author | krauss |
Fri, 01 Jun 2007 15:57:45 +0200 | |
changeset 23189 | 4574ab8f3b21 |
parent 23056 | 448827ccd9e9 |
child 23203 | a5026e73cfcf |
permissions | -rw-r--r-- |
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First usable version of the new function definition package (HOL/function_packake/...).
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(* Title: HOL/Tools/function_package/fundef_datatype.ML |
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
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ID: $Id$ |
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First usable version of the new function definition package (HOL/function_packake/...).
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Author: Alexander Krauss, TU Muenchen |
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First usable version of the new function definition package (HOL/function_packake/...).
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|
20344 | 5 |
A package for general recursive function definitions. |
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A tactic to prove completeness of datatype patterns. |
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First usable version of the new function definition package (HOL/function_packake/...).
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7 |
*) |
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First usable version of the new function definition package (HOL/function_packake/...).
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|
20344 | 9 |
signature FUNDEF_DATATYPE = |
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First usable version of the new function definition package (HOL/function_packake/...).
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sig |
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val pat_complete_tac: int -> tactic |
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12 |
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20523
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Major update to function package, including new syntax and the (only theoretical)
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val pat_completeness : method |
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First usable version of the new function definition package (HOL/function_packake/...).
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val setup : theory -> theory |
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end |
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|
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structure FundefDatatype : FUNDEF_DATATYPE = |
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First usable version of the new function definition package (HOL/function_packake/...).
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struct |
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19 |
|
21051
c49467a9c1e1
Switched function package to use the new package for inductive predicates.
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20 |
open FundefLib |
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21 |
open FundefCommon |
19770
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HOL/Tools/function_package: Added support for mutual recursive definitions.
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23189 | 23 |
fun check_constr_pattern thy err (Bound _) = () |
24 |
| check_constr_pattern thy err t = |
|
25 |
let |
|
26 |
val (hd, args) = strip_comb t |
|
27 |
in |
|
28 |
(((case DatatypePackage.datatype_of_constr thy (fst (dest_Const hd)) of |
|
29 |
SOME _ => () |
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30 |
| NONE => err t) |
|
31 |
handle TERM ("dest_Const", _) => err t); |
|
32 |
map (check_constr_pattern thy err) args; |
|
33 |
()) |
|
34 |
end |
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35 |
||
36 |
||
37 |
fun check_pats ctxt geq = |
|
38 |
let |
|
39 |
fun err str = error (cat_lines ["Malformed \"fun\" definition:", |
|
40 |
str, |
|
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ProofContext.string_of_term ctxt geq]) |
|
42 |
val thy = ProofContext.theory_of ctxt |
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43 |
||
44 |
val (fname, qs, gs, args, rhs) = split_def geq |
|
45 |
||
46 |
val _ = if not (null gs) then err "Conditional equations not allowed with \"fun\"" else () |
|
47 |
val _ = map (check_constr_pattern thy (fn t => err "Not a constructor pattern")) args |
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48 |
||
49 |
(* just count occurrences to check linearity *) |
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val _ = if fold (fold_aterms (fn Bound _ => curry (op +) 1 | _ => I)) args 0 < length qs |
|
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then err "Nonlinear pattern" else () |
|
52 |
in |
|
53 |
() |
|
54 |
end |
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55 |
||
56 |
||
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fun mk_argvar i T = Free ("_av" ^ (string_of_int i), T) |
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fun mk_patvar i T = Free ("_pv" ^ (string_of_int i), T) |
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|
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fun inst_free var inst thm = |
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forall_elim inst (forall_intr var thm) |
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|
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fun inst_case_thm thy x P thm = |
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let |
20344 | 66 |
val [Pv, xv] = term_vars (prop_of thm) |
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67 |
in |
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cterm_instantiate [(cterm_of thy xv, cterm_of thy x), (cterm_of thy Pv, cterm_of thy P)] thm |
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69 |
end |
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|
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fun invent_vars constr i = |
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73 |
let |
20344 | 74 |
val Ts = binder_types (fastype_of constr) |
75 |
val j = i + length Ts |
|
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val is = i upto (j - 1) |
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val avs = map2 mk_argvar is Ts |
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val pvs = map2 mk_patvar is Ts |
|
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79 |
in |
20344 | 80 |
(avs, pvs, j) |
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First usable version of the new function definition package (HOL/function_packake/...).
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81 |
end |
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82 |
|
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83 |
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fun filter_pats thy cons pvars [] = [] |
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| filter_pats thy cons pvars (([], thm) :: pts) = raise Match |
20344 | 86 |
| filter_pats thy cons pvars ((pat :: pats, thm) :: pts) = |
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case pat of |
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Free _ => let val inst = list_comb (cons, pvars) |
89 |
in (inst :: pats, inst_free (cterm_of thy pat) (cterm_of thy inst) thm) |
|
90 |
:: (filter_pats thy cons pvars pts) end |
|
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| _ => if fst (strip_comb pat) = cons |
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then (pat :: pats, thm) :: (filter_pats thy cons pvars pts) |
93 |
else filter_pats thy cons pvars pts |
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94 |
|
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95 |
|
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First usable version of the new function definition package (HOL/function_packake/...).
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fun inst_constrs_of thy (T as Type (name, _)) = |
20344 | 97 |
map (fn (Cn,CT) => Envir.subst_TVars (Sign.typ_match thy (body_type CT, T) Vartab.empty) (Const (Cn, CT))) |
98 |
(the (DatatypePackage.get_datatype_constrs thy name)) |
|
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99 |
| inst_constrs_of thy _ = raise Match |
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100 |
|
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First usable version of the new function definition package (HOL/function_packake/...).
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101 |
|
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First usable version of the new function definition package (HOL/function_packake/...).
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102 |
fun transform_pat thy avars c_assum ([] , thm) = raise Match |
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
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103 |
| transform_pat thy avars c_assum (pat :: pats, thm) = |
d3e2f532459a
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104 |
let |
20344 | 105 |
val (_, subps) = strip_comb pat |
106 |
val eqs = map (cterm_of thy o HOLogic.mk_Trueprop o HOLogic.mk_eq) (avars ~~ subps) |
|
107 |
val a_eqs = map assume eqs |
|
108 |
val c_eq_pat = simplify (HOL_basic_ss addsimps a_eqs) c_assum |
|
19564
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109 |
in |
20344 | 110 |
(subps @ pats, fold_rev implies_intr eqs |
111 |
(implies_elim thm c_eq_pat)) |
|
19564
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112 |
end |
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First usable version of the new function definition package (HOL/function_packake/...).
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113 |
|
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114 |
|
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115 |
exception COMPLETENESS |
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116 |
|
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fun constr_case thy P idx (v :: vs) pats cons = |
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118 |
let |
20344 | 119 |
val (avars, pvars, newidx) = invent_vars cons idx |
120 |
val c_hyp = cterm_of thy (HOLogic.mk_Trueprop (HOLogic.mk_eq (v, list_comb (cons, avars)))) |
|
121 |
val c_assum = assume c_hyp |
|
122 |
val newpats = map (transform_pat thy avars c_assum) (filter_pats thy cons pvars pats) |
|
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123 |
in |
20344 | 124 |
o_alg thy P newidx (avars @ vs) newpats |
125 |
|> implies_intr c_hyp |
|
126 |
|> fold_rev (forall_intr o cterm_of thy) avars |
|
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127 |
end |
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First usable version of the new function definition package (HOL/function_packake/...).
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128 |
| constr_case _ _ _ _ _ _ = raise Match |
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First usable version of the new function definition package (HOL/function_packake/...).
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129 |
and o_alg thy P idx [] (([], Pthm) :: _) = Pthm |
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130 |
| o_alg thy P idx (v :: vs) [] = raise COMPLETENESS |
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First usable version of the new function definition package (HOL/function_packake/...).
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131 |
| o_alg thy P idx (v :: vs) pts = |
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132 |
if forall (is_Free o hd o fst) pts (* Var case *) |
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133 |
then o_alg thy P idx vs (map (fn (pv :: pats, thm) => |
20344 | 134 |
(pats, refl RS (inst_free (cterm_of thy pv) (cterm_of thy v) thm))) pts) |
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First usable version of the new function definition package (HOL/function_packake/...).
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135 |
else (* Cons case *) |
20344 | 136 |
let |
137 |
val T = fastype_of v |
|
138 |
val (tname, _) = dest_Type T |
|
139 |
val {exhaustion=case_thm, ...} = DatatypePackage.the_datatype thy tname |
|
140 |
val constrs = inst_constrs_of thy T |
|
141 |
val c_cases = map (constr_case thy P idx (v :: vs) pts) constrs |
|
142 |
in |
|
143 |
inst_case_thm thy v P case_thm |
|
144 |
|> fold (curry op COMP) c_cases |
|
145 |
end |
|
19564
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146 |
| o_alg _ _ _ _ _ = raise Match |
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
krauss
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|
147 |
|
20344 | 148 |
|
19564
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First usable version of the new function definition package (HOL/function_packake/...).
krauss
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|
149 |
fun prove_completeness thy x P qss pats = |
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
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|
150 |
let |
20344 | 151 |
fun mk_assum qs pat = Logic.mk_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (x,pat)), |
152 |
HOLogic.mk_Trueprop P) |
|
153 |
|> fold_rev mk_forall qs |
|
154 |
|> cterm_of thy |
|
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First usable version of the new function definition package (HOL/function_packake/...).
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155 |
|
20344 | 156 |
val hyps = map2 mk_assum qss pats |
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First usable version of the new function definition package (HOL/function_packake/...).
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157 |
|
20344 | 158 |
fun inst_hyps hyp qs = fold (forall_elim o cterm_of thy) qs (assume hyp) |
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First usable version of the new function definition package (HOL/function_packake/...).
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159 |
|
20344 | 160 |
val assums = map2 inst_hyps hyps qss |
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|
161 |
in |
20344 | 162 |
o_alg thy P 2 [x] (map2 (pair o single) pats assums) |
163 |
|> fold_rev implies_intr hyps |
|
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164 |
end |
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First usable version of the new function definition package (HOL/function_packake/...).
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|
165 |
|
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First usable version of the new function definition package (HOL/function_packake/...).
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|
166 |
|
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First usable version of the new function definition package (HOL/function_packake/...).
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167 |
|
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First usable version of the new function definition package (HOL/function_packake/...).
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|
168 |
fun pat_complete_tac i thm = |
20344 | 169 |
let |
19922 | 170 |
val thy = theory_of_thm thm |
171 |
||
20344 | 172 |
val subgoal = nth (prems_of thm) (i - 1) (* FIXME SUBGOAL tactical *) |
19922 | 173 |
|
174 |
val ([P, x], subgf) = dest_all_all subgoal |
|
175 |
||
20344 | 176 |
val assums = Logic.strip_imp_prems subgf |
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177 |
|
20344 | 178 |
fun pat_of assum = |
179 |
let |
|
180 |
val (qs, imp) = dest_all_all assum |
|
181 |
in |
|
182 |
case Logic.dest_implies imp of |
|
183 |
(_ $ (_ $ _ $ pat), _) => (qs, pat) |
|
184 |
| _ => raise COMPLETENESS |
|
185 |
end |
|
19564
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First usable version of the new function definition package (HOL/function_packake/...).
krauss
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|
186 |
|
20344 | 187 |
val (qss, pats) = split_list (map pat_of assums) |
188 |
||
189 |
val complete_thm = prove_completeness thy x P qss pats |
|
19922 | 190 |
|> forall_intr (cterm_of thy x) |
191 |
|> forall_intr (cterm_of thy P) |
|
19564
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First usable version of the new function definition package (HOL/function_packake/...).
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|
192 |
in |
20344 | 193 |
Seq.single (Drule.compose_single(complete_thm, i, thm)) |
19564
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First usable version of the new function definition package (HOL/function_packake/...).
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|
194 |
end |
d3e2f532459a
First usable version of the new function definition package (HOL/function_packake/...).
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|
195 |
handle COMPLETENESS => Seq.empty |
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val pat_completeness = Method.SIMPLE_METHOD' pat_complete_tac |
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val by_pat_completeness_simp = |
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Proof.global_terminal_proof |
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(Method.Basic (K pat_completeness), |
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SOME (Method.Source_i (Args.src (("HOL.auto", []), Position.none)))) |
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val termination_by_lexicographic_order = |
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FundefPackage.setup_termination_proof NONE |
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#> Proof.global_terminal_proof (Method.Basic (LexicographicOrder.lexicographic_order []), NONE) |
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val setup = |
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Method.add_methods [("pat_completeness", Method.no_args pat_completeness, |
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"Completeness prover for datatype patterns")] |
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local structure P = OuterParse and K = OuterKeyword in |
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fun fun_cmd config fixes statements lthy = |
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lthy |
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|> FundefPackage.add_fundef fixes statements config |
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|> by_pat_completeness_simp |
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|> termination_by_lexicographic_order |
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|
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val funP = |
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OuterSyntax.command "fun" "define general recursive functions (short version)" K.thy_decl |
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(fundef_parser FundefCommon.fun_config |
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>> (fn ((config, fixes), statements) => |
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(Toplevel.local_theory (target_of config) (fun_cmd config fixes statements)))); |
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val _ = OuterSyntax.add_parsers [funP]; |
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end |
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end |