, along with the list of free variables.*) |
|
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181 |
fun c_variant_abs_multi (ct0, vars) = |
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let val (cv,ct) = Thm.dest_abs NONE ct0 |
183 |
in c_variant_abs_multi (ct, cv::vars) end |
|
184 |
handle CTERM _ => (ct0, rev vars); |
|
185 |
||
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(* Given the definition of a Skolem function, return a theorem to replace |
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187 |
an existential formula by a use of that function. |
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188 |
Example: "EX x. x : A & x ~: B ==> sko A B : A & sko A B ~: B" [.] *) |
57466 | 189 |
fun old_skolem_theorem_of_def ctxt rhs0 = |
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|
190 |
let |
59632 | 191 |
val rhs = rhs0 |> Type.legacy_freeze_thaw |> #1 |> Thm.cterm_of ctxt |
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192 |
val rhs' = rhs |> Thm.dest_comb |> snd |
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
193 |
val (ch, frees) = c_variant_abs_multi (rhs', []) |
59582 | 194 |
val (hilbert, cabs) = ch |> Thm.dest_comb |>> Thm.term_of |
37617
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|
195 |
val T = |
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parents:
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changeset
|
196 |
case hilbert of |
67149 | 197 |
Const (_, Type (\<^type_name>\<open>fun\<close>, [_, T])) => T |
57466 | 198 |
| _ => raise TERM ("old_skolem_theorem_of_def: expected \"Eps\"", [hilbert]) |
59632 | 199 |
val cex = Thm.cterm_of ctxt (HOLogic.exists_const T) |
46497
89ccf66aa73d
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wenzelm
parents:
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diff
changeset
|
200 |
val ex_tm = Thm.apply cTrueprop (Thm.apply cex cabs) |
37629 | 201 |
val conc = |
37617
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parents:
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diff
changeset
|
202 |
Drule.list_comb (rhs, frees) |
46497
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parents:
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diff
changeset
|
203 |
|> Drule.beta_conv cabs |> Thm.apply cTrueprop |
37617
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parents:
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changeset
|
204 |
fun tacf [prem] = |
54742
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proper context for basic Simplifier operations: rewrite_rule, rewrite_goals_rule, rewrite_goals_tac etc.;
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parents:
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diff
changeset
|
205 |
rewrite_goals_tac ctxt @{thms skolem_def [abs_def]} |
59632 | 206 |
THEN resolve_tac ctxt |
207 |
[(prem |> rewrite_rule ctxt @{thms skolem_def [abs_def]}) |
|
208 |
RS Global_Theory.get_thm (Proof_Context.theory_of ctxt) "Hilbert_Choice.someI_ex"] 1 |
|
37617
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blanchet
parents:
37616
diff
changeset
|
209 |
in |
54883
dd04a8b654fc
proper context for norm_hhf and derived operations;
wenzelm
parents:
54742
diff
changeset
|
210 |
Goal.prove_internal ctxt [ex_tm] conc tacf |
37629 | 211 |
|> forall_intr_list frees |
212 |
|> Thm.forall_elim_vars 0 (*Introduce Vars, but don't discharge defs.*) |
|
213 |
|> Thm.varifyT_global |
|
37617
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parents:
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changeset
|
214 |
end |
24742
73b8b42a36b6
removal of some "ref"s from res_axioms.ML; a side-effect is that the ordering
paulson
parents:
24669
diff
changeset
|
215 |
|
42335 | 216 |
fun to_definitional_cnf_with_quantifiers ctxt th = |
39036
dff91b90d74c
use definitional CNFs in Metis rather than plain CNF, following a suggestion by Joe Hurd;
blanchet
parents:
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diff
changeset
|
217 |
let |
59582 | 218 |
val eqth = CNF.make_cnfx_thm ctxt (HOLogic.dest_Trueprop (Thm.prop_of th)) |
39036
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blanchet
parents:
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diff
changeset
|
219 |
val eqth = eqth RS @{thm eq_reflection} |
dff91b90d74c
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blanchet
parents:
38864
diff
changeset
|
220 |
val eqth = eqth RS @{thm TruepropI} |
dff91b90d74c
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blanchet
parents:
38864
diff
changeset
|
221 |
in Thm.equal_elim eqth th end |
dff91b90d74c
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blanchet
parents:
38864
diff
changeset
|
222 |
|
39932
acde1b606b0e
reverted 0bfaaa81fc62, since "Thm.rename_boundvars" can't be relied upon to give unique names to bound variables
blanchet
parents:
39931
diff
changeset
|
223 |
fun zapped_var_name ((ax_no, cluster_no), skolem) index_no s = |
39896
13b3a2ba9ea7
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blanchet
parents:
39894
diff
changeset
|
224 |
(if skolem then new_skolem_var_prefix else new_nonskolem_var_prefix) ^ |
39932
acde1b606b0e
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blanchet
parents:
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diff
changeset
|
225 |
"_" ^ string_of_int ax_no ^ "_" ^ string_of_int cluster_no ^ "_" ^ |
56811 | 226 |
string_of_int index_no ^ "_" ^ Name.desymbolize (SOME false) s |
39896
13b3a2ba9ea7
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blanchet
parents:
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diff
changeset
|
227 |
|
39899
608b108ec979
compute quantifier dependency graph in new skolemizer
blanchet
parents:
39897
diff
changeset
|
228 |
fun cluster_of_zapped_var_name s = |
39932
acde1b606b0e
reverted 0bfaaa81fc62, since "Thm.rename_boundvars" can't be relied upon to give unique names to bound variables
blanchet
parents:
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diff
changeset
|
229 |
let val get_int = the o Int.fromString o nth (space_explode "_" s) in |
acde1b606b0e
reverted 0bfaaa81fc62, since "Thm.rename_boundvars" can't be relied upon to give unique names to bound variables
blanchet
parents:
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diff
changeset
|
230 |
((get_int 1, (get_int 2, get_int 3)), |
acde1b606b0e
reverted 0bfaaa81fc62, since "Thm.rename_boundvars" can't be relied upon to give unique names to bound variables
blanchet
parents:
39931
diff
changeset
|
231 |
String.isPrefix new_skolem_var_prefix s) |
acde1b606b0e
reverted 0bfaaa81fc62, since "Thm.rename_boundvars" can't be relied upon to give unique names to bound variables
blanchet
parents:
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diff
changeset
|
232 |
end |
39897 | 233 |
|
40260
73ecbe2d432b
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blanchet
parents:
39962
diff
changeset
|
234 |
fun rename_bound_vars_to_be_zapped ax_no = |
73ecbe2d432b
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blanchet
parents:
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diff
changeset
|
235 |
let |
73ecbe2d432b
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blanchet
parents:
39962
diff
changeset
|
236 |
fun aux (cluster as (cluster_no, cluster_skolem)) index_no pos t = |
73ecbe2d432b
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blanchet
parents:
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diff
changeset
|
237 |
case t of |
73ecbe2d432b
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blanchet
parents:
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diff
changeset
|
238 |
(t1 as Const (s, _)) $ Abs (s', T, t') => |
67149 | 239 |
if s = \<^const_name>\<open>Pure.all\<close> orelse s = \<^const_name>\<open>All\<close> orelse |
240 |
s = \<^const_name>\<open>Ex\<close> then |
|
39932
acde1b606b0e
reverted 0bfaaa81fc62, since "Thm.rename_boundvars" can't be relied upon to give unique names to bound variables
blanchet
parents:
39931
diff
changeset
|
241 |
let |
67149 | 242 |
val skolem = (pos = (s = \<^const_name>\<open>Ex\<close>)) |
39932
acde1b606b0e
reverted 0bfaaa81fc62, since "Thm.rename_boundvars" can't be relied upon to give unique names to bound variables
blanchet
parents:
39931
diff
changeset
|
243 |
val (cluster, index_no) = |
acde1b606b0e
reverted 0bfaaa81fc62, since "Thm.rename_boundvars" can't be relied upon to give unique names to bound variables
blanchet
parents:
39931
diff
changeset
|
244 |
if skolem = cluster_skolem then (cluster, index_no) |
acde1b606b0e
reverted 0bfaaa81fc62, since "Thm.rename_boundvars" can't be relied upon to give unique names to bound variables
blanchet
parents:
39931
diff
changeset
|
245 |
else ((cluster_no ||> cluster_skolem ? Integer.add 1, skolem), 0) |
40260
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
246 |
val s' = zapped_var_name cluster index_no s' |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
247 |
in t1 $ Abs (s', T, aux cluster (index_no + 1) pos t') end |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
248 |
else |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
249 |
t |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
250 |
| (t1 as Const (s, _)) $ t2 $ t3 => |
67149 | 251 |
if s = \<^const_name>\<open>Pure.imp\<close> orelse s = \<^const_name>\<open>HOL.implies\<close> then |
40260
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
252 |
t1 $ aux cluster index_no (not pos) t2 $ aux cluster index_no pos t3 |
67149 | 253 |
else if s = \<^const_name>\<open>HOL.conj\<close> orelse |
254 |
s = \<^const_name>\<open>HOL.disj\<close> then |
|
40260
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
255 |
t1 $ aux cluster index_no pos t2 $ aux cluster index_no pos t3 |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
256 |
else |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
257 |
t |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
258 |
| (t1 as Const (s, _)) $ t2 => |
67149 | 259 |
if s = \<^const_name>\<open>Trueprop\<close> then |
40260
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
260 |
t1 $ aux cluster index_no pos t2 |
67149 | 261 |
else if s = \<^const_name>\<open>Not\<close> then |
40260
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
262 |
t1 $ aux cluster index_no (not pos) t2 |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
263 |
else |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
264 |
t |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
265 |
| _ => t |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
266 |
in aux ((ax_no, 0), true) 0 true end |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
267 |
|
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
268 |
fun zap pos ct = |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
269 |
ct |
59582 | 270 |
|> (case Thm.term_of ct of |
40260
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
271 |
Const (s, _) $ Abs (s', _, _) => |
67149 | 272 |
if s = \<^const_name>\<open>Pure.all\<close> orelse s = \<^const_name>\<open>All\<close> orelse |
273 |
s = \<^const_name>\<open>Ex\<close> then |
|
40260
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
274 |
Thm.dest_comb #> snd #> Thm.dest_abs (SOME s') #> snd #> zap pos |
39906 | 275 |
else |
276 |
Conv.all_conv |
|
277 |
| Const (s, _) $ _ $ _ => |
|
67149 | 278 |
if s = \<^const_name>\<open>Pure.imp\<close> orelse s = \<^const_name>\<open>implies\<close> then |
40260
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
279 |
Conv.combination_conv (Conv.arg_conv (zap (not pos))) (zap pos) |
67149 | 280 |
else if s = \<^const_name>\<open>conj\<close> orelse s = \<^const_name>\<open>disj\<close> then |
40260
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
281 |
Conv.combination_conv (Conv.arg_conv (zap pos)) (zap pos) |
39906 | 282 |
else |
283 |
Conv.all_conv |
|
284 |
| Const (s, _) $ _ => |
|
67149 | 285 |
if s = \<^const_name>\<open>Trueprop\<close> then Conv.arg_conv (zap pos) |
286 |
else if s = \<^const_name>\<open>Not\<close> then Conv.arg_conv (zap (not pos)) |
|
40260
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
287 |
else Conv.all_conv |
39906 | 288 |
| _ => Conv.all_conv) |
39887
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
289 |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
50705
diff
changeset
|
290 |
fun ss_only ths ctxt = clear_simpset (put_simpset HOL_basic_ss ctxt) addsimps ths |
39901
75d792edf634
make "cnf_axiom" work (after a fashion) in the absence of the axiom of choice
blanchet
parents:
39900
diff
changeset
|
291 |
|
40261
7a02144874f3
more work on new Skolemizer without Hilbert_Choice
blanchet
parents:
40260
diff
changeset
|
292 |
val cheat_choice = |
67149 | 293 |
\<^prop>\<open>\<forall>x. \<exists>y. Q x y \<Longrightarrow> \<exists>f. \<forall>x. Q x (f x)\<close> |
39901
75d792edf634
make "cnf_axiom" work (after a fashion) in the absence of the axiom of choice
blanchet
parents:
39900
diff
changeset
|
294 |
|> Logic.varify_global |
69593 | 295 |
|> Skip_Proof.make_thm \<^theory> |
39887
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
296 |
|
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
297 |
(* Converts an Isabelle theorem into NNF. *) |
50705
0e943b33d907
use new skolemizer for reconstructing skolemization steps in Isar proofs (because the old skolemizer messes up the order of the Skolem arguments)
blanchet
parents:
47954
diff
changeset
|
298 |
fun nnf_axiom choice_ths new_skolem ax_no th ctxt = |
39887
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
299 |
let |
42361 | 300 |
val thy = Proof_Context.theory_of ctxt |
39887
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
301 |
val th = |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
302 |
th |> transform_elim_theorem |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
303 |
|> zero_var_indexes |
50705
0e943b33d907
use new skolemizer for reconstructing skolemization steps in Isar proofs (because the old skolemizer messes up the order of the Skolem arguments)
blanchet
parents:
47954
diff
changeset
|
304 |
|> new_skolem ? forall_intr_vars |
39887
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
305 |
val (th, ctxt) = Variable.import true [th] ctxt |>> snd |>> the_single |
54742
7a86358a3c0b
proper context for basic Simplifier operations: rewrite_rule, rewrite_goals_rule, rewrite_goals_tac etc.;
wenzelm
parents:
52031
diff
changeset
|
306 |
val th = th |> Conv.fconv_rule (Object_Logic.atomize ctxt) |
70507 | 307 |
|> Meson.cong_extensionalize_thm ctxt |
308 |
|> Meson.abs_extensionalize_thm ctxt |
|
309 |
|> Meson.make_nnf ctxt |
|
39887
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
310 |
in |
50705
0e943b33d907
use new skolemizer for reconstructing skolemization steps in Isar proofs (because the old skolemizer messes up the order of the Skolem arguments)
blanchet
parents:
47954
diff
changeset
|
311 |
if new_skolem then |
39887
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
312 |
let |
39901
75d792edf634
make "cnf_axiom" work (after a fashion) in the absence of the axiom of choice
blanchet
parents:
39900
diff
changeset
|
313 |
fun skolemize choice_ths = |
70507 | 314 |
Meson.skolemize_with_choice_theorems ctxt choice_ths |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
50705
diff
changeset
|
315 |
#> simplify (ss_only @{thms all_simps[symmetric]} ctxt) |
42347
53e444ecb525
properly implemented definitional CNF for the new Skolemizer (and moved the code for the old Skolemizer -- tuning), removing big chunks for experimental/debugging code
blanchet
parents:
42336
diff
changeset
|
316 |
val no_choice = null choice_ths |
39901
75d792edf634
make "cnf_axiom" work (after a fashion) in the absence of the axiom of choice
blanchet
parents:
39900
diff
changeset
|
317 |
val pull_out = |
42347
53e444ecb525
properly implemented definitional CNF for the new Skolemizer (and moved the code for the old Skolemizer -- tuning), removing big chunks for experimental/debugging code
blanchet
parents:
42336
diff
changeset
|
318 |
if no_choice then |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
50705
diff
changeset
|
319 |
simplify (ss_only @{thms all_simps[symmetric] ex_simps[symmetric]} ctxt) |
42347
53e444ecb525
properly implemented definitional CNF for the new Skolemizer (and moved the code for the old Skolemizer -- tuning), removing big chunks for experimental/debugging code
blanchet
parents:
42336
diff
changeset
|
320 |
else |
53e444ecb525
properly implemented definitional CNF for the new Skolemizer (and moved the code for the old Skolemizer -- tuning), removing big chunks for experimental/debugging code
blanchet
parents:
42336
diff
changeset
|
321 |
skolemize choice_ths |
53e444ecb525
properly implemented definitional CNF for the new Skolemizer (and moved the code for the old Skolemizer -- tuning), removing big chunks for experimental/debugging code
blanchet
parents:
42336
diff
changeset
|
322 |
val discharger_th = th |> pull_out |
40260
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
323 |
val discharger_th = |
70507 | 324 |
discharger_th |> Meson.has_too_many_clauses ctxt (Thm.concl_of discharger_th) |
42347
53e444ecb525
properly implemented definitional CNF for the new Skolemizer (and moved the code for the old Skolemizer -- tuning), removing big chunks for experimental/debugging code
blanchet
parents:
42336
diff
changeset
|
325 |
? (to_definitional_cnf_with_quantifiers ctxt |
53e444ecb525
properly implemented definitional CNF for the new Skolemizer (and moved the code for the old Skolemizer -- tuning), removing big chunks for experimental/debugging code
blanchet
parents:
42336
diff
changeset
|
326 |
#> pull_out) |
42099
447fa058ab22
avoid evil "export_without_context", which breaks if there are local "fixes"
blanchet
parents:
42098
diff
changeset
|
327 |
val zapped_th = |
59582 | 328 |
discharger_th |> Thm.prop_of |> rename_bound_vars_to_be_zapped ax_no |
40263 | 329 |
|> (if no_choice then |
59582 | 330 |
Skip_Proof.make_thm thy #> skolemize [cheat_choice] #> Thm.cprop_of |
40263 | 331 |
else |
59632 | 332 |
Thm.cterm_of ctxt) |
42099
447fa058ab22
avoid evil "export_without_context", which breaks if there are local "fixes"
blanchet
parents:
42098
diff
changeset
|
333 |
|> zap true |
447fa058ab22
avoid evil "export_without_context", which breaks if there are local "fixes"
blanchet
parents:
42098
diff
changeset
|
334 |
val fixes = |
59582 | 335 |
[] |> Term.add_free_names (Thm.prop_of zapped_th) |
42335 | 336 |
|> filter is_zapped_var_name |
42269 | 337 |
val ctxt' = ctxt |> Variable.add_fixes_direct fixes |
42099
447fa058ab22
avoid evil "export_without_context", which breaks if there are local "fixes"
blanchet
parents:
42098
diff
changeset
|
338 |
val fully_skolemized_t = |
42333 | 339 |
zapped_th |> singleton (Variable.export ctxt' ctxt) |
59582 | 340 |
|> Thm.cprop_of |> Thm.dest_equals |> snd |> Thm.term_of |
39887
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
341 |
in |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
342 |
if exists_subterm (fn Var ((s, _), _) => |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
343 |
String.isPrefix new_skolem_var_prefix s |
40260
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
344 |
| _ => false) fully_skolemized_t then |
39887
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
345 |
let |
40260
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
346 |
val (fully_skolemized_ct, ctxt) = |
70326 | 347 |
yield_singleton (Variable.import_terms true) fully_skolemized_t ctxt |
348 |
|>> Thm.cterm_of ctxt |
|
40260
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
349 |
in |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
350 |
(SOME (discharger_th, fully_skolemized_ct), |
40262
8403085384eb
ensure that MESON correctly preserves the name of variables (needed by the new Skolemizer)
blanchet
parents:
40261
diff
changeset
|
351 |
(Thm.assume fully_skolemized_ct, ctxt)) |
40260
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
352 |
end |
39887
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
353 |
else |
40262
8403085384eb
ensure that MESON correctly preserves the name of variables (needed by the new Skolemizer)
blanchet
parents:
40261
diff
changeset
|
354 |
(NONE, (th, ctxt)) |
39887
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
355 |
end |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
356 |
else |
70507 | 357 |
(NONE, (th |> Meson.has_too_many_clauses ctxt (Thm.concl_of th) |
42347
53e444ecb525
properly implemented definitional CNF for the new Skolemizer (and moved the code for the old Skolemizer -- tuning), removing big chunks for experimental/debugging code
blanchet
parents:
42336
diff
changeset
|
358 |
? to_definitional_cnf_with_quantifiers ctxt, ctxt)) |
39887
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
359 |
end |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
360 |
|
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
361 |
(* Convert a theorem to CNF, with additional premises due to skolemization. *) |
50705
0e943b33d907
use new skolemizer for reconstructing skolemization steps in Isar proofs (because the old skolemizer messes up the order of the Skolem arguments)
blanchet
parents:
47954
diff
changeset
|
362 |
fun cnf_axiom ctxt0 new_skolem combinators ax_no th = |
37626
1146291fe718
move blacklisting completely out of the clausifier;
blanchet
parents:
37620
diff
changeset
|
363 |
let |
70507 | 364 |
val choice_ths = Meson.choice_theorems (Proof_Context.theory_of ctxt0) |
70320
59258a3192bf
misc tuning and clarification, notably wrt. flow of context;
wenzelm
parents:
70159
diff
changeset
|
365 |
val (opt, (nnf_th, ctxt1)) = |
50705
0e943b33d907
use new skolemizer for reconstructing skolemization steps in Isar proofs (because the old skolemizer messes up the order of the Skolem arguments)
blanchet
parents:
47954
diff
changeset
|
366 |
nnf_axiom choice_ths new_skolem ax_no th ctxt0 |
39894
35ae5cf8c96a
encode number of skolem assumptions in them, for more efficient retrieval later
blanchet
parents:
39891
diff
changeset
|
367 |
fun clausify th = |
70507 | 368 |
Meson.make_cnf |
59165 | 369 |
(if new_skolem orelse null choice_ths then [] |
70320
59258a3192bf
misc tuning and clarification, notably wrt. flow of context;
wenzelm
parents:
70159
diff
changeset
|
370 |
else map (old_skolem_theorem_of_def ctxt1) (old_skolem_defs th)) |
59258a3192bf
misc tuning and clarification, notably wrt. flow of context;
wenzelm
parents:
70159
diff
changeset
|
371 |
th ctxt1 |
59258a3192bf
misc tuning and clarification, notably wrt. flow of context;
wenzelm
parents:
70159
diff
changeset
|
372 |
val (cnf_ths, ctxt2) = clausify nnf_th |
39894
35ae5cf8c96a
encode number of skolem assumptions in them, for more efficient retrieval later
blanchet
parents:
39891
diff
changeset
|
373 |
fun intr_imp ct th = |
70320
59258a3192bf
misc tuning and clarification, notably wrt. flow of context;
wenzelm
parents:
70159
diff
changeset
|
374 |
Thm.instantiate ([], [((("i", 0), \<^typ>\<open>nat\<close>), Thm.cterm_of ctxt2 (HOLogic.mk_nat ax_no))]) |
39962
d42ddd7407ca
qualify "Meson." and "Metis." constants so that the ML files can be reloaded later (e.g. for testing/development)
blanchet
parents:
39950
diff
changeset
|
375 |
(zero_var_indexes @{thm skolem_COMBK_D}) |
39894
35ae5cf8c96a
encode number of skolem assumptions in them, for more efficient retrieval later
blanchet
parents:
39891
diff
changeset
|
376 |
RS Thm.implies_intr ct th |
37626
1146291fe718
move blacklisting completely out of the clausifier;
blanchet
parents:
37620
diff
changeset
|
377 |
in |
70320
59258a3192bf
misc tuning and clarification, notably wrt. flow of context;
wenzelm
parents:
70159
diff
changeset
|
378 |
(opt |> Option.map (I #>> singleton (Variable.export ctxt2 ctxt0) |
59582 | 379 |
##> (Thm.term_of #> HOLogic.dest_Trueprop |
70320
59258a3192bf
misc tuning and clarification, notably wrt. flow of context;
wenzelm
parents:
70159
diff
changeset
|
380 |
#> singleton (Variable.export_terms ctxt2 ctxt0))), |
59258a3192bf
misc tuning and clarification, notably wrt. flow of context;
wenzelm
parents:
70159
diff
changeset
|
381 |
cnf_ths |> map (combinators ? introduce_combinators_in_theorem ctxt2 |
39894
35ae5cf8c96a
encode number of skolem assumptions in them, for more efficient retrieval later
blanchet
parents:
39891
diff
changeset
|
382 |
#> (case opt of SOME (_, ct) => intr_imp ct | NONE => I)) |
70320
59258a3192bf
misc tuning and clarification, notably wrt. flow of context;
wenzelm
parents:
70159
diff
changeset
|
383 |
|> Variable.export ctxt2 ctxt0 |
70507 | 384 |
|> Meson.finish_cnf |
70494 | 385 |
|> map (Thm.close_derivation \<^here>)) |
37626
1146291fe718
move blacklisting completely out of the clausifier;
blanchet
parents:
37620
diff
changeset
|
386 |
end |
39887
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
387 |
handle THM _ => (NONE, []) |
27184 | 388 |
|
20461
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset
|
389 |
end; |