author | blanchet |
Tue, 05 Oct 2010 10:30:50 +0200 | |
changeset 39949 | 186a3b447e0b |
parent 39948 | 317010af8972 |
child 39950 | f3c4849868b8 |
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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support readable names even when Isar proof reconstruction is enabled -- useful for debugging
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Author: Jasmin Blanchette, TU Muenchen |
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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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treat "using X by metis" (more or less) the same as "by (metis X)"
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val extensionalize_theorem : thm -> thm |
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val introduce_combinators_in_cterm : cterm -> thm |
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val introduce_combinators_in_theorem : thm -> thm |
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Let MESON take an additional "preskolemization tactic", which can be used to put the goal in definitional CNF
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val to_definitional_cnf_with_quantifiers : theory -> thm -> thm |
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reverted 0bfaaa81fc62, since "Thm.rename_boundvars" can't be relied upon to give unique names to bound variables
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val cluster_of_zapped_var_name : string -> (int * (int * int)) * bool |
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val cnf_axiom : |
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make "cnf_axiom" work (after a fashion) in the absence of the axiom of choice
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Proof.context -> bool -> int -> thm -> (thm * term) option * thm list |
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end; |
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structure Meson_Clausify : MESON_CLAUSIFY = |
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struct |
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|
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compute quantifier dependency graph in new skolemizer
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(* the extra "?" helps prevent clashes *) |
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val new_skolem_var_prefix = "?SK" |
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compute quantifier dependency graph in new skolemizer
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val new_nonskolem_var_prefix = "?V" |
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(**** Transformation of Elimination Rules into First-Order Formulas****) |
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val cfalse = cterm_of @{theory HOL} HOLogic.false_const; |
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val ctp_false = cterm_of @{theory HOL} (HOLogic.mk_Trueprop HOLogic.false_const); |
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skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
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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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the conclusion variable to False. (Cf. "transform_elim_term" 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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New transformation of eliminatino rules: we simply replace the final conclusion variable by False
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case concl_of th of (*conclusion variable*) |
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@{const Trueprop} $ (v as Var (_, @{typ bool})) => |
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Thm.instantiate ([], [(cterm_of @{theory HOL} v, cfalse)]) th |
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| v as Var(_, @{typ prop}) => |
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Thm.instantiate ([], [(cterm_of @{theory HOL} v, ctp_false)]) th |
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| _ => th |
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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 skolem}, T --> T) $ t |
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end |
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adjusted the polymorphism handling of Skolem constants so that proof reconstruction doesn't fail in "equality_inf"
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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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Skolemization by inference, but not quite finished
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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 Ex}, _) $ (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 = OldTerm.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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thread original theorem along with CNF theorem, as a step toward killing the Skolem cache
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val rhs = |
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thread original theorem along with CNF theorem, as a step toward killing the Skolem cache
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list_abs_free (map 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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use Skolem inlining also in the nonpolymorphic case, as a step toward simplifying the source code
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val comb = list_comb (rhs, args) |
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always perform "inline" skolemization, polymorphism or not, Skolem cache or not
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in dec_sko (subst_bound (comb, p)) (rhs :: rhss) end |
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always perform "inline" skolemization, polymorphism or not, Skolem cache or not
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| dec_sko (Const (@{const_name All},_) $ 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 = Name.variant (OldTerm.add_term_names (p,[])) a |
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always perform "inline" skolemization, polymorphism or not, Skolem cache or not
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in dec_sko (subst_bound (Free(fname,T), p)) rhss end |
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| dec_sko (@{const conj} $ p $ q) rhss = rhss |> dec_sko p |> dec_sko q |
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| dec_sko (@{const disj} $ p $ q) rhss = rhss |> dec_sko p |> dec_sko q |
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| dec_sko (@{const Trueprop} $ p) rhss = dec_sko p rhss |
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| dec_sko _ rhss = rhss |
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in dec_sko (prop_of th) [] end; |
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||
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(**** REPLACING ABSTRACTIONS BY COMBINATORS ****) |
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|
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renamed lemmas: ext_iff -> fun_eq_iff, set_ext_iff -> set_eq_iff, set_ext -> set_eqI
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val fun_cong_all = @{thm fun_eq_iff [THEN iffD1]} |
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(* Removes the lambdas from an equation of the form "t = (%x. u)". |
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beta eta contract the Sledgehammer conjecture (and also the axioms, although this might not be needed), just like Metis does (implicitly);
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(Cf. "extensionalize_term" in "Sledgehammer_Translate".) *) |
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added extensionalization to Sledgehammer, mimicking what the Clausifier used to do
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fun extensionalize_theorem th = |
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better eta-expansion in Sledgehammer's clausification;
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case prop_of th of |
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formerly unnamed infix equality now named HOL.eq
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_ $ (Const (@{const_name HOL.eq}, Type (_, [Type (@{type_name fun}, _), _])) |
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$ _ $ Abs _) => extensionalize_theorem (th RS fun_cong_all) |
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| _ => th |
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|
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fun is_quasi_lambda_free (Const (@{const_name skolem}, _) $ _) = 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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no point in introducing combinators for inlined Skolem functions
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| is_quasi_lambda_free _ = true |
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val [f_B,g_B] = map (cterm_of @{theory}) (OldTerm.term_vars (prop_of @{thm abs_B})); |
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val [g_C,f_C] = map (cterm_of @{theory}) (OldTerm.term_vars (prop_of @{thm abs_C})); |
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val [f_S,g_S] = map (cterm_of @{theory}) (OldTerm.term_vars (prop_of @{thm abs_S})); |
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101 |
|
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move Sledgehammer's HOL -> FOL translation to separate file (sledgehammer_translate.ML)
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(* FIXME: Requires more use of cterm constructors. *) |
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fun abstract ct = |
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let |
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val thy = theory_of_cterm ct |
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Catch exceptions arising during the abstraction operation.
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val Abs(x,_,body) = term_of ct |
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val Type(@{type_name fun}, [xT,bodyT]) = typ_of (ctyp_of_term ct) |
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val cxT = ctyp_of thy xT |
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val cbodyT = ctyp_of thy bodyT |
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fun makeK () = |
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instantiate' [SOME cxT, SOME cbodyT] [SOME (cterm_of thy body)] |
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prevent schematic variable clash in combinator-introduction code, when invoked from Sledgehammer (another consequence of the CNF -> FOF transition)
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112 |
@{thm abs_K} |
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in |
114 |
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 => instantiate' [SOME cxT] [] @{thm abs_I} (*identity: I*) |
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| rator$rand => |
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if loose_bvar1 (rator,0) then (*C or S*) |
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if loose_bvar1 (rand,0) then (*S*) |
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let val crator = cterm_of thy (Abs(x,xT,rator)) |
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val crand = cterm_of thy (Abs(x,xT,rand)) |
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val abs_S' = cterm_instantiate [(f_S,crator),(g_S,crand)] @{thm abs_S} |
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val (_,rhs) = Thm.dest_equals (cprop_of abs_S') |
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126 |
in |
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Thm.transitive abs_S' (Conv.binop_conv abstract rhs) |
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128 |
end |
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else (*C*) |
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let val crator = cterm_of thy (Abs(x,xT,rator)) |
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val abs_C' = cterm_instantiate [(f_C,crator),(g_C,cterm_of thy rand)] @{thm abs_C} |
132 |
val (_,rhs) = Thm.dest_equals (cprop_of abs_C') |
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in |
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Thm.transitive abs_C' (Conv.fun_conv (Conv.arg_conv abstract) rhs) |
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135 |
end |
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else if loose_bvar1 (rand,0) 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 crand = cterm_of thy (Abs(x,xT,rand)) |
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val crator = cterm_of thy rator |
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val abs_B' = cterm_instantiate [(f_B,crator),(g_B,crand)] @{thm abs_B} |
142 |
val (_,rhs) = Thm.dest_equals (cprop_of abs_B') |
|
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in Thm.transitive abs_B' (Conv.arg_conv abstract rhs) end |
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else makeK() |
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| _ => raise Fail "abstract: Bad term" |
24827 | 146 |
end; |
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improvements to abstraction, ensuring more re-use of abstraction functions
paulson
parents:
20789
diff
changeset
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147 |
|
37349 | 148 |
(* Traverse a theorem, remplacing lambda-abstractions with combinators. *) |
38001
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reintroduced more preprocessing steps to Sledgehammer, adapted to the new FOF setting
blanchet
parents:
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diff
changeset
|
149 |
fun introduce_combinators_in_cterm ct = |
37416
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no point in introducing combinators for inlined Skolem functions
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if is_quasi_lambda_free (term_of ct) then |
37349 | 151 |
Thm.reflexive ct |
152 |
else case term_of ct of |
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153 |
Abs _ => |
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154 |
let |
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155 |
val (cv, cta) = Thm.dest_abs NONE ct |
|
156 |
val (v, _) = dest_Free (term_of cv) |
|
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|
157 |
val u_th = introduce_combinators_in_cterm cta |
37349 | 158 |
val cu = Thm.rhs_of u_th |
159 |
val comb_eq = abstract (Thm.cabs cv cu) |
|
160 |
in Thm.transitive (Thm.abstract_rule v cv u_th) comb_eq end |
|
161 |
| _ $ _ => |
|
162 |
let val (ct1, ct2) = Thm.dest_comb ct in |
|
38001
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reintroduced more preprocessing steps to Sledgehammer, adapted to the new FOF setting
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parents:
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diff
changeset
|
163 |
Thm.combination (introduce_combinators_in_cterm ct1) |
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parents:
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diff
changeset
|
164 |
(introduce_combinators_in_cterm ct2) |
37349 | 165 |
end |
166 |
||
38001
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parents:
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diff
changeset
|
167 |
fun introduce_combinators_in_theorem th = |
37416
d5ac8280497e
no point in introducing combinators for inlined Skolem functions
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parents:
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diff
changeset
|
168 |
if is_quasi_lambda_free (prop_of th) then |
37349 | 169 |
th |
24827 | 170 |
else |
37349 | 171 |
let |
172 |
val th = Drule.eta_contraction_rule th |
|
38001
a9b47b85ca24
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blanchet
parents:
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diff
changeset
|
173 |
val eqth = introduce_combinators_in_cterm (cprop_of th) |
37349 | 174 |
in Thm.equal_elim eqth th end |
175 |
handle THM (msg, _, _) => |
|
176 |
(warning ("Error in the combinator translation of " ^ |
|
177 |
Display.string_of_thm_without_context th ^ |
|
178 |
"\nException message: " ^ msg ^ "."); |
|
179 |
(* A type variable of sort "{}" will make abstraction fail. *) |
|
180 |
TrueI) |
|
16009 | 181 |
|
182 |
(*cterms are used throughout for efficiency*) |
|
38280 | 183 |
val cTrueprop = cterm_of @{theory HOL} HOLogic.Trueprop; |
16009 | 184 |
|
185 |
(*Given an abstraction over n variables, replace the bound variables by free |
|
186 |
ones. Return the body, along with the list of free variables.*) |
|
20461
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
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diff
changeset
|
187 |
fun c_variant_abs_multi (ct0, vars) = |
16009 | 188 |
let val (cv,ct) = Thm.dest_abs NONE ct0 |
189 |
in c_variant_abs_multi (ct, cv::vars) end |
|
190 |
handle CTERM _ => (ct0, rev vars); |
|
191 |
||
39355 | 192 |
val skolem_def_raw = @{thms skolem_def_raw} |
37617
f73cd4069f69
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blanchet
parents:
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diff
changeset
|
193 |
|
f73cd4069f69
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blanchet
parents:
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diff
changeset
|
194 |
(* Given the definition of a Skolem function, return a theorem to replace |
f73cd4069f69
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blanchet
parents:
37616
diff
changeset
|
195 |
an existential formula by a use of that function. |
18141
89e2e8bed08f
Skolemization by inference, but not quite finished
paulson
parents:
18009
diff
changeset
|
196 |
Example: "EX x. x : A & x ~: B ==> sko A B : A & sko A B ~: B" [.] *) |
39886
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first step towards a new skolemizer that doesn't require "Eps"
blanchet
parents:
39721
diff
changeset
|
197 |
fun old_skolem_theorem_from_def thy rhs0 = |
37399
34f080a12063
proper polymorphic Skolemization of uncached facts + synchronization of caching and relevance filter
blanchet
parents:
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diff
changeset
|
198 |
let |
38280 | 199 |
val rhs = rhs0 |> Type.legacy_freeze_thaw |> #1 |> cterm_of thy |
37617
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blanchet
parents:
37616
diff
changeset
|
200 |
val rhs' = rhs |> Thm.dest_comb |> snd |
f73cd4069f69
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blanchet
parents:
37616
diff
changeset
|
201 |
val (ch, frees) = c_variant_abs_multi (rhs', []) |
f73cd4069f69
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blanchet
parents:
37616
diff
changeset
|
202 |
val (hilbert, cabs) = ch |> Thm.dest_comb |>> term_of |
f73cd4069f69
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blanchet
parents:
37616
diff
changeset
|
203 |
val T = |
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
204 |
case hilbert of |
39941 | 205 |
Const (_, Type (@{type_name fun}, [_, T])) => T |
39886
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first step towards a new skolemizer that doesn't require "Eps"
blanchet
parents:
39721
diff
changeset
|
206 |
| _ => raise TERM ("old_skolem_theorem_from_def: expected \"Eps\"", |
8a9f0c97d550
first step towards a new skolemizer that doesn't require "Eps"
blanchet
parents:
39721
diff
changeset
|
207 |
[hilbert]) |
38280 | 208 |
val cex = cterm_of thy (HOLogic.exists_const T) |
37617
f73cd4069f69
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blanchet
parents:
37616
diff
changeset
|
209 |
val ex_tm = Thm.capply cTrueprop (Thm.capply cex cabs) |
37629 | 210 |
val conc = |
37617
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
211 |
Drule.list_comb (rhs, frees) |
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
212 |
|> Drule.beta_conv cabs |> Thm.capply cTrueprop |
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
213 |
fun tacf [prem] = |
39355 | 214 |
rewrite_goals_tac skolem_def_raw |
39941 | 215 |
THEN rtac ((prem |> rewrite_rule skolem_def_raw) |
39949 | 216 |
RS Global_Theory.get_thm thy "Hilbert_Choice.someI_ex") 1 |
37617
f73cd4069f69
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blanchet
parents:
37616
diff
changeset
|
217 |
in |
37629 | 218 |
Goal.prove_internal [ex_tm] conc tacf |
219 |
|> forall_intr_list frees |
|
220 |
|> Thm.forall_elim_vars 0 (*Introduce Vars, but don't discharge defs.*) |
|
221 |
|> Thm.varifyT_global |
|
37617
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
222 |
end |
24742
73b8b42a36b6
removal of some "ref"s from res_axioms.ML; a side-effect is that the ordering
paulson
parents:
24669
diff
changeset
|
223 |
|
39036
dff91b90d74c
use definitional CNFs in Metis rather than plain CNF, following a suggestion by Joe Hurd;
blanchet
parents:
38864
diff
changeset
|
224 |
fun to_definitional_cnf_with_quantifiers thy th = |
dff91b90d74c
use definitional CNFs in Metis rather than plain CNF, following a suggestion by Joe Hurd;
blanchet
parents:
38864
diff
changeset
|
225 |
let |
dff91b90d74c
use definitional CNFs in Metis rather than plain CNF, following a suggestion by Joe Hurd;
blanchet
parents:
38864
diff
changeset
|
226 |
val eqth = cnf.make_cnfx_thm thy (HOLogic.dest_Trueprop (prop_of th)) |
dff91b90d74c
use definitional CNFs in Metis rather than plain CNF, following a suggestion by Joe Hurd;
blanchet
parents:
38864
diff
changeset
|
227 |
val eqth = eqth RS @{thm eq_reflection} |
dff91b90d74c
use definitional CNFs in Metis rather than plain CNF, following a suggestion by Joe Hurd;
blanchet
parents:
38864
diff
changeset
|
228 |
val eqth = eqth RS @{thm TruepropI} |
dff91b90d74c
use definitional CNFs in Metis rather than plain CNF, following a suggestion by Joe Hurd;
blanchet
parents:
38864
diff
changeset
|
229 |
in Thm.equal_elim eqth th end |
dff91b90d74c
use definitional CNFs in Metis rather than plain CNF, following a suggestion by Joe Hurd;
blanchet
parents:
38864
diff
changeset
|
230 |
|
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
|
231 |
fun zapped_var_name ((ax_no, cluster_no), skolem) index_no s = |
39896
13b3a2ba9ea7
encode axiom number and cluster number in all zapped quantifiers to help discharging new skolemizer assumptions
blanchet
parents:
39894
diff
changeset
|
232 |
(if skolem then new_skolem_var_prefix else new_nonskolem_var_prefix) ^ |
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
|
233 |
"_" ^ string_of_int ax_no ^ "_" ^ string_of_int cluster_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
|
234 |
string_of_int index_no ^ "_" ^ s |
39896
13b3a2ba9ea7
encode axiom number and cluster number in all zapped quantifiers to help discharging new skolemizer assumptions
blanchet
parents:
39894
diff
changeset
|
235 |
|
39899
608b108ec979
compute quantifier dependency graph in new skolemizer
blanchet
parents:
39897
diff
changeset
|
236 |
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:
39931
diff
changeset
|
237 |
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:
39931
diff
changeset
|
238 |
((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
|
239 |
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:
39931
diff
changeset
|
240 |
end |
39897 | 241 |
|
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
|
242 |
fun zap (cluster as (cluster_no, cluster_skolem)) index_no pos ct = |
39906 | 243 |
ct |
244 |
|> (case term_of ct of |
|
245 |
Const (s, _) $ Abs (s', _, _) => |
|
246 |
if s = @{const_name all} orelse s = @{const_name All} orelse |
|
247 |
s = @{const_name Ex} 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
|
248 |
let |
acde1b606b0e
reverted 0bfaaa81fc62, since "Thm.rename_boundvars" can't be relied upon to give unique names to bound variables
blanchet
parents:
39931
diff
changeset
|
249 |
val skolem = (pos = (s = @{const_name Ex})) |
acde1b606b0e
reverted 0bfaaa81fc62, since "Thm.rename_boundvars" can't be relied upon to give unique names to bound variables
blanchet
parents:
39931
diff
changeset
|
250 |
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
|
251 |
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
|
252 |
else ((cluster_no ||> cluster_skolem ? Integer.add 1, skolem), 0) |
acde1b606b0e
reverted 0bfaaa81fc62, since "Thm.rename_boundvars" can't be relied upon to give unique names to bound variables
blanchet
parents:
39931
diff
changeset
|
253 |
in |
acde1b606b0e
reverted 0bfaaa81fc62, since "Thm.rename_boundvars" can't be relied upon to give unique names to bound variables
blanchet
parents:
39931
diff
changeset
|
254 |
Thm.dest_comb #> snd |
acde1b606b0e
reverted 0bfaaa81fc62, since "Thm.rename_boundvars" can't be relied upon to give unique names to bound variables
blanchet
parents:
39931
diff
changeset
|
255 |
#> Thm.dest_abs (SOME (zapped_var_name cluster index_no s')) |
acde1b606b0e
reverted 0bfaaa81fc62, since "Thm.rename_boundvars" can't be relied upon to give unique names to bound variables
blanchet
parents:
39931
diff
changeset
|
256 |
#> snd #> zap cluster (index_no + 1) pos |
acde1b606b0e
reverted 0bfaaa81fc62, since "Thm.rename_boundvars" can't be relied upon to give unique names to bound variables
blanchet
parents:
39931
diff
changeset
|
257 |
end |
39906 | 258 |
else |
259 |
Conv.all_conv |
|
260 |
| Const (s, _) $ _ $ _ => |
|
261 |
if s = @{const_name "==>"} orelse s = @{const_name implies} 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
|
262 |
Conv.combination_conv (Conv.arg_conv (zap cluster index_no (not pos))) |
acde1b606b0e
reverted 0bfaaa81fc62, since "Thm.rename_boundvars" can't be relied upon to give unique names to bound variables
blanchet
parents:
39931
diff
changeset
|
263 |
(zap cluster index_no pos) |
39906 | 264 |
else if s = @{const_name conj} orelse s = @{const_name disj} 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
|
265 |
Conv.combination_conv (Conv.arg_conv (zap cluster index_no pos)) |
acde1b606b0e
reverted 0bfaaa81fc62, since "Thm.rename_boundvars" can't be relied upon to give unique names to bound variables
blanchet
parents:
39931
diff
changeset
|
266 |
(zap cluster index_no pos) |
39906 | 267 |
else |
268 |
Conv.all_conv |
|
269 |
| Const (s, _) $ _ => |
|
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
|
270 |
if s = @{const_name Trueprop} then |
acde1b606b0e
reverted 0bfaaa81fc62, since "Thm.rename_boundvars" can't be relied upon to give unique names to bound variables
blanchet
parents:
39931
diff
changeset
|
271 |
Conv.arg_conv (zap cluster index_no pos) |
acde1b606b0e
reverted 0bfaaa81fc62, since "Thm.rename_boundvars" can't be relied upon to give unique names to bound variables
blanchet
parents:
39931
diff
changeset
|
272 |
else if s = @{const_name Not} then |
acde1b606b0e
reverted 0bfaaa81fc62, since "Thm.rename_boundvars" can't be relied upon to give unique names to bound variables
blanchet
parents:
39931
diff
changeset
|
273 |
Conv.arg_conv (zap cluster index_no (not pos)) |
acde1b606b0e
reverted 0bfaaa81fc62, since "Thm.rename_boundvars" can't be relied upon to give unique names to bound variables
blanchet
parents:
39931
diff
changeset
|
274 |
else |
acde1b606b0e
reverted 0bfaaa81fc62, since "Thm.rename_boundvars" can't be relied upon to give unique names to bound variables
blanchet
parents:
39931
diff
changeset
|
275 |
Conv.all_conv |
39906 | 276 |
| _ => Conv.all_conv) |
39887
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
277 |
|
39901
75d792edf634
make "cnf_axiom" work (after a fashion) in the absence of the axiom of choice
blanchet
parents:
39900
diff
changeset
|
278 |
fun ss_only ths = MetaSimplifier.clear_ss HOL_basic_ss addsimps ths |
75d792edf634
make "cnf_axiom" work (after a fashion) in the absence of the axiom of choice
blanchet
parents:
39900
diff
changeset
|
279 |
|
75d792edf634
make "cnf_axiom" work (after a fashion) in the absence of the axiom of choice
blanchet
parents:
39900
diff
changeset
|
280 |
val no_choice = |
75d792edf634
make "cnf_axiom" work (after a fashion) in the absence of the axiom of choice
blanchet
parents:
39900
diff
changeset
|
281 |
@{prop "ALL x. EX y. Q x y ==> EX f. ALL x. Q x (f x)"} |
75d792edf634
make "cnf_axiom" work (after a fashion) in the absence of the axiom of choice
blanchet
parents:
39900
diff
changeset
|
282 |
|> Logic.varify_global |
75d792edf634
make "cnf_axiom" work (after a fashion) in the absence of the axiom of choice
blanchet
parents:
39900
diff
changeset
|
283 |
|> 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
|
284 |
|
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
285 |
(* Converts an Isabelle theorem into NNF. *) |
39901
75d792edf634
make "cnf_axiom" work (after a fashion) in the absence of the axiom of choice
blanchet
parents:
39900
diff
changeset
|
286 |
fun nnf_axiom choice_ths new_skolemizer 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
|
287 |
let |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
288 |
val thy = ProofContext.theory_of ctxt |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
289 |
val th = |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
290 |
th |> transform_elim_theorem |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
291 |
|> zero_var_indexes |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
292 |
|> new_skolemizer ? forall_intr_vars |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
293 |
val (th, ctxt) = Variable.import true [th] ctxt |>> snd |>> the_single |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
294 |
val th = th |> Conv.fconv_rule Object_Logic.atomize |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
295 |
|> extensionalize_theorem |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
296 |
|> Meson.make_nnf ctxt |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
297 |
in |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
298 |
if new_skolemizer then |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
299 |
let |
39901
75d792edf634
make "cnf_axiom" work (after a fashion) in the absence of the axiom of choice
blanchet
parents:
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fun skolemize choice_ths = |
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Meson.skolemize_with_choice_thms ctxt choice_ths |
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#> simplify (ss_only @{thms all_simps[symmetric]}) |
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val pull_out = |
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simplify (ss_only @{thms all_simps[symmetric] ex_simps[symmetric]}) |
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val (discharger_th, fully_skolemized_th) = |
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if null choice_ths then |
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th |> `I |>> pull_out ||> skolemize [no_choice] |
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else |
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th |> skolemize choice_ths |> `I |
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val t = |
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fully_skolemized_th |> cprop_of |
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|> zap ((ax_no, 0), true) 0 true |> Drule.export_without_context |
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|> cprop_of |> Thm.dest_equals |> snd |> term_of |
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in |
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if exists_subterm (fn Var ((s, _), _) => |
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String.isPrefix new_skolem_var_prefix s |
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| _ => false) t then |
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let |
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val (ct, ctxt) = |
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Variable.import_terms true [t] ctxt |
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321 |
|>> the_single |>> cterm_of thy |
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in (SOME (discharger_th, ct), Thm.assume ct, ctxt) end |
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323 |
else |
39908 | 324 |
(NONE, th, ctxt) |
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325 |
end |
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326 |
else |
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327 |
(NONE, th, ctxt) |
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328 |
end |
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|
329 |
|
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330 |
(* Convert a theorem to CNF, with additional premises due to skolemization. *) |
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331 |
fun cnf_axiom ctxt0 new_skolemizer ax_no th = |
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332 |
let |
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333 |
val thy = ProofContext.theory_of ctxt0 |
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334 |
val choice_ths = Meson_Choices.get ctxt0 |
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|
335 |
val (opt, nnf_th, ctxt) = nnf_axiom choice_ths new_skolemizer ax_no th ctxt0 |
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|
336 |
fun clausify th = |
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|
337 |
Meson.make_cnf (if new_skolemizer then |
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|
338 |
[] |
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|
339 |
else |
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340 |
map (old_skolem_theorem_from_def thy) |
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parents:
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|
341 |
(old_skolem_defs th)) th ctxt |
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changeset
|
342 |
val (cnf_ths, ctxt) = |
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|
343 |
clausify nnf_th |
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|
344 |
|> (fn ([], _) => |
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changeset
|
345 |
clausify (to_definitional_cnf_with_quantifiers thy nnf_th) |
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|
346 |
| p => p) |
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|
347 |
fun intr_imp ct th = |
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|
348 |
Thm.instantiate ([], map (pairself (cterm_of @{theory})) |
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|
349 |
[(Var (("i", 1), @{typ nat}), |
39902 | 350 |
HOLogic.mk_nat ax_no)]) |
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|
351 |
@{thm skolem_COMBK_D} |
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|
352 |
RS Thm.implies_intr ct th |
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parents:
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|
353 |
in |
39897 | 354 |
(opt |> Option.map (I #>> singleton (Variable.export ctxt ctxt0) |
355 |
##> (term_of #> HOLogic.dest_Trueprop |
|
356 |
#> singleton (Variable.export_terms ctxt ctxt0))), |
|
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|
357 |
cnf_ths |> map (introduce_combinators_in_theorem |
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|
358 |
#> (case opt of SOME (_, ct) => intr_imp ct | NONE => I)) |
39897 | 359 |
|> Variable.export ctxt ctxt0 |
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|
360 |
|> Meson.finish_cnf |
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|
361 |
|> map Thm.close_derivation) |
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parents:
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|
362 |
end |
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parents:
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changeset
|
363 |
handle THM _ => (NONE, []) |
27184 | 364 |
|
20461
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skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
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diff
changeset
|
365 |
end; |