author | blanchet |
Wed, 29 Sep 2010 23:06:02 +0200 | |
changeset 39887 | 74939e2afb95 |
parent 39886 | 8a9f0c97d550 |
permissions | -rw-r--r-- |
37574
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renamed "Sledgehammer_Fact_Preprocessor" to "Clausifier";
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1 |
(* Title: HOL/Tools/Sledgehammer/clausifier.ML |
38027 | 2 |
Author: Jia Meng, Cambridge University Computer Laboratory and NICTA |
36393
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support readable names even when Isar proof reconstruction is enabled -- useful for debugging
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3 |
Author: Jasmin Blanchette, TU Muenchen |
15347 | 4 |
|
20461
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skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
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5 |
Transformation of axiom rules (elim/intro/etc) into CNF forms. |
15347 | 6 |
*) |
7 |
||
39720
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rename "Clausifier" to "Meson_Clausifier" and merge with "Meson_Tactic"
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8 |
signature MESON_CLAUSIFIER = |
21505 | 9 |
sig |
39886
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first step towards a new skolemizer that doesn't require "Eps"
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10 |
val new_skolemizer : bool Config.T |
39887
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second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
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11 |
val new_skolem_var_prefix : string |
38632
9cde57cdd0e3
treat "using X by metis" (more or less) the same as "by (metis X)"
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12 |
val extensionalize_theorem : thm -> thm |
38001
a9b47b85ca24
reintroduced more preprocessing steps to Sledgehammer, adapted to the new FOF setting
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13 |
val introduce_combinators_in_cterm : cterm -> thm |
38028 | 14 |
val introduce_combinators_in_theorem : thm -> thm |
39037
5146d640aa4a
Let MESON take an additional "preskolemization tactic", which can be used to put the goal in definitional CNF
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15 |
val to_definitional_cnf_with_quantifiers : theory -> thm -> thm |
39887
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
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16 |
val cnf_axiom : theory -> thm -> thm option * thm list |
39720
0b93a954da4f
rename "Clausifier" to "Meson_Clausifier" and merge with "Meson_Tactic"
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parents:
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17 |
val meson_general_tac : Proof.context -> thm list -> int -> tactic |
0b93a954da4f
rename "Clausifier" to "Meson_Clausifier" and merge with "Meson_Tactic"
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parents:
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18 |
val setup: theory -> theory |
21505 | 19 |
end; |
19196
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Added functions to retrieve local and global atpset rules.
mengj
parents:
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20 |
|
39720
0b93a954da4f
rename "Clausifier" to "Meson_Clausifier" and merge with "Meson_Tactic"
blanchet
parents:
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diff
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21 |
structure Meson_Clausifier : MESON_CLAUSIFIER = |
15997 | 22 |
struct |
15347 | 23 |
|
39886
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first step towards a new skolemizer that doesn't require "Eps"
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parents:
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24 |
val (new_skolemizer, new_skolemizer_setup) = |
8a9f0c97d550
first step towards a new skolemizer that doesn't require "Eps"
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25 |
Attrib.config_bool "meson_new_skolemizer" (K false) |
8a9f0c97d550
first step towards a new skolemizer that doesn't require "Eps"
blanchet
parents:
39721
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|
26 |
|
39887
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
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27 |
val new_skolem_var_prefix = "SK?" (* purposedly won't parse *) |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
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28 |
|
15997 | 29 |
(**** Transformation of Elimination Rules into First-Order Formulas****) |
15347 | 30 |
|
29064 | 31 |
val cfalse = cterm_of @{theory HOL} HOLogic.false_const; |
32 |
val ctp_false = cterm_of @{theory HOL} (HOLogic.mk_Trueprop HOLogic.false_const); |
|
20461
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
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33 |
|
38001
a9b47b85ca24
reintroduced more preprocessing steps to Sledgehammer, adapted to the new FOF setting
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parents:
38000
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34 |
(* Converts an elim-rule into an equivalent theorem that does not have the |
a9b47b85ca24
reintroduced more preprocessing steps to Sledgehammer, adapted to the new FOF setting
blanchet
parents:
38000
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35 |
predicate variable. Leaves other theorems unchanged. We simply instantiate |
a9b47b85ca24
reintroduced more preprocessing steps to Sledgehammer, adapted to the new FOF setting
blanchet
parents:
38000
diff
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36 |
the conclusion variable to False. (Cf. "transform_elim_term" in |
38652
e063be321438
perform eta-expansion of quantifier bodies in Sledgehammer translation when needed + transform elim rules later;
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parents:
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37 |
"Sledgehammer_Util".) *) |
38001
a9b47b85ca24
reintroduced more preprocessing steps to Sledgehammer, adapted to the new FOF setting
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parents:
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38 |
fun transform_elim_theorem th = |
21430
77651b6d9d6c
New transformation of eliminatino rules: we simply replace the final conclusion variable by False
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39 |
case concl_of th of (*conclusion variable*) |
35963 | 40 |
@{const Trueprop} $ (v as Var (_, @{typ bool})) => |
29064 | 41 |
Thm.instantiate ([], [(cterm_of @{theory HOL} v, cfalse)]) th |
35963 | 42 |
| v as Var(_, @{typ prop}) => |
29064 | 43 |
Thm.instantiate ([], [(cterm_of @{theory HOL} v, ctp_false)]) th |
38001
a9b47b85ca24
reintroduced more preprocessing steps to Sledgehammer, adapted to the new FOF setting
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parents:
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44 |
| _ => th |
15997 | 45 |
|
28544
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improved performance of skolem cache, due to parallel map;
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parents:
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46 |
|
16009 | 47 |
(**** SKOLEMIZATION BY INFERENCE (lcp) ****) |
48 |
||
39886
8a9f0c97d550
first step towards a new skolemizer that doesn't require "Eps"
blanchet
parents:
39721
diff
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49 |
fun mk_old_skolem_term_wrapper t = |
37436 | 50 |
let val T = fastype_of t in |
39355 | 51 |
Const (@{const_name skolem}, T --> T) $ t |
37436 | 52 |
end |
37410
2bf7e6136047
adjusted the polymorphism handling of Skolem constants so that proof reconstruction doesn't fail in "equality_inf"
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37403
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53 |
|
37617
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
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54 |
fun beta_eta_under_lambdas (Abs (s, T, t')) = |
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
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parents:
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55 |
Abs (s, T, beta_eta_under_lambdas t') |
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
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parents:
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56 |
| beta_eta_under_lambdas t = Envir.beta_eta_contract t |
37512
ff72d3ddc898
this looks like the most appropriate place to do the beta-eta-contraction
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57 |
|
18141
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Skolemization by inference, but not quite finished
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(*Traverse a theorem, accumulating Skolem function definitions.*) |
39886
8a9f0c97d550
first step towards a new skolemizer that doesn't require "Eps"
blanchet
parents:
39721
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changeset
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59 |
fun old_skolem_defs th = |
37399
34f080a12063
proper polymorphic Skolemization of uncached facts + synchronization of caching and relevance filter
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parents:
37349
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60 |
let |
39376 | 61 |
fun dec_sko (Const (@{const_name Ex}, _) $ (body as Abs (_, T, p))) rhss = |
37399
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proper polymorphic Skolemization of uncached facts + synchronization of caching and relevance filter
blanchet
parents:
37349
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62 |
(*Existential: declare a Skolem function, then insert into body and continue*) |
34f080a12063
proper polymorphic Skolemization of uncached facts + synchronization of caching and relevance filter
blanchet
parents:
37349
diff
changeset
|
63 |
let |
37617
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
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64 |
val args = OldTerm.term_frees body |
37500
7587b6e63454
thread original theorem along with CNF theorem, as a step toward killing the Skolem cache
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37498
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65 |
(* Forms a lambda-abstraction over the formal parameters *) |
7587b6e63454
thread original theorem along with CNF theorem, as a step toward killing the Skolem cache
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parents:
37498
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66 |
val rhs = |
7587b6e63454
thread original theorem along with CNF theorem, as a step toward killing the Skolem cache
blanchet
parents:
37498
diff
changeset
|
67 |
list_abs_free (map dest_Free args, |
37617
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
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diff
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68 |
HOLogic.choice_const T $ beta_eta_under_lambdas body) |
39886
8a9f0c97d550
first step towards a new skolemizer that doesn't require "Eps"
blanchet
parents:
39721
diff
changeset
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69 |
|> mk_old_skolem_term_wrapper |
37518
efb0923cc098
use Skolem inlining also in the nonpolymorphic case, as a step toward simplifying the source code
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70 |
val comb = list_comb (rhs, args) |
37617
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
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71 |
in dec_sko (subst_bound (comb, p)) (rhs :: rhss) end |
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
72 |
| dec_sko (Const (@{const_name All},_) $ Abs (a, T, p)) rhss = |
37399
34f080a12063
proper polymorphic Skolemization of uncached facts + synchronization of caching and relevance filter
blanchet
parents:
37349
diff
changeset
|
73 |
(*Universal quant: insert a free variable into body and continue*) |
34f080a12063
proper polymorphic Skolemization of uncached facts + synchronization of caching and relevance filter
blanchet
parents:
37349
diff
changeset
|
74 |
let val fname = Name.variant (OldTerm.add_term_names (p,[])) a |
37617
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
75 |
in dec_sko (subst_bound (Free(fname,T), p)) rhss end |
38795
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formerly unnamed infix conjunction and disjunction now named HOL.conj and HOL.disj
haftmann
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76 |
| dec_sko (@{const HOL.conj} $ p $ q) rhss = rhss |> dec_sko p |> dec_sko q |
848be46708dc
formerly unnamed infix conjunction and disjunction now named HOL.conj and HOL.disj
haftmann
parents:
38652
diff
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|
77 |
| dec_sko (@{const HOL.disj} $ p $ q) rhss = rhss |> dec_sko p |> dec_sko q |
37617
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
78 |
| dec_sko (@{const Trueprop} $ p) rhss = dec_sko p rhss |
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
79 |
| dec_sko _ rhss = rhss |
20419 | 80 |
in dec_sko (prop_of th) [] end; |
81 |
||
82 |
||
24827 | 83 |
(**** REPLACING ABSTRACTIONS BY COMBINATORS ****) |
20419 | 84 |
|
39302
d7728f65b353
renamed lemmas: ext_iff -> fun_eq_iff, set_ext_iff -> set_eq_iff, set_ext -> set_eqI
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85 |
val fun_cong_all = @{thm fun_eq_iff [THEN iffD1]} |
20419 | 86 |
|
38001
a9b47b85ca24
reintroduced more preprocessing steps to Sledgehammer, adapted to the new FOF setting
blanchet
parents:
38000
diff
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87 |
(* Removes the lambdas from an equation of the form "t = (%x. u)". |
38608
01ed56c46259
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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88 |
(Cf. "extensionalize_term" in "Sledgehammer_Translate".) *) |
38000
c0b9efa8bfca
added extensionalization to Sledgehammer, mimicking what the Clausifier used to do
blanchet
parents:
37995
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89 |
fun extensionalize_theorem th = |
37540
48273d1ea331
better eta-expansion in Sledgehammer's clausification;
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90 |
case prop_of th of |
38864
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formerly unnamed infix equality now named HOL.eq
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91 |
_ $ (Const (@{const_name HOL.eq}, Type (_, [Type (@{type_name fun}, _), _])) |
39376 | 92 |
$ _ $ Abs _) => extensionalize_theorem (th RS fun_cong_all) |
37540
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better eta-expansion in Sledgehammer's clausification;
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parents:
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93 |
| _ => th |
20419 | 94 |
|
39355 | 95 |
fun is_quasi_lambda_free (Const (@{const_name skolem}, _) $ _) = true |
37416
d5ac8280497e
no point in introducing combinators for inlined Skolem functions
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parents:
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diff
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96 |
| is_quasi_lambda_free (t1 $ t2) = |
d5ac8280497e
no point in introducing combinators for inlined Skolem functions
blanchet
parents:
37410
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97 |
is_quasi_lambda_free t1 andalso is_quasi_lambda_free t2 |
d5ac8280497e
no point in introducing combinators for inlined Skolem functions
blanchet
parents:
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diff
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98 |
| is_quasi_lambda_free (Abs _) = false |
d5ac8280497e
no point in introducing combinators for inlined Skolem functions
blanchet
parents:
37410
diff
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99 |
| is_quasi_lambda_free _ = true |
20461
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset
|
100 |
|
32010 | 101 |
val [f_B,g_B] = map (cterm_of @{theory}) (OldTerm.term_vars (prop_of @{thm abs_B})); |
102 |
val [g_C,f_C] = map (cterm_of @{theory}) (OldTerm.term_vars (prop_of @{thm abs_C})); |
|
103 |
val [f_S,g_S] = map (cterm_of @{theory}) (OldTerm.term_vars (prop_of @{thm abs_S})); |
|
20863
4ee61dbf192d
improvements to abstraction, ensuring more re-use of abstraction functions
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20789
diff
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104 |
|
38282
319c59682c51
move Sledgehammer's HOL -> FOL translation to separate file (sledgehammer_translate.ML)
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105 |
(* FIXME: Requires more use of cterm constructors. *) |
24827 | 106 |
fun abstract ct = |
28544
26743a1591f5
improved performance of skolem cache, due to parallel map;
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parents:
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107 |
let |
26743a1591f5
improved performance of skolem cache, due to parallel map;
wenzelm
parents:
28262
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|
108 |
val thy = theory_of_cterm ct |
25256
fe467fdf129a
Catch exceptions arising during the abstraction operation.
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|
109 |
val Abs(x,_,body) = term_of ct |
35963 | 110 |
val Type(@{type_name fun}, [xT,bodyT]) = typ_of (ctyp_of_term ct) |
38005
b6555e9c5de4
prevent schematic variable clash in combinator-introduction code, when invoked from Sledgehammer (another consequence of the CNF -> FOF transition)
blanchet
parents:
38001
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111 |
val cxT = ctyp_of thy xT |
b6555e9c5de4
prevent schematic variable clash in combinator-introduction code, when invoked from Sledgehammer (another consequence of the CNF -> FOF transition)
blanchet
parents:
38001
diff
changeset
|
112 |
val cbodyT = ctyp_of thy bodyT |
b6555e9c5de4
prevent schematic variable clash in combinator-introduction code, when invoked from Sledgehammer (another consequence of the CNF -> FOF transition)
blanchet
parents:
38001
diff
changeset
|
113 |
fun makeK () = |
b6555e9c5de4
prevent schematic variable clash in combinator-introduction code, when invoked from Sledgehammer (another consequence of the CNF -> FOF transition)
blanchet
parents:
38001
diff
changeset
|
114 |
instantiate' [SOME cxT, SOME cbodyT] [SOME (cterm_of thy body)] |
b6555e9c5de4
prevent schematic variable clash in combinator-introduction code, when invoked from Sledgehammer (another consequence of the CNF -> FOF transition)
blanchet
parents:
38001
diff
changeset
|
115 |
@{thm abs_K} |
24827 | 116 |
in |
117 |
case body of |
|
118 |
Const _ => makeK() |
|
119 |
| Free _ => makeK() |
|
120 |
| Var _ => makeK() (*though Var isn't expected*) |
|
27184 | 121 |
| Bound 0 => instantiate' [SOME cxT] [] @{thm abs_I} (*identity: I*) |
24827 | 122 |
| rator$rand => |
27184 | 123 |
if loose_bvar1 (rator,0) then (*C or S*) |
27179
8f29fed3dc9a
ResAxioms.cnf_axiom/cnf_rules_pairs: pass explicit theory context;
wenzelm
parents:
27174
diff
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124 |
if loose_bvar1 (rand,0) then (*S*) |
8f29fed3dc9a
ResAxioms.cnf_axiom/cnf_rules_pairs: pass explicit theory context;
wenzelm
parents:
27174
diff
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125 |
let val crator = cterm_of thy (Abs(x,xT,rator)) |
8f29fed3dc9a
ResAxioms.cnf_axiom/cnf_rules_pairs: pass explicit theory context;
wenzelm
parents:
27174
diff
changeset
|
126 |
val crand = cterm_of thy (Abs(x,xT,rand)) |
27184 | 127 |
val abs_S' = cterm_instantiate [(f_S,crator),(g_S,crand)] @{thm abs_S} |
128 |
val (_,rhs) = Thm.dest_equals (cprop_of abs_S') |
|
27179
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ResAxioms.cnf_axiom/cnf_rules_pairs: pass explicit theory context;
wenzelm
parents:
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129 |
in |
8f29fed3dc9a
ResAxioms.cnf_axiom/cnf_rules_pairs: pass explicit theory context;
wenzelm
parents:
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130 |
Thm.transitive abs_S' (Conv.binop_conv abstract rhs) |
8f29fed3dc9a
ResAxioms.cnf_axiom/cnf_rules_pairs: pass explicit theory context;
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parents:
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changeset
|
131 |
end |
8f29fed3dc9a
ResAxioms.cnf_axiom/cnf_rules_pairs: pass explicit theory context;
wenzelm
parents:
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diff
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132 |
else (*C*) |
8f29fed3dc9a
ResAxioms.cnf_axiom/cnf_rules_pairs: pass explicit theory context;
wenzelm
parents:
27174
diff
changeset
|
133 |
let val crator = cterm_of thy (Abs(x,xT,rator)) |
27184 | 134 |
val abs_C' = cterm_instantiate [(f_C,crator),(g_C,cterm_of thy rand)] @{thm abs_C} |
135 |
val (_,rhs) = Thm.dest_equals (cprop_of abs_C') |
|
27179
8f29fed3dc9a
ResAxioms.cnf_axiom/cnf_rules_pairs: pass explicit theory context;
wenzelm
parents:
27174
diff
changeset
|
136 |
in |
8f29fed3dc9a
ResAxioms.cnf_axiom/cnf_rules_pairs: pass explicit theory context;
wenzelm
parents:
27174
diff
changeset
|
137 |
Thm.transitive abs_C' (Conv.fun_conv (Conv.arg_conv abstract) rhs) |
8f29fed3dc9a
ResAxioms.cnf_axiom/cnf_rules_pairs: pass explicit theory context;
wenzelm
parents:
27174
diff
changeset
|
138 |
end |
27184 | 139 |
else if loose_bvar1 (rand,0) then (*B or eta*) |
36945 | 140 |
if rand = Bound 0 then Thm.eta_conversion ct |
27179
8f29fed3dc9a
ResAxioms.cnf_axiom/cnf_rules_pairs: pass explicit theory context;
wenzelm
parents:
27174
diff
changeset
|
141 |
else (*B*) |
8f29fed3dc9a
ResAxioms.cnf_axiom/cnf_rules_pairs: pass explicit theory context;
wenzelm
parents:
27174
diff
changeset
|
142 |
let val crand = cterm_of thy (Abs(x,xT,rand)) |
8f29fed3dc9a
ResAxioms.cnf_axiom/cnf_rules_pairs: pass explicit theory context;
wenzelm
parents:
27174
diff
changeset
|
143 |
val crator = cterm_of thy rator |
27184 | 144 |
val abs_B' = cterm_instantiate [(f_B,crator),(g_B,crand)] @{thm abs_B} |
145 |
val (_,rhs) = Thm.dest_equals (cprop_of abs_B') |
|
37349 | 146 |
in Thm.transitive abs_B' (Conv.arg_conv abstract rhs) end |
27179
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ResAxioms.cnf_axiom/cnf_rules_pairs: pass explicit theory context;
wenzelm
parents:
27174
diff
changeset
|
147 |
else makeK() |
37349 | 148 |
| _ => raise Fail "abstract: Bad term" |
24827 | 149 |
end; |
20863
4ee61dbf192d
improvements to abstraction, ensuring more re-use of abstraction functions
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parents:
20789
diff
changeset
|
150 |
|
37349 | 151 |
(* Traverse a theorem, remplacing lambda-abstractions with combinators. *) |
38001
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blanchet
parents:
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diff
changeset
|
152 |
fun introduce_combinators_in_cterm ct = |
37416
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no point in introducing combinators for inlined Skolem functions
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parents:
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diff
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|
153 |
if is_quasi_lambda_free (term_of ct) then |
37349 | 154 |
Thm.reflexive ct |
155 |
else case term_of ct of |
|
156 |
Abs _ => |
|
157 |
let |
|
158 |
val (cv, cta) = Thm.dest_abs NONE ct |
|
159 |
val (v, _) = dest_Free (term_of cv) |
|
38001
a9b47b85ca24
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parents:
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diff
changeset
|
160 |
val u_th = introduce_combinators_in_cterm cta |
37349 | 161 |
val cu = Thm.rhs_of u_th |
162 |
val comb_eq = abstract (Thm.cabs cv cu) |
|
163 |
in Thm.transitive (Thm.abstract_rule v cv u_th) comb_eq end |
|
164 |
| _ $ _ => |
|
165 |
let val (ct1, ct2) = Thm.dest_comb ct in |
|
38001
a9b47b85ca24
reintroduced more preprocessing steps to Sledgehammer, adapted to the new FOF setting
blanchet
parents:
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diff
changeset
|
166 |
Thm.combination (introduce_combinators_in_cterm ct1) |
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blanchet
parents:
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diff
changeset
|
167 |
(introduce_combinators_in_cterm ct2) |
37349 | 168 |
end |
169 |
||
38001
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parents:
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diff
changeset
|
170 |
fun introduce_combinators_in_theorem th = |
37416
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no point in introducing combinators for inlined Skolem functions
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parents:
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diff
changeset
|
171 |
if is_quasi_lambda_free (prop_of th) then |
37349 | 172 |
th |
24827 | 173 |
else |
37349 | 174 |
let |
175 |
val th = Drule.eta_contraction_rule th |
|
38001
a9b47b85ca24
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blanchet
parents:
38000
diff
changeset
|
176 |
val eqth = introduce_combinators_in_cterm (cprop_of th) |
37349 | 177 |
in Thm.equal_elim eqth th end |
178 |
handle THM (msg, _, _) => |
|
179 |
(warning ("Error in the combinator translation of " ^ |
|
180 |
Display.string_of_thm_without_context th ^ |
|
181 |
"\nException message: " ^ msg ^ "."); |
|
182 |
(* A type variable of sort "{}" will make abstraction fail. *) |
|
183 |
TrueI) |
|
16009 | 184 |
|
185 |
(*cterms are used throughout for efficiency*) |
|
38280 | 186 |
val cTrueprop = cterm_of @{theory HOL} HOLogic.Trueprop; |
16009 | 187 |
|
188 |
(*Given an abstraction over n variables, replace the bound variables by free |
|
189 |
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
|
190 |
fun c_variant_abs_multi (ct0, vars) = |
16009 | 191 |
let val (cv,ct) = Thm.dest_abs NONE ct0 |
192 |
in c_variant_abs_multi (ct, cv::vars) end |
|
193 |
handle CTERM _ => (ct0, rev vars); |
|
194 |
||
39355 | 195 |
val skolem_def_raw = @{thms skolem_def_raw} |
37617
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
196 |
|
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
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diff
changeset
|
197 |
(* Given the definition of a Skolem function, return a theorem to replace |
f73cd4069f69
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blanchet
parents:
37616
diff
changeset
|
198 |
an existential formula by a use of that function. |
18141
89e2e8bed08f
Skolemization by inference, but not quite finished
paulson
parents:
18009
diff
changeset
|
199 |
Example: "EX x. x : A & x ~: B ==> sko A B : A & sko A B ~: B" [.] *) |
39886
8a9f0c97d550
first step towards a new skolemizer that doesn't require "Eps"
blanchet
parents:
39721
diff
changeset
|
200 |
fun old_skolem_theorem_from_def thy rhs0 = |
37399
34f080a12063
proper polymorphic Skolemization of uncached facts + synchronization of caching and relevance filter
blanchet
parents:
37349
diff
changeset
|
201 |
let |
38280 | 202 |
val rhs = rhs0 |> Type.legacy_freeze_thaw |> #1 |> cterm_of thy |
37617
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
203 |
val rhs' = rhs |> Thm.dest_comb |> snd |
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
204 |
val (ch, frees) = c_variant_abs_multi (rhs', []) |
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
205 |
val (hilbert, cabs) = ch |> Thm.dest_comb |>> term_of |
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
206 |
val T = |
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
207 |
case hilbert of |
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
208 |
Const (@{const_name Eps}, Type (@{type_name fun}, [_, T])) => T |
39886
8a9f0c97d550
first step towards a new skolemizer that doesn't require "Eps"
blanchet
parents:
39721
diff
changeset
|
209 |
| _ => 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
|
210 |
[hilbert]) |
38280 | 211 |
val cex = cterm_of thy (HOLogic.exists_const T) |
37617
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
212 |
val ex_tm = Thm.capply cTrueprop (Thm.capply cex cabs) |
37629 | 213 |
val conc = |
37617
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
214 |
Drule.list_comb (rhs, frees) |
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
215 |
|> Drule.beta_conv cabs |> Thm.capply cTrueprop |
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
216 |
fun tacf [prem] = |
39355 | 217 |
rewrite_goals_tac skolem_def_raw |
218 |
THEN rtac ((prem |> rewrite_rule skolem_def_raw) RS @{thm someI_ex}) 1 |
|
37617
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
219 |
in |
37629 | 220 |
Goal.prove_internal [ex_tm] conc tacf |
221 |
|> forall_intr_list frees |
|
222 |
|> Thm.forall_elim_vars 0 (*Introduce Vars, but don't discharge defs.*) |
|
223 |
|> Thm.varifyT_global |
|
37617
f73cd4069f69
always perform "inline" skolemization, polymorphism or not, Skolem cache or not
blanchet
parents:
37616
diff
changeset
|
224 |
end |
24742
73b8b42a36b6
removal of some "ref"s from res_axioms.ML; a side-effect is that the ordering
paulson
parents:
24669
diff
changeset
|
225 |
|
39036
dff91b90d74c
use definitional CNFs in Metis rather than plain CNF, following a suggestion by Joe Hurd;
blanchet
parents:
38864
diff
changeset
|
226 |
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
|
227 |
let |
dff91b90d74c
use definitional CNFs in Metis rather than plain CNF, following a suggestion by Joe Hurd;
blanchet
parents:
38864
diff
changeset
|
228 |
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
|
229 |
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
|
230 |
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
|
231 |
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
|
232 |
|
39887
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
233 |
val kill_quantifiers = |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
234 |
let |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
235 |
fun conv pos ct = |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
236 |
ct |> (case term_of ct of |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
237 |
Const (s, _) $ Abs (s', _, _) => |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
238 |
if s = @{const_name all} orelse s = @{const_name All} orelse |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
239 |
s = @{const_name Ex} then |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
240 |
Thm.dest_comb #> snd |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
241 |
#> Thm.dest_abs (SOME (s' |> pos = (s = @{const_name Ex}) |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
242 |
? prefix new_skolem_var_prefix)) |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
243 |
#> snd #> conv pos |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
244 |
else |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
245 |
Conv.all_conv |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
246 |
| Const (s, _) $ _ $ _ => |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
247 |
if s = @{const_name "==>"} orelse |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
248 |
s = @{const_name HOL.implies} then |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
249 |
Conv.combination_conv (Conv.arg_conv (conv (not pos))) |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
250 |
(conv pos) |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
251 |
else if s = @{const_name HOL.conj} orelse |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
252 |
s = @{const_name HOL.disj} then |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
253 |
Conv.combination_conv (Conv.arg_conv (conv pos)) (conv pos) |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
254 |
else |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
255 |
Conv.all_conv |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
256 |
| Const (s, _) $ _ => |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
257 |
if s = @{const_name Trueprop} then |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
258 |
Conv.arg_conv (conv pos) |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
259 |
else if s = @{const_name Not} then |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
260 |
Conv.arg_conv (conv (not pos)) |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
261 |
else |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
262 |
Conv.all_conv |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
263 |
| _ => Conv.all_conv) |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
264 |
in |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
265 |
conv true #> Drule.export_without_context |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
266 |
#> cprop_of #> Thm.dest_equals #> snd |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
267 |
end |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
268 |
|
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
269 |
val pull_out_quant_ss = |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
270 |
MetaSimplifier.clear_ss HOL_basic_ss |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
271 |
addsimps @{thms all_simps[symmetric]} |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
272 |
|
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
273 |
(* Converts an Isabelle theorem into NNF. *) |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
274 |
fun nnf_axiom new_skolemizer th ctxt = |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
275 |
let |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
276 |
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
|
277 |
val th = |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
278 |
th |> transform_elim_theorem |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
279 |
|> zero_var_indexes |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
280 |
|> 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
|
281 |
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
|
282 |
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
|
283 |
|> extensionalize_theorem |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
284 |
|> Meson.make_nnf ctxt |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
285 |
in |
74939e2afb95
second step in introducing the new Skolemizer -- notably, added procedure for discharging Skolem assumptions
blanchet
parents:
39886
diff
changeset
|
286 |
if new_skolemizer then |
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let |
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val th' = th |> Meson.skolemize ctxt |
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|> simplify pull_out_quant_ss |
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290 |
|> Drule.eta_contraction_rule |
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val t = th' |> cprop_of |> kill_quantifiers |> term_of |
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|
292 |
in |
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293 |
if exists_subterm (fn Var ((s, _), _) => |
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294 |
String.isPrefix new_skolem_var_prefix s |
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| _ => false) t then |
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296 |
let |
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297 |
val (ct, ctxt) = |
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298 |
Variable.import_terms true [t] ctxt |
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299 |
|>> the_single |>> cterm_of thy |
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300 |
in (SOME (th', ct), ct |> Thm.assume, ctxt) end |
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301 |
else |
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302 |
(NONE, th, ctxt) |
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303 |
end |
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304 |
else |
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305 |
(NONE, th, ctxt) |
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306 |
end |
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|
307 |
|
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|
308 |
(* Convert a theorem to CNF, with additional premises due to skolemization. *) |
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309 |
fun cnf_axiom thy th = |
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310 |
let |
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311 |
val ctxt0 = Variable.global_thm_context th |
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312 |
val new_skolemizer = Config.get ctxt0 new_skolemizer |
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val (opt, nnf_th, ctxt) = nnf_axiom new_skolemizer th ctxt0 |
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|
314 |
fun aux th = |
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|
315 |
Meson.make_cnf (if new_skolemizer then |
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|
316 |
[] |
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|
317 |
else |
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|
318 |
map (old_skolem_theorem_from_def thy) |
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|
319 |
(old_skolem_defs th)) th ctxt |
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320 |
val (cnf_ths, ctxt) = |
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|
321 |
aux nnf_th |
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322 |
|> (fn ([], _) => aux (to_definitional_cnf_with_quantifiers thy nnf_th) |
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|
323 |
| p => p) |
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324 |
val export = Variable.export ctxt ctxt0 |
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|
325 |
in |
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|
326 |
(opt |> Option.map (singleton export o fst), |
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|
327 |
cnf_ths |> map (introduce_combinators_in_theorem |
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|
328 |
#> (case opt of |
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|
329 |
SOME (_, ct) => Thm.implies_intr ct |
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|
330 |
| NONE => I)) |
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|
331 |
|> export |
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|
332 |
|> Meson.finish_cnf |
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parents:
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|
333 |
|> map Thm.close_derivation) |
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|
334 |
end |
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parents:
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|
335 |
handle THM _ => (NONE, []) |
27184 | 336 |
|
39720
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parents:
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|
337 |
fun meson_general_tac ctxt ths = |
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|
338 |
let |
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parents:
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|
339 |
val thy = ProofContext.theory_of ctxt |
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parents:
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|
340 |
val ctxt0 = Classical.put_claset HOL_cs ctxt |
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parents:
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|
341 |
in Meson.meson_tac ctxt0 (maps (snd o cnf_axiom thy) ths) end |
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|
342 |
|
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parents:
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|
343 |
val setup = |
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|
344 |
new_skolemizer_setup |
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|
345 |
#> Method.setup @{binding meson} (Attrib.thms >> (fn ths => fn ctxt => |
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parents:
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|
346 |
SIMPLE_METHOD' (CHANGED_PROP o meson_general_tac ctxt ths))) |
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parents:
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|
347 |
"MESON resolution proof procedure" |
39720
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parents:
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|
348 |
|
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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|
349 |
end; |