author | bulwahn |
Tue, 23 Feb 2010 13:36:15 +0100 | |
changeset 35324 | c9f428269b38 |
parent 34948 | 2d5f2a9f7601 |
child 35411 | cafb74a131da |
permissions | -rw-r--r-- |
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(* Title: HOL/Tools/Predicate_Compile/predicate_compile_pred.ML |
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Author: Lukas Bulwahn, TU Muenchen |
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Preprocessing definitions of predicates to introduction rules. |
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*) |
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signature PREDICATE_COMPILE_PRED = |
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sig |
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(* preprocesses an equation to a set of intro rules; defines new constants *) |
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val preprocess : Predicate_Compile_Aux.options -> (string * thm list) -> theory |
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-> ((string * thm list) list * theory) |
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val flat_higher_order_arguments : ((string * thm list) list * theory) |
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-> ((string * thm list) list * ((string * thm list) list * theory)) |
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end; |
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structure Predicate_Compile_Pred : PREDICATE_COMPILE_PRED = |
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struct |
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open Predicate_Compile_Aux |
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fun datatype_names_of_case_name thy case_name = |
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map (#1 o #2) (#descr (the (Datatype_Data.info_of_case thy case_name))) |
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fun make_case_rewrites new_type_names descr sorts thy = |
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let |
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val case_combs = Datatype_Prop.make_case_combs new_type_names descr sorts thy "f"; |
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fun make comb = |
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let |
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val Type ("fun", [T, T']) = fastype_of comb; |
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val (Const (case_name, _), fs) = strip_comb comb |
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val used = Term.add_tfree_names comb [] |
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val U = TFree (Name.variant used "'t", HOLogic.typeS) |
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val x = Free ("x", T) |
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val f = Free ("f", T' --> U) |
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fun apply_f f' = |
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let |
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val Ts = binder_types (fastype_of f') |
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val bs = map Bound ((length Ts - 1) downto 0) |
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in |
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fold (curry absdummy) (rev Ts) (f $ (list_comb (f', bs))) |
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end |
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val fs' = map apply_f fs |
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val case_c' = Const (case_name, (map fastype_of fs') @ [T] ---> U) |
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HOLogic.mk_eq (f $ (comb $ x), list_comb (case_c', fs') $ x) |
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end |
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map make case_combs |
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end |
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fun case_rewrites thy Tcon = |
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let |
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val info = Datatype.the_info thy Tcon |
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val descr = #descr info |
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val sorts = #sorts info |
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val typ_names = the_default [Tcon] (#alt_names info) |
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in |
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map (Drule.export_without_context o Skip_Proof.make_thm thy o HOLogic.mk_Trueprop) |
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(make_case_rewrites typ_names [descr] sorts thy) |
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end |
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fun instantiated_case_rewrites thy Tcon = |
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let |
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val rew_ths = case_rewrites thy Tcon |
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val ctxt = ProofContext.init thy |
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fun instantiate th = |
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let |
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val f = (fst (strip_comb (fst (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of th)))))) |
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val Type ("fun", [uninst_T, uninst_T']) = fastype_of f |
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val ([tname, tname', uname, yname], ctxt') = Variable.add_fixes ["'t", "'t'", "'u", "y"] ctxt |
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val T = TFree (tname, HOLogic.typeS) |
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val T' = TFree (tname', HOLogic.typeS) |
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val U = TFree (uname, HOLogic.typeS) |
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val y = Free (yname, U) |
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val f' = absdummy (U --> T', Bound 0 $ y) |
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val th' = Thm.certify_instantiate |
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([(dest_TVar uninst_T, U --> T'), (dest_TVar uninst_T', T')], |
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[((fst (dest_Var f), (U --> T') --> T'), f')]) th |
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val [th'] = Variable.export ctxt' ctxt [th'] |
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in |
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th' |
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end |
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in |
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map instantiate rew_ths |
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end |
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88 |
|
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89 |
fun is_compound ((Const ("Not", _)) $ t) = |
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90 |
error "is_compound: Negation should not occur; preprocessing is defect" |
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91 |
| is_compound ((Const ("Ex", _)) $ _) = true |
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92 |
| is_compound ((Const (@{const_name "op |"}, _)) $ _ $ _) = true |
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93 |
| is_compound ((Const ("op &", _)) $ _ $ _) = |
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|
94 |
error "is_compound: Conjunction should not occur; preprocessing is defect" |
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|
95 |
| is_compound _ = false |
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|
96 |
|
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97 |
fun flatten constname atom (defs, thy) = |
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|
98 |
if is_compound atom then |
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|
99 |
let |
35324
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100 |
val atom = Envir.beta_norm (Pattern.eta_long [] atom) |
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101 |
val constname = Name.variant (map (Long_Name.base_name o fst) defs) |
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102 |
((Long_Name.base_name constname) ^ "_aux") |
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|
103 |
val full_constname = Sign.full_bname thy constname |
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|
104 |
val (params, args) = List.partition (is_predT o fastype_of) |
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|
105 |
(map Free (Term.add_frees atom [])) |
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|
106 |
val constT = map fastype_of (params @ args) ---> HOLogic.boolT |
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|
107 |
val lhs = list_comb (Const (full_constname, constT), params @ args) |
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|
108 |
val def = Logic.mk_equals (lhs, atom) |
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|
109 |
val ([definition], thy') = thy |
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|
110 |
|> Sign.add_consts_i [(Binding.name constname, constT, NoSyn)] |
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111 |
|> PureThy.add_defs false [((Binding.name (constname ^ "_def"), def), [])] |
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|
112 |
in |
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113 |
(lhs, ((full_constname, [definition]) :: defs, thy')) |
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|
114 |
end |
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115 |
else |
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116 |
(case (fst (strip_comb atom)) of |
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117 |
(Const (@{const_name If}, _)) => let |
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118 |
val if_beta = @{lemma "(if c then x else y) z = (if c then x z else y z)" by simp} |
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119 |
val atom' = MetaSimplifier.rewrite_term thy |
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120 |
(map (fn th => th RS @{thm eq_reflection}) [@{thm if_bool_eq_disj}, if_beta]) [] atom |
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121 |
val _ = assert (not (atom = atom')) |
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122 |
in |
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|
123 |
flatten constname atom' (defs, thy) |
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124 |
end |
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125 |
| _ => |
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126 |
if (has_split_thm thy (fst (strip_comb atom))) then |
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127 |
let |
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|
128 |
val (f, args) = strip_comb atom |
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129 |
val split_thm = prepare_split_thm (ProofContext.init thy) (the (find_split_thm' thy f)) |
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130 |
(* TODO: contextify things - this line is to unvarify the split_thm *) |
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|
131 |
(*val ((_, [isplit_thm]), _) = Variable.import true [split_thm] (ProofContext.init thy)*) |
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|
132 |
val (assms, concl) = Logic.strip_horn (Thm.prop_of split_thm) |
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|
133 |
val (P, [split_t]) = strip_comb (HOLogic.dest_Trueprop concl) |
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|
134 |
val Tcons = datatype_names_of_case_name thy (fst (dest_Const f)) |
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|
135 |
val ths = maps (instantiated_case_rewrites thy) Tcons |
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|
136 |
val atom = MetaSimplifier.rewrite_term thy |
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|
137 |
(map (fn th => th RS @{thm eq_reflection}) ths) [] atom |
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|
138 |
val (f, args) = strip_comb atom |
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|
139 |
val subst = Pattern.match thy (split_t, atom) (Vartab.empty, Vartab.empty) |
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|
140 |
val (_, split_args) = strip_comb split_t |
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|
141 |
val match = split_args ~~ args |
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adopting mutabelle and quickcheck to return timing information; exporting make_case_combs in datatype package for predicate compiler; adding Spec_Rules declaration for tail recursive functions; improving the predicate compiler and function flattening
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|
142 |
|
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|
143 |
(* |
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adopting mutabelle and quickcheck to return timing information; exporting make_case_combs in datatype package for predicate compiler; adding Spec_Rules declaration for tail recursive functions; improving the predicate compiler and function flattening
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|
144 |
fun mk_prems_of_assm assm = |
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|
145 |
let |
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adopting mutabelle and quickcheck to return timing information; exporting make_case_combs in datatype package for predicate compiler; adding Spec_Rules declaration for tail recursive functions; improving the predicate compiler and function flattening
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|
146 |
val (vTs, assm') = strip_all (Envir.beta_norm (Envir.subst_term subst assm)) |
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adopting mutabelle and quickcheck to return timing information; exporting make_case_combs in datatype package for predicate compiler; adding Spec_Rules declaration for tail recursive functions; improving the predicate compiler and function flattening
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|
147 |
val names = [] (* TODO *) |
c9f428269b38
adopting mutabelle and quickcheck to return timing information; exporting make_case_combs in datatype package for predicate compiler; adding Spec_Rules declaration for tail recursive functions; improving the predicate compiler and function flattening
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|
148 |
val var_names = Name.variant_list names (map fst vTs) |
c9f428269b38
adopting mutabelle and quickcheck to return timing information; exporting make_case_combs in datatype package for predicate compiler; adding Spec_Rules declaration for tail recursive functions; improving the predicate compiler and function flattening
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|
149 |
val vars = map Free (var_names ~~ (map snd vTs)) |
c9f428269b38
adopting mutabelle and quickcheck to return timing information; exporting make_case_combs in datatype package for predicate compiler; adding Spec_Rules declaration for tail recursive functions; improving the predicate compiler and function flattening
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|
150 |
val (prems', pre_res) = Logic.strip_horn (subst_bounds (rev vars, assm')) |
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adopting mutabelle and quickcheck to return timing information; exporting make_case_combs in datatype package for predicate compiler; adding Spec_Rules declaration for tail recursive functions; improving the predicate compiler and function flattening
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|
151 |
val (HOLogic.dest_eq (HOLogic.dest_Trueprop prem)) |
c9f428269b38
adopting mutabelle and quickcheck to return timing information; exporting make_case_combs in datatype package for predicate compiler; adding Spec_Rules declaration for tail recursive functions; improving the predicate compiler and function flattening
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|
152 |
val (_, [inner_t]) = strip_comb (HOLogic.dest_Trueprop pre_res) |
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|
153 |
in |
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adopting mutabelle and quickcheck to return timing information; exporting make_case_combs in datatype package for predicate compiler; adding Spec_Rules declaration for tail recursive functions; improving the predicate compiler and function flattening
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|
154 |
(*mk_prems' inner_t (var_names @ names, prems' @ prems)*) error "asda" |
c9f428269b38
adopting mutabelle and quickcheck to return timing information; exporting make_case_combs in datatype package for predicate compiler; adding Spec_Rules declaration for tail recursive functions; improving the predicate compiler and function flattening
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|
155 |
end |
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adopting mutabelle and quickcheck to return timing information; exporting make_case_combs in datatype package for predicate compiler; adding Spec_Rules declaration for tail recursive functions; improving the predicate compiler and function flattening
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|
156 |
*) |
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adopting mutabelle and quickcheck to return timing information; exporting make_case_combs in datatype package for predicate compiler; adding Spec_Rules declaration for tail recursive functions; improving the predicate compiler and function flattening
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|
157 |
val names = Term.add_free_names atom [] |
c9f428269b38
adopting mutabelle and quickcheck to return timing information; exporting make_case_combs in datatype package for predicate compiler; adding Spec_Rules declaration for tail recursive functions; improving the predicate compiler and function flattening
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|
158 |
val frees = map Free (Term.add_frees atom []) |
c9f428269b38
adopting mutabelle and quickcheck to return timing information; exporting make_case_combs in datatype package for predicate compiler; adding Spec_Rules declaration for tail recursive functions; improving the predicate compiler and function flattening
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|
159 |
val constname = Name.variant (map (Long_Name.base_name o fst) defs) |
c9f428269b38
adopting mutabelle and quickcheck to return timing information; exporting make_case_combs in datatype package for predicate compiler; adding Spec_Rules declaration for tail recursive functions; improving the predicate compiler and function flattening
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|
160 |
((Long_Name.base_name constname) ^ "_aux") |
c9f428269b38
adopting mutabelle and quickcheck to return timing information; exporting make_case_combs in datatype package for predicate compiler; adding Spec_Rules declaration for tail recursive functions; improving the predicate compiler and function flattening
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|
161 |
val full_constname = Sign.full_bname thy constname |
c9f428269b38
adopting mutabelle and quickcheck to return timing information; exporting make_case_combs in datatype package for predicate compiler; adding Spec_Rules declaration for tail recursive functions; improving the predicate compiler and function flattening
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|
162 |
val constT = map fastype_of frees ---> HOLogic.boolT |
c9f428269b38
adopting mutabelle and quickcheck to return timing information; exporting make_case_combs in datatype package for predicate compiler; adding Spec_Rules declaration for tail recursive functions; improving the predicate compiler and function flattening
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|
163 |
val lhs = list_comb (Const (full_constname, constT), frees) |
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adopting mutabelle and quickcheck to return timing information; exporting make_case_combs in datatype package for predicate compiler; adding Spec_Rules declaration for tail recursive functions; improving the predicate compiler and function flattening
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|
164 |
fun new_def assm = |
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adopting mutabelle and quickcheck to return timing information; exporting make_case_combs in datatype package for predicate compiler; adding Spec_Rules declaration for tail recursive functions; improving the predicate compiler and function flattening
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|
165 |
let |
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|
166 |
val (vTs, assm') = strip_all (Envir.beta_norm (Envir.subst_term subst assm)) |
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|
167 |
val var_names = Name.variant_list names (map fst vTs) |
c9f428269b38
adopting mutabelle and quickcheck to return timing information; exporting make_case_combs in datatype package for predicate compiler; adding Spec_Rules declaration for tail recursive functions; improving the predicate compiler and function flattening
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|
168 |
val vars = map Free (var_names ~~ (map snd vTs)) |
c9f428269b38
adopting mutabelle and quickcheck to return timing information; exporting make_case_combs in datatype package for predicate compiler; adding Spec_Rules declaration for tail recursive functions; improving the predicate compiler and function flattening
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|
169 |
val (prems', pre_res) = Logic.strip_horn (subst_bounds (rev vars, assm')) |
c9f428269b38
adopting mutabelle and quickcheck to return timing information; exporting make_case_combs in datatype package for predicate compiler; adding Spec_Rules declaration for tail recursive functions; improving the predicate compiler and function flattening
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|
170 |
fun mk_subst prem = |
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|
171 |
let |
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adopting mutabelle and quickcheck to return timing information; exporting make_case_combs in datatype package for predicate compiler; adding Spec_Rules declaration for tail recursive functions; improving the predicate compiler and function flattening
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|
172 |
val (Free (x, T), r) = HOLogic.dest_eq (HOLogic.dest_Trueprop prem) |
c9f428269b38
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|
173 |
in |
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adopting mutabelle and quickcheck to return timing information; exporting make_case_combs in datatype package for predicate compiler; adding Spec_Rules declaration for tail recursive functions; improving the predicate compiler and function flattening
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|
174 |
((x, T), r) |
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end |
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val subst = map mk_subst prems' |
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val (_, [inner_t]) = strip_comb (HOLogic.dest_Trueprop pre_res) |
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val def = Logic.mk_equals (lhs, inner_t) |
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in |
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Envir.expand_term_frees subst def |
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181 |
end |
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val new_defs = map new_def assms |
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val (definition, thy') = thy |
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|> Sign.add_consts_i [(Binding.name constname, constT, NoSyn)] |
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|> PureThy.add_axioms (map_index |
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(fn (i, t) => ((Binding.name (constname ^ "_def" ^ string_of_int i), t), [])) new_defs) |
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187 |
in |
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(lhs, ((full_constname, definition) :: defs, thy')) |
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189 |
end |
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190 |
else |
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(atom, (defs, thy))) |
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192 |
|
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193 |
fun flatten_intros constname intros thy = |
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let |
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val ctxt = ProofContext.init thy |
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val ((_, intros), ctxt') = Variable.import true intros ctxt |
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val (intros', (local_defs, thy')) = (fold_map o fold_map_atoms) |
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(flatten constname) (map prop_of intros) ([], thy) |
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val tac = fn _ => Skip_Proof.cheat_tac thy' |
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val intros'' = map (fn t => Goal.prove ctxt' [] [] t tac) intros' |
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|> Variable.export ctxt' ctxt |
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in |
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(intros'', (local_defs, thy')) |
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204 |
end |
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205 |
|
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206 |
(* TODO: same function occurs in inductive package *) |
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207 |
fun select_disj 1 1 = [] |
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| select_disj _ 1 = [rtac @{thm disjI1}] |
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| select_disj n i = (rtac @{thm disjI2})::(select_disj (n - 1) (i - 1)); |
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210 |
|
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211 |
fun introrulify thy ths = |
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212 |
let |
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val ctxt = ProofContext.init thy |
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val ((_, ths'), ctxt') = Variable.import true ths ctxt |
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fun introrulify' th = |
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216 |
let |
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217 |
val (lhs, rhs) = Logic.dest_equals (prop_of th) |
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218 |
val frees = Term.add_free_names rhs [] |
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219 |
val disjuncts = HOLogic.dest_disj rhs |
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220 |
val nctxt = Name.make_context frees |
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221 |
fun mk_introrule t = |
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222 |
let |
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223 |
val ((ps, t'), nctxt') = focus_ex t nctxt |
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val prems = map HOLogic.mk_Trueprop (HOLogic.dest_conj t') |
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225 |
in |
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226 |
(ps, Logic.list_implies (prems, HOLogic.mk_Trueprop lhs)) |
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|
227 |
end |
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228 |
val x = ((cterm_of thy) o the_single o snd o strip_comb o HOLogic.dest_Trueprop o fst o |
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229 |
Logic.dest_implies o prop_of) @{thm exI} |
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230 |
fun prove_introrule (index, (ps, introrule)) = |
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|
231 |
let |
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232 |
val tac = Simplifier.simp_tac (HOL_basic_ss addsimps [th]) 1 |
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233 |
THEN EVERY1 (select_disj (length disjuncts) (index + 1)) |
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234 |
THEN (EVERY (map (fn y => |
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|
235 |
rtac (Drule.cterm_instantiate [(x, cterm_of thy (Free y))] @{thm exI}) 1) ps)) |
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236 |
THEN REPEAT_DETERM (rtac @{thm conjI} 1 THEN atac 1) |
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|
237 |
THEN TRY (atac 1) |
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|
238 |
in |
33441
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|
239 |
Goal.prove ctxt' (map fst ps) [] introrule (fn _ => tac) |
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240 |
end |
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|
241 |
in |
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|
242 |
map_index prove_introrule (map mk_introrule disjuncts) |
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|
243 |
end |
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|
244 |
in maps introrulify' ths' |> Variable.export ctxt' ctxt end |
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245 |
|
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246 |
val rewrite = |
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247 |
Simplifier.simplify (HOL_basic_ss addsimps [@{thm Ball_def}, @{thm Bex_def}]) |
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248 |
#> Simplifier.simplify (HOL_basic_ss addsimps [@{thm all_not_ex}]) |
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249 |
#> Conv.fconv_rule nnf_conv |
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|
250 |
#> Simplifier.simplify (HOL_basic_ss addsimps [@{thm ex_disj_distrib}]) |
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|
251 |
|
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252 |
fun split_conjs thy t = |
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253 |
let |
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254 |
fun split_conjunctions (Const (@{const_name "op &"}, _) $ t1 $ t2) = |
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255 |
(split_conjunctions t1) @ (split_conjunctions t2) |
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256 |
| split_conjunctions t = [t] |
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|
257 |
in |
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258 |
map HOLogic.mk_Trueprop (split_conjunctions (HOLogic.dest_Trueprop t)) |
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259 |
end |
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|
260 |
|
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261 |
fun rewrite_intros thy = |
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262 |
Simplifier.full_simplify (HOL_basic_ss addsimps [@{thm all_not_ex}]) |
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263 |
#> Simplifier.full_simplify (HOL_basic_ss addsimps @{thms bool_simps} addsimps @{thms nnf_simps}) |
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264 |
#> map_term thy (maps_premises (split_conjs thy)) |
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265 |
|
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266 |
fun print_specs options thy msg ths = |
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267 |
if show_intermediate_results options then |
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268 |
(tracing (msg); tracing (commas (map (Display.string_of_thm_global thy) ths))) |
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269 |
else |
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270 |
() |
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271 |
(* |
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272 |
fun split_cases thy th = |
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273 |
let |
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274 |
|
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275 |
in |
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276 |
map_term thy th |
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277 |
end |
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278 |
*) |
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279 |
fun preprocess options (constname, specs) thy = |
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280 |
(* case Predicate_Compile_Data.processed_specs thy constname of |
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281 |
SOME specss => (specss, thy) |
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282 |
| NONE =>*) |
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283 |
let |
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284 |
val ctxt = ProofContext.init thy |
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285 |
val intros = |
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286 |
if forall is_pred_equation specs then |
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287 |
map (map_term thy (maps_premises (split_conjs thy))) (introrulify thy (map rewrite specs)) |
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288 |
else if forall (is_intro constname) specs then |
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289 |
map (rewrite_intros thy) specs |
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290 |
else |
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291 |
error ("unexpected specification for constant " ^ quote constname ^ ":\n" |
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292 |
^ commas (map (quote o Display.string_of_thm_global thy) specs)) |
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293 |
val _ = print_specs options thy "normalized intros" intros |
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294 |
(*val intros = maps (split_cases thy) intros*) |
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295 |
val (intros', (local_defs, thy')) = flatten_intros constname intros thy |
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296 |
val (intross, thy'') = fold_map (preprocess options) local_defs thy' |
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297 |
val full_spec = (constname, intros') :: flat intross |
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298 |
(*val thy''' = Predicate_Compile_Data.store_processed_specs (constname, full_spec) thy''*) |
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299 |
in |
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300 |
(full_spec, thy'') |
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301 |
end; |
33250
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302 |
|
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303 |
fun preprocess_term t thy = error "preprocess_pred_term: to implement" |
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304 |
|
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305 |
fun is_Abs (Abs _) = true |
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|
306 |
| is_Abs _ = false |
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|
307 |
|
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308 |
fun flat_higher_order_arguments (intross, thy) = |
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309 |
let |
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310 |
fun process constname atom (new_defs, thy) = |
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311 |
let |
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312 |
val (pred, args) = strip_comb atom |
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313 |
fun replace_abs_arg (abs_arg as Abs _ ) (new_defs, thy) = |
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|
314 |
let |
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|
315 |
val vars = map Var (Term.add_vars abs_arg []) |
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|
316 |
val abs_arg' = Logic.unvarify abs_arg |
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|
317 |
val frees = map Free (Term.add_frees abs_arg' []) |
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|
318 |
val constname = Name.variant (map (Long_Name.base_name o fst) new_defs) |
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319 |
((Long_Name.base_name constname) ^ "_hoaux") |
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|
320 |
val full_constname = Sign.full_bname thy constname |
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|
321 |
val constT = map fastype_of frees ---> (fastype_of abs_arg') |
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|
322 |
val const = Const (full_constname, constT) |
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|
323 |
val lhs = list_comb (const, frees) |
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|
324 |
val def = Logic.mk_equals (lhs, abs_arg') |
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|
325 |
val ([definition], thy') = thy |
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|
326 |
|> Sign.add_consts_i [(Binding.name constname, constT, NoSyn)] |
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|
327 |
|> PureThy.add_defs false [((Binding.name (constname ^ "_def"), def), [])] |
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|
328 |
in |
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|
329 |
(list_comb (Logic.varify const, vars), ((full_constname, [definition])::new_defs, thy')) |
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|
330 |
end |
33403
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|
331 |
| replace_abs_arg arg (new_defs, thy) = |
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|
332 |
if (is_predT (fastype_of arg)) then |
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|
333 |
process constname arg (new_defs, thy) |
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|
334 |
else |
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|
335 |
(arg, (new_defs, thy)) |
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|
336 |
|
35324
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|
337 |
val (args', (new_defs', thy')) = fold_map replace_abs_arg |
c9f428269b38
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|
338 |
(map Envir.beta_eta_contract args) (new_defs, thy) |
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|
339 |
in |
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|
340 |
(list_comb (pred, args'), (new_defs', thy')) |
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|
341 |
end |
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|
342 |
fun flat_intro intro (new_defs, thy) = |
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|
343 |
let |
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|
344 |
val constname = fst (dest_Const (fst (strip_comb |
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|
345 |
(HOLogic.dest_Trueprop (Logic.strip_imp_concl (prop_of intro)))))) |
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|
346 |
val (intro_ts, (new_defs, thy)) = fold_map_atoms (process constname) (prop_of intro) (new_defs, thy) |
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|
347 |
val th = Skip_Proof.make_thm thy intro_ts |
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|
348 |
in |
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|
349 |
(th, (new_defs, thy)) |
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|
350 |
end |
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|
351 |
fun fold_map_spec f [] s = ([], s) |
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|
352 |
| fold_map_spec f ((c, ths) :: specs) s = |
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|
353 |
let |
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|
354 |
val (ths', s') = f ths s |
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|
355 |
val (specs', s'') = fold_map_spec f specs s' |
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|
356 |
in ((c, ths') :: specs', s'') end |
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|
357 |
val (intross', (new_defs, thy')) = fold_map_spec (fold_map flat_intro) intross ([], thy) |
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|
358 |
in |
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|
359 |
(intross', (new_defs, thy')) |
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|
360 |
end |
5c2af18a3237
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changeset
|
361 |
|
5c2af18a3237
including the predicate compiler in HOL-Main; added RandomPredicate monad to Quickcheck
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changeset
|
362 |
end; |