author | wenzelm |
Wed, 04 Mar 2015 22:05:01 +0100 | |
changeset 59586 | ddf6deaadfe8 |
parent 59582 | 0fbed69ff081 |
child 59621 | 291934bac95e |
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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more robust handling of variables in new Skolemizer
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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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continued implementation of lambda-lifting in Metis
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val is_quasi_lambda_free : term -> bool |
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val introduce_combinators_in_cterm : cterm -> thm |
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val introduce_combinators_in_theorem : Proof.context -> 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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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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Added functions to retrieve local and global atpset rules.
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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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open Meson |
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||
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avoid illegal variable names, which then yield "Not an identifier" errors in "rename_tac"
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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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second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
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|
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avoid evil "export_without_context", which breaks if there are local "fixes"
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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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val cfalse = Thm.cterm_of @{theory HOL} @{term False}; |
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val ctp_false = Thm.cterm_of @{theory HOL} (HOLogic.mk_Trueprop @{term False}); |
|
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skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
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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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reintroduced more preprocessing steps to Sledgehammer, adapted to the new FOF setting
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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 Trueprop} $ (v as Var (_, @{typ bool})) => |
|
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Thm.instantiate ([], [(Thm.cterm_of @{theory HOL} v, cfalse)]) th |
|
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| v as Var(_, @{typ prop}) => |
|
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Thm.instantiate ([], [(Thm.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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first step towards a new skolemizer that doesn't require "Eps"
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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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qualify "Meson." and "Metis." constants so that the ML files can be reloaded later (e.g. for testing/development)
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Const (@{const_name Meson.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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63 |
|
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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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proper polymorphic Skolemization of uncached facts + synchronization of caching and relevance filter
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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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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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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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first step towards a new skolemizer that doesn't require "Eps"
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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 = singleton (Name.variant_list (Misc_Legacy.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 |
83 |
| dec_sko (@{const disj} $ p $ q) rhss = rhss |> dec_sko p |> dec_sko q |
|
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always perform "inline" skolemization, polymorphism or not, Skolem cache or not
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parents:
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| dec_sko (@{const Trueprop} $ p) rhss = dec_sko p rhss |
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always perform "inline" skolemization, polymorphism or not, Skolem cache or not
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parents:
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85 |
| 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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qualify "Meson." and "Metis." constants so that the ML files can be reloaded later (e.g. for testing/development)
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fun is_quasi_lambda_free (Const (@{const_name Meson.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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skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
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parents:
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96 |
|
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val [f_B,g_B] = map (Thm.cterm_of @{theory}) (Misc_Legacy.term_vars (Thm.prop_of @{thm abs_B})); |
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val [g_C,f_C] = map (Thm.cterm_of @{theory}) (Misc_Legacy.term_vars (Thm.prop_of @{thm abs_C})); |
|
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val [f_S,g_S] = map (Thm.cterm_of @{theory}) (Misc_Legacy.term_vars (Thm.prop_of @{thm abs_S})); |
|
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improvements to abstraction, ensuring more re-use of abstraction functions
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|
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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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103 |
let |
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val thy = Thm.theory_of_cterm ct |
105 |
val Abs(x,_,body) = Thm.term_of ct |
|
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val Type (@{type_name fun}, [xT,bodyT]) = Thm.typ_of_cterm ct |
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val cxT = Thm.ctyp_of thy xT |
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val cbodyT = Thm.ctyp_of thy bodyT |
|
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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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fun makeK () = |
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instantiate' [SOME cxT, SOME cbodyT] [SOME (Thm.cterm_of thy body)] |
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111 |
@{thm abs_K} |
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in |
113 |
case body of |
|
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Const _ => makeK() |
|
115 |
| Free _ => makeK() |
|
116 |
| 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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added Term.is_open and Term.is_dependent convenience, to cover common situations of loose bounds;
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119 |
if Term.is_dependent rator then (*C or S*) |
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added Term.is_open and Term.is_dependent convenience, to cover common situations of loose bounds;
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120 |
if Term.is_dependent rand then (*S*) |
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let val crator = Thm.cterm_of thy (Abs(x,xT,rator)) |
122 |
val crand = Thm.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 (Thm.cprop_of abs_S') |
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ResAxioms.cnf_axiom/cnf_rules_pairs: pass explicit theory context;
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125 |
in |
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126 |
Thm.transitive abs_S' (Conv.binop_conv abstract rhs) |
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127 |
end |
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128 |
else (*C*) |
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let val crator = Thm.cterm_of thy (Abs(x,xT,rator)) |
130 |
val abs_C' = |
|
131 |
cterm_instantiate [(f_C,crator),(g_C,Thm.cterm_of thy rand)] @{thm abs_C} |
|
132 |
val (_,rhs) = Thm.dest_equals (Thm.cprop_of abs_C') |
|
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133 |
in |
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134 |
Thm.transitive abs_C' (Conv.fun_conv (Conv.arg_conv abstract) rhs) |
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135 |
end |
42083
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added Term.is_open and Term.is_dependent convenience, to cover common situations of loose bounds;
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parents:
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136 |
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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138 |
else (*B*) |
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let val crand = Thm.cterm_of thy (Abs(x,xT,rand)) |
140 |
val crator = Thm.cterm_of thy rator |
|
27184 | 141 |
val abs_B' = cterm_instantiate [(f_B,crator),(g_B,crand)] @{thm abs_B} |
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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 rhs) end |
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ResAxioms.cnf_axiom/cnf_rules_pairs: pass explicit theory context;
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144 |
else makeK() |
37349 | 145 |
| _ => raise Fail "abstract: Bad term" |
24827 | 146 |
end; |
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improvements to abstraction, ensuring more re-use of abstraction functions
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parents:
20789
diff
changeset
|
147 |
|
37349 | 148 |
(* Traverse a theorem, remplacing lambda-abstractions with combinators. *) |
38001
a9b47b85ca24
reintroduced more preprocessing steps to Sledgehammer, adapted to the new FOF setting
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parents:
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diff
changeset
|
149 |
fun introduce_combinators_in_cterm ct = |
59582 | 150 |
if is_quasi_lambda_free (Thm.term_of ct) then |
37349 | 151 |
Thm.reflexive ct |
59582 | 152 |
else case Thm.term_of ct of |
37349 | 153 |
Abs _ => |
154 |
let |
|
155 |
val (cv, cta) = Thm.dest_abs NONE ct |
|
59582 | 156 |
val (v, _) = dest_Free (Thm.term_of cv) |
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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|
157 |
val u_th = introduce_combinators_in_cterm cta |
37349 | 158 |
val cu = Thm.rhs_of u_th |
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renamed Thm.capply to Thm.apply, and Thm.cabs to Thm.lambda in conformance with similar operations in structure Term and Logic;
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159 |
val comb_eq = abstract (Thm.lambda cv cu) |
37349 | 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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163 |
Thm.combination (introduce_combinators_in_cterm ct1) |
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reintroduced more preprocessing steps to Sledgehammer, adapted to the new FOF setting
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164 |
(introduce_combinators_in_cterm ct2) |
37349 | 165 |
end |
166 |
||
55236 | 167 |
fun introduce_combinators_in_theorem ctxt th = |
59582 | 168 |
if is_quasi_lambda_free (Thm.prop_of th) then |
37349 | 169 |
th |
24827 | 170 |
else |
37349 | 171 |
let |
172 |
val th = Drule.eta_contraction_rule th |
|
59582 | 173 |
val eqth = introduce_combinators_in_cterm (Thm.cprop_of th) |
37349 | 174 |
in Thm.equal_elim eqth th end |
175 |
handle THM (msg, _, _) => |
|
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removed final periods in messages for proof methods
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176 |
(warning ("Error in the combinator translation of " ^ Display.string_of_thm ctxt th ^ |
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removed final periods in messages for proof methods
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177 |
"\nException message: " ^ msg); |
45511
9b0f8ca4388e
continued implementation of lambda-lifting in Metis
blanchet
parents:
45508
diff
changeset
|
178 |
(* A type variable of sort "{}" will make "abstraction" fail. *) |
37349 | 179 |
TrueI) |
16009 | 180 |
|
181 |
(*cterms are used throughout for efficiency*) |
|
59582 | 182 |
val cTrueprop = Thm.cterm_of @{theory HOL} HOLogic.Trueprop; |
16009 | 183 |
|
184 |
(*Given an abstraction over n variables, replace the bound variables by free |
|
185 |
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:
20457
diff
changeset
|
186 |
fun c_variant_abs_multi (ct0, vars) = |
16009 | 187 |
let val (cv,ct) = Thm.dest_abs NONE ct0 |
188 |
in c_variant_abs_multi (ct, cv::vars) end |
|
189 |
handle CTERM _ => (ct0, rev vars); |
|
190 |
||
37617
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always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
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diff
changeset
|
191 |
(* Given the definition of a Skolem function, return a theorem to replace |
f73cd4069f69
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blanchet
parents:
37616
diff
changeset
|
192 |
an existential formula by a use of that function. |
18141
89e2e8bed08f
Skolemization by inference, but not quite finished
paulson
parents:
18009
diff
changeset
|
193 |
Example: "EX x. x : A & x ~: B ==> sko A B : A & sko A B ~: B" [.] *) |
57466 | 194 |
fun old_skolem_theorem_of_def ctxt rhs0 = |
37399
34f080a12063
proper polymorphic Skolemization of uncached facts + synchronization of caching and relevance filter
blanchet
parents:
37349
diff
changeset
|
195 |
let |
57466 | 196 |
val thy = Proof_Context.theory_of ctxt |
59582 | 197 |
val rhs = rhs0 |> Type.legacy_freeze_thaw |> #1 |> Thm.cterm_of thy |
37617
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
198 |
val rhs' = rhs |> Thm.dest_comb |> snd |
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
199 |
val (ch, frees) = c_variant_abs_multi (rhs', []) |
59582 | 200 |
val (hilbert, cabs) = ch |> Thm.dest_comb |>> Thm.term_of |
37617
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
201 |
val T = |
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
202 |
case hilbert of |
39941 | 203 |
Const (_, Type (@{type_name fun}, [_, T])) => T |
57466 | 204 |
| _ => raise TERM ("old_skolem_theorem_of_def: expected \"Eps\"", [hilbert]) |
59582 | 205 |
val cex = Thm.cterm_of thy (HOLogic.exists_const T) |
46497
89ccf66aa73d
renamed Thm.capply to Thm.apply, and Thm.cabs to Thm.lambda in conformance with similar operations in structure Term and Logic;
wenzelm
parents:
46071
diff
changeset
|
206 |
val ex_tm = Thm.apply cTrueprop (Thm.apply cex cabs) |
37629 | 207 |
val conc = |
37617
f73cd4069f69
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blanchet
parents:
37616
diff
changeset
|
208 |
Drule.list_comb (rhs, frees) |
46497
89ccf66aa73d
renamed Thm.capply to Thm.apply, and Thm.cabs to Thm.lambda in conformance with similar operations in structure Term and Logic;
wenzelm
parents:
46071
diff
changeset
|
209 |
|> Drule.beta_conv cabs |> Thm.apply cTrueprop |
37617
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
210 |
fun tacf [prem] = |
54742
7a86358a3c0b
proper context for basic Simplifier operations: rewrite_rule, rewrite_goals_rule, rewrite_goals_tac etc.;
wenzelm
parents:
52031
diff
changeset
|
211 |
rewrite_goals_tac ctxt @{thms skolem_def [abs_def]} |
59498
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
59165
diff
changeset
|
212 |
THEN resolve_tac ctxt [(prem |> rewrite_rule ctxt @{thms skolem_def [abs_def]}) |
58839 | 213 |
RS Global_Theory.get_thm thy "Hilbert_Choice.someI_ex"] 1 |
37617
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
214 |
in |
54883
dd04a8b654fc
proper context for norm_hhf and derived operations;
wenzelm
parents:
54742
diff
changeset
|
215 |
Goal.prove_internal ctxt [ex_tm] conc tacf |
37629 | 216 |
|> forall_intr_list frees |
217 |
|> Thm.forall_elim_vars 0 (*Introduce Vars, but don't discharge defs.*) |
|
218 |
|> Thm.varifyT_global |
|
37617
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
219 |
end |
24742
73b8b42a36b6
removal of some "ref"s from res_axioms.ML; a side-effect is that the ordering
paulson
parents:
24669
diff
changeset
|
220 |
|
42335 | 221 |
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:
38864
diff
changeset
|
222 |
let |
59582 | 223 |
val eqth = CNF.make_cnfx_thm ctxt (HOLogic.dest_Trueprop (Thm.prop_of th)) |
39036
dff91b90d74c
use definitional CNFs in Metis rather than plain CNF, following a suggestion by Joe Hurd;
blanchet
parents:
38864
diff
changeset
|
224 |
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
|
225 |
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
|
226 |
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
|
227 |
|
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
|
228 |
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
|
229 |
(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
|
230 |
"_" ^ string_of_int ax_no ^ "_" ^ string_of_int cluster_no ^ "_" ^ |
56811 | 231 |
string_of_int index_no ^ "_" ^ Name.desymbolize (SOME false) 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 |
|
39899
608b108ec979
compute quantifier dependency graph in new skolemizer
blanchet
parents:
39897
diff
changeset
|
233 |
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
|
234 |
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
|
235 |
((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
|
236 |
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
|
237 |
end |
39897 | 238 |
|
40260
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
239 |
fun rename_bound_vars_to_be_zapped ax_no = |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
240 |
let |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
241 |
fun aux (cluster as (cluster_no, cluster_skolem)) index_no pos t = |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
242 |
case t of |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
243 |
(t1 as Const (s, _)) $ Abs (s', T, t') => |
56245 | 244 |
if s = @{const_name Pure.all} orelse s = @{const_name All} orelse |
39906 | 245 |
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
|
246 |
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
|
247 |
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
|
248 |
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
|
249 |
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
|
250 |
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
|
251 |
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
|
252 |
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
|
253 |
else |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
254 |
t |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
255 |
| (t1 as Const (s, _)) $ t2 $ t3 => |
56245 | 256 |
if s = @{const_name Pure.imp} orelse s = @{const_name HOL.implies} then |
40260
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
257 |
t1 $ aux cluster index_no (not 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
|
258 |
else if s = @{const_name HOL.conj} orelse |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
259 |
s = @{const_name HOL.disj} then |
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 $ 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
|
261 |
else |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
262 |
t |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
263 |
| (t1 as Const (s, _)) $ t2 => |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
264 |
if s = @{const_name Trueprop} then |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
265 |
t1 $ aux cluster index_no pos t2 |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
266 |
else if s = @{const_name Not} then |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
267 |
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
|
268 |
else |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
269 |
t |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
270 |
| _ => t |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
271 |
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
|
272 |
|
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
273 |
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
|
274 |
ct |
59582 | 275 |
|> (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
|
276 |
Const (s, _) $ Abs (s', _, _) => |
56245 | 277 |
if s = @{const_name Pure.all} orelse s = @{const_name All} orelse |
40260
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
278 |
s = @{const_name Ex} then |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
279 |
Thm.dest_comb #> snd #> Thm.dest_abs (SOME s') #> snd #> zap pos |
39906 | 280 |
else |
281 |
Conv.all_conv |
|
282 |
| Const (s, _) $ _ $ _ => |
|
56245 | 283 |
if s = @{const_name Pure.imp} orelse s = @{const_name implies} then |
40260
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
284 |
Conv.combination_conv (Conv.arg_conv (zap (not pos))) (zap pos) |
39906 | 285 |
else if s = @{const_name conj} orelse s = @{const_name disj} then |
40260
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
286 |
Conv.combination_conv (Conv.arg_conv (zap pos)) (zap pos) |
39906 | 287 |
else |
288 |
Conv.all_conv |
|
289 |
| Const (s, _) $ _ => |
|
40260
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
290 |
if s = @{const_name Trueprop} then Conv.arg_conv (zap pos) |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
291 |
else if s = @{const_name Not} then Conv.arg_conv (zap (not pos)) |
73ecbe2d432b
fix cluster numbering in the absense of Hilbert_Choice (reverts acde1b606b0e, effectively reintroducing most of 0bfaaa81fc62)
blanchet
parents:
39962
diff
changeset
|
292 |
else Conv.all_conv |
39906 | 293 |
| _ => Conv.all_conv) |
39887
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
294 |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
50705
diff
changeset
|
295 |
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
|
296 |
|
40261
7a02144874f3
more work on new Skolemizer without Hilbert_Choice
blanchet
parents:
40260
diff
changeset
|
297 |
val cheat_choice = |
39901
75d792edf634
make "cnf_axiom" work (after a fashion) in the absence of the axiom of choice
blanchet
parents:
39900
diff
changeset
|
298 |
@{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
|
299 |
|> Logic.varify_global |
75d792edf634
make "cnf_axiom" work (after a fashion) in the absence of the axiom of choice
blanchet
parents:
39900
diff
changeset
|
300 |
|> 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
|
301 |
|
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
302 |
(* Converts an Isabelle theorem into NNF. *) |
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fun nnf_axiom choice_ths new_skolem ax_no th ctxt = |
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let |
42361 | 305 |
val thy = Proof_Context.theory_of ctxt |
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val th = |
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th |> transform_elim_theorem |
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|> zero_var_indexes |
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|> new_skolem ? forall_intr_vars |
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val (th, ctxt) = Variable.import true [th] ctxt |>> snd |>> the_single |
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proper context for basic Simplifier operations: rewrite_rule, rewrite_goals_rule, rewrite_goals_tac etc.;
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val th = th |> Conv.fconv_rule (Object_Logic.atomize ctxt) |
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|> cong_extensionalize_thm thy |
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|> abs_extensionalize_thm ctxt |
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|> make_nnf ctxt |
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|
315 |
in |
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use new skolemizer for reconstructing skolemization steps in Isar proofs (because the old skolemizer messes up the order of the Skolem arguments)
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parents:
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316 |
if new_skolem then |
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let |
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fun skolemize choice_ths = |
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skolemize_with_choice_theorems ctxt choice_ths |
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#> simplify (ss_only @{thms all_simps[symmetric]} ctxt) |
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val no_choice = null choice_ths |
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val pull_out = |
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if no_choice then |
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324 |
simplify (ss_only @{thms all_simps[symmetric] ex_simps[symmetric]} ctxt) |
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325 |
else |
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326 |
skolemize choice_ths |
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val discharger_th = th |> pull_out |
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val discharger_th = |
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discharger_th |> has_too_many_clauses ctxt (Thm.concl_of discharger_th) |
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? (to_definitional_cnf_with_quantifiers ctxt |
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331 |
#> pull_out) |
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332 |
val zapped_th = |
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discharger_th |> Thm.prop_of |> rename_bound_vars_to_be_zapped ax_no |
40263 | 334 |
|> (if no_choice then |
59582 | 335 |
Skip_Proof.make_thm thy #> skolemize [cheat_choice] #> Thm.cprop_of |
40263 | 336 |
else |
59582 | 337 |
Thm.cterm_of thy) |
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|> zap true |
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val fixes = |
59582 | 340 |
[] |> Term.add_free_names (Thm.prop_of zapped_th) |
42335 | 341 |
|> filter is_zapped_var_name |
42269 | 342 |
val ctxt' = ctxt |> Variable.add_fixes_direct fixes |
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val fully_skolemized_t = |
42333 | 344 |
zapped_th |> singleton (Variable.export ctxt' ctxt) |
59582 | 345 |
|> Thm.cprop_of |> Thm.dest_equals |> snd |> Thm.term_of |
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|
346 |
in |
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|
347 |
if exists_subterm (fn Var ((s, _), _) => |
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348 |
String.isPrefix new_skolem_var_prefix s |
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349 |
| _ => false) fully_skolemized_t then |
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|
350 |
let |
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351 |
val (fully_skolemized_ct, ctxt) = |
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|
352 |
Variable.import_terms true [fully_skolemized_t] ctxt |
59582 | 353 |
|>> the_single |>> Thm.cterm_of thy |
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|
354 |
in |
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|
355 |
(SOME (discharger_th, fully_skolemized_ct), |
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|
356 |
(Thm.assume fully_skolemized_ct, ctxt)) |
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|
357 |
end |
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|
358 |
else |
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|
359 |
(NONE, (th, ctxt)) |
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|
360 |
end |
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|
361 |
else |
59582 | 362 |
(NONE, (th |> has_too_many_clauses ctxt (Thm.concl_of th) |
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|
363 |
? to_definitional_cnf_with_quantifiers ctxt, ctxt)) |
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|
364 |
end |
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parents:
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|
365 |
|
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|
366 |
(* Convert a theorem to CNF, with additional premises due to skolemization. *) |
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parents:
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|
367 |
fun cnf_axiom ctxt0 new_skolem combinators ax_no th = |
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|
368 |
let |
42361 | 369 |
val thy = Proof_Context.theory_of ctxt0 |
39950 | 370 |
val choice_ths = choice_theorems thy |
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|
371 |
val (opt, (nnf_th, ctxt)) = |
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|
372 |
nnf_axiom choice_ths new_skolem ax_no th ctxt0 |
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|
373 |
fun clausify th = |
59165 | 374 |
make_cnf |
375 |
(if new_skolem orelse null choice_ths then [] |
|
376 |
else map (old_skolem_theorem_of_def ctxt) (old_skolem_defs th)) |
|
377 |
th ctxt |
|
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|
378 |
val (cnf_ths, ctxt) = clausify nnf_th |
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|
379 |
fun intr_imp ct th = |
59582 | 380 |
Thm.instantiate ([], map (apply2 (Thm.cterm_of thy)) |
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|
381 |
[(Var (("i", 0), @{typ nat}), |
39902 | 382 |
HOLogic.mk_nat ax_no)]) |
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|
383 |
(zero_var_indexes @{thm skolem_COMBK_D}) |
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parents:
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|
384 |
RS Thm.implies_intr ct th |
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parents:
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diff
changeset
|
385 |
in |
39897 | 386 |
(opt |> Option.map (I #>> singleton (Variable.export ctxt ctxt0) |
59582 | 387 |
##> (Thm.term_of #> HOLogic.dest_Trueprop |
39897 | 388 |
#> singleton (Variable.export_terms ctxt ctxt0))), |
55236 | 389 |
cnf_ths |> map (combinators ? introduce_combinators_in_theorem ctxt |
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changeset
|
390 |
#> (case opt of SOME (_, ct) => intr_imp ct | NONE => I)) |
39897 | 391 |
|> Variable.export ctxt ctxt0 |
39950 | 392 |
|> finish_cnf |
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parents:
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|
393 |
|> map Thm.close_derivation) |
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parents:
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diff
changeset
|
394 |
end |
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parents:
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changeset
|
395 |
handle THM _ => (NONE, []) |
27184 | 396 |
|
20461
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skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
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parents:
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diff
changeset
|
397 |
end; |