author | wenzelm |
Thu, 18 Oct 2001 21:01:59 +0200 | |
changeset 11827 | 16ef206e6648 |
parent 11822 | 122834177ec1 |
child 11968 | 859a141085d0 |
permissions | -rw-r--r-- |
4866 | 1 |
(* Title: HOL/Tools/typedef_package.ML |
2 |
ID: $Id$ |
|
3 |
Author: Markus Wenzel, TU Muenchen |
|
9230 | 4 |
License: GPL (GNU GENERAL PUBLIC LICENSE) |
4866 | 5 |
|
6357 | 6 |
Gordon/HOL-style type definitions. |
4866 | 7 |
*) |
8 |
||
9 |
signature TYPEDEF_PACKAGE = |
|
10 |
sig |
|
5697 | 11 |
val quiet_mode: bool ref |
5104 | 12 |
val add_typedecls: (bstring * string list * mixfix) list -> theory -> theory |
11822 | 13 |
val add_typedef_x: string -> bstring * string list * mixfix -> |
4866 | 14 |
string -> string list -> thm list -> tactic option -> theory -> theory |
11827 | 15 |
val add_typedef: bool -> string option -> bstring * string list * mixfix -> |
11822 | 16 |
string -> (bstring * bstring) option -> tactic -> theory -> theory * |
17 |
{type_definition: thm, set_def: thm option, Rep: thm, Rep_inverse: thm, |
|
18 |
Abs_inverse: thm, Rep_inject: thm, Abs_inject: thm, Rep_cases: thm, Abs_cases: thm, |
|
19 |
Rep_induct: thm, Abs_induct: thm} |
|
11827 | 20 |
val add_typedef_i: bool -> string option -> bstring * string list * mixfix -> |
11822 | 21 |
term -> (bstring * bstring) option -> tactic -> theory -> theory * |
22 |
{type_definition: thm, set_def: thm option, Rep: thm, Rep_inverse: thm, |
|
23 |
Abs_inverse: thm, Rep_inject: thm, Abs_inject: thm, Rep_cases: thm, Abs_cases: thm, |
|
24 |
Rep_induct: thm, Abs_induct: thm} |
|
11744 | 25 |
val typedef_proof: |
26 |
(string * (bstring * string list * mixfix) * string * (string * string) option) * Comment.text |
|
6690 | 27 |
-> bool -> theory -> ProofHistory.T |
11744 | 28 |
val typedef_proof_i: |
29 |
(string * (bstring * string list * mixfix) * term * (string * string) option) * Comment.text |
|
6690 | 30 |
-> bool -> theory -> ProofHistory.T |
4866 | 31 |
end; |
32 |
||
33 |
structure TypedefPackage: TYPEDEF_PACKAGE = |
|
34 |
struct |
|
35 |
||
36 |
||
10280 | 37 |
(** theory context references **) |
38 |
||
11608 | 39 |
val type_definitionN = "Typedef.type_definition"; |
10280 | 40 |
val type_definition_def = thm "type_definition_def"; |
41 |
||
42 |
val Rep = thm "Rep"; |
|
43 |
val Rep_inverse = thm "Rep_inverse"; |
|
44 |
val Abs_inverse = thm "Abs_inverse"; |
|
45 |
val Rep_inject = thm "Rep_inject"; |
|
46 |
val Abs_inject = thm "Abs_inject"; |
|
47 |
val Rep_cases = thm "Rep_cases"; |
|
48 |
val Abs_cases = thm "Abs_cases"; |
|
49 |
val Rep_induct = thm "Rep_induct"; |
|
50 |
val Abs_induct = thm "Abs_induct"; |
|
51 |
||
52 |
||
53 |
||
5104 | 54 |
(** type declarations **) |
55 |
||
56 |
fun add_typedecls decls thy = |
|
57 |
let |
|
58 |
val full = Sign.full_name (Theory.sign_of thy); |
|
59 |
||
60 |
fun arity_of (raw_name, args, mx) = |
|
61 |
(full (Syntax.type_name raw_name mx), replicate (length args) HOLogic.termS, HOLogic.termS); |
|
62 |
in |
|
8141 | 63 |
if can (Theory.assert_super HOL.thy) thy then |
64 |
thy |
|
65 |
|> PureThy.add_typedecls decls |
|
66 |
|> Theory.add_arities_i (map arity_of decls) |
|
67 |
else thy |> PureThy.add_typedecls decls |
|
5104 | 68 |
end; |
69 |
||
70 |
||
71 |
||
72 |
(** type definitions **) |
|
73 |
||
5697 | 74 |
(* messages *) |
75 |
||
76 |
val quiet_mode = ref false; |
|
77 |
fun message s = if ! quiet_mode then () else writeln s; |
|
78 |
||
79 |
||
11426
f280d4b29a2c
abtract non-emptiness statements (no longer use Eps);
wenzelm
parents:
10697
diff
changeset
|
80 |
(* prove_nonempty -- tactical version *) (*exception ERROR*) |
4866 | 81 |
|
11827 | 82 |
fun prove_nonempty thy cset goal (witn1_tac, witn_names, witn_thms, witn2_tac) = |
6383 | 83 |
let |
84 |
val is_def = Logic.is_equals o #prop o Thm.rep_thm; |
|
85 |
val thms = PureThy.get_thmss thy witn_names @ witn_thms; |
|
4866 | 86 |
val tac = |
11827 | 87 |
witn1_tac THEN |
4866 | 88 |
TRY (rewrite_goals_tac (filter is_def thms)) THEN |
89 |
TRY (REPEAT_FIRST (resolve_tac (filter_out is_def thms))) THEN |
|
11827 | 90 |
if_none witn2_tac (TRY (ALLGOALS (CLASET' blast_tac))); |
4866 | 91 |
in |
6383 | 92 |
message ("Proving non-emptiness of set " ^ quote (string_of_cterm cset) ^ " ..."); |
11426
f280d4b29a2c
abtract non-emptiness statements (no longer use Eps);
wenzelm
parents:
10697
diff
changeset
|
93 |
prove_goalw_cterm [] (cterm_of (sign_of thy) goal) (K [tac]) |
6383 | 94 |
end handle ERROR => error ("Failed to prove non-emptiness of " ^ quote (string_of_cterm cset)); |
4866 | 95 |
|
96 |
||
6383 | 97 |
(* prepare_typedef *) |
98 |
||
99 |
fun read_term sg used s = |
|
8100 | 100 |
#1 (Thm.read_def_cterm (sg, K None, K None) used true (s, HOLogic.termT)); |
4866 | 101 |
|
6383 | 102 |
fun cert_term sg _ t = Thm.cterm_of sg t handle TERM (msg, _) => error msg; |
103 |
||
104 |
fun err_in_typedef name = |
|
105 |
error ("The error(s) above occurred in typedef " ^ quote name); |
|
106 |
||
11822 | 107 |
fun prepare_typedef prep_term def name (t, vs, mx) raw_set opt_morphs thy = |
4866 | 108 |
let |
11608 | 109 |
val _ = Theory.requires thy "Typedef" "typedefs"; |
6383 | 110 |
val sign = Theory.sign_of thy; |
10280 | 111 |
val full = Sign.full_name sign; |
4866 | 112 |
|
113 |
(*rhs*) |
|
10280 | 114 |
val full_name = full name; |
6383 | 115 |
val cset = prep_term sign vs raw_set; |
116 |
val {T = setT, t = set, ...} = Thm.rep_cterm cset; |
|
4866 | 117 |
val rhs_tfrees = term_tfrees set; |
118 |
val oldT = HOLogic.dest_setT setT handle TYPE _ => |
|
119 |
error ("Not a set type: " ^ quote (Sign.string_of_typ sign setT)); |
|
11426
f280d4b29a2c
abtract non-emptiness statements (no longer use Eps);
wenzelm
parents:
10697
diff
changeset
|
120 |
fun mk_nonempty A = |
f280d4b29a2c
abtract non-emptiness statements (no longer use Eps);
wenzelm
parents:
10697
diff
changeset
|
121 |
HOLogic.mk_Trueprop (HOLogic.mk_exists ("x", oldT, HOLogic.mk_mem (Free ("x", oldT), A))); |
f280d4b29a2c
abtract non-emptiness statements (no longer use Eps);
wenzelm
parents:
10697
diff
changeset
|
122 |
val goal = mk_nonempty set; |
11744 | 123 |
val vname = take_suffix Symbol.is_digit (Symbol.explode name) |
124 |
|> apfst implode |> apsnd (#1 o Term.read_int); |
|
125 |
val goal_pat = mk_nonempty (Var (vname, setT)); |
|
4866 | 126 |
|
127 |
(*lhs*) |
|
6383 | 128 |
val lhs_tfrees = map (fn v => (v, if_none (assoc (rhs_tfrees, v)) HOLogic.termS)) vs; |
4866 | 129 |
val tname = Syntax.type_name t mx; |
10280 | 130 |
val full_tname = full tname; |
131 |
val newT = Type (full_tname, map TFree lhs_tfrees); |
|
4866 | 132 |
|
11744 | 133 |
val (Rep_name, Abs_name) = if_none opt_morphs ("Rep_" ^ name, "Abs_" ^ name); |
10280 | 134 |
val setC = Const (full_name, setT); |
135 |
val RepC = Const (full Rep_name, newT --> oldT); |
|
136 |
val AbsC = Const (full Abs_name, oldT --> newT); |
|
4866 | 137 |
val x_new = Free ("x", newT); |
138 |
val y_old = Free ("y", oldT); |
|
10280 | 139 |
|
11822 | 140 |
val set' = if def then setC else set; |
4866 | 141 |
|
10280 | 142 |
val typedef_name = "type_definition_" ^ name; |
143 |
val typedefC = |
|
144 |
Const (type_definitionN, (newT --> oldT) --> (oldT --> newT) --> setT --> HOLogic.boolT); |
|
11426
f280d4b29a2c
abtract non-emptiness statements (no longer use Eps);
wenzelm
parents:
10697
diff
changeset
|
145 |
val typedef_prop = |
f280d4b29a2c
abtract non-emptiness statements (no longer use Eps);
wenzelm
parents:
10697
diff
changeset
|
146 |
Logic.mk_implies (goal, HOLogic.mk_Trueprop (typedefC $ RepC $ AbsC $ set')); |
4866 | 147 |
|
11822 | 148 |
fun typedef_result (theory, nonempty) = |
6383 | 149 |
theory |
150 |
|> add_typedecls [(t, vs, mx)] |
|
151 |
|> Theory.add_consts_i |
|
11822 | 152 |
((if def then [(name, setT, NoSyn)] else []) @ |
6383 | 153 |
[(Rep_name, newT --> oldT, NoSyn), |
154 |
(Abs_name, oldT --> newT, NoSyn)]) |
|
11822 | 155 |
|> (if def then (apsnd (Some o hd) oo (PureThy.add_defs_i false o map Thm.no_attributes)) |
156 |
[Logic.mk_defpair (setC, set)] |
|
157 |
else rpair None) |
|
158 |
|>> PureThy.add_axioms_i [((typedef_name, typedef_prop), |
|
11727
a27150cc8fa5
test: use SkipProof.make_thm instead of Thm.assume;
wenzelm
parents:
11608
diff
changeset
|
159 |
[apsnd (fn cond_axm => Drule.standard (nonempty RS cond_axm))])] |
11822 | 160 |
|> (fn ((theory', [type_definition]), set_def) => |
161 |
let |
|
162 |
fun make th = Drule.standard (th OF [type_definition]); |
|
163 |
val (theory'', [Rep, Rep_inverse, Abs_inverse, Rep_inject, Abs_inject, |
|
164 |
Rep_cases, Abs_cases, Rep_induct, Abs_induct]) = |
|
165 |
theory' |> PureThy.add_thms |
|
166 |
([((Rep_name, make Rep), []), |
|
167 |
((Rep_name ^ "_inverse", make Rep_inverse), []), |
|
168 |
((Abs_name ^ "_inverse", make Abs_inverse), []), |
|
169 |
((Rep_name ^ "_inject", make Rep_inject), []), |
|
170 |
((Abs_name ^ "_inject", make Abs_inject), []), |
|
171 |
((Rep_name ^ "_cases", make Rep_cases), |
|
172 |
[RuleCases.case_names [Rep_name], InductAttrib.cases_set_global full_name]), |
|
173 |
((Abs_name ^ "_cases", make Abs_cases), |
|
174 |
[RuleCases.case_names [Abs_name], InductAttrib.cases_type_global full_tname]), |
|
175 |
((Rep_name ^ "_induct", make Rep_induct), |
|
176 |
[RuleCases.case_names [Rep_name], InductAttrib.induct_set_global full_name]), |
|
177 |
((Abs_name ^ "_induct", make Abs_induct), |
|
178 |
[RuleCases.case_names [Abs_name], InductAttrib.induct_type_global full_tname])]); |
|
179 |
val result = {type_definition = type_definition, set_def = set_def, |
|
180 |
Rep = Rep, Rep_inverse = Rep_inverse, Abs_inverse = Abs_inverse, |
|
181 |
Rep_inject = Rep_inject, Abs_inject = Abs_inject, Rep_cases = Rep_cases, |
|
182 |
Abs_cases = Abs_cases, Rep_induct = Rep_induct, Abs_induct = Abs_induct}; |
|
183 |
in ((theory'', type_definition), result) end); |
|
6383 | 184 |
|
4866 | 185 |
|
186 |
(* errors *) |
|
187 |
||
188 |
fun show_names pairs = commas_quote (map fst pairs); |
|
189 |
||
190 |
val illegal_vars = |
|
191 |
if null (term_vars set) andalso null (term_tvars set) then [] |
|
192 |
else ["Illegal schematic variable(s) on rhs"]; |
|
193 |
||
194 |
val dup_lhs_tfrees = |
|
195 |
(case duplicates lhs_tfrees of [] => [] |
|
196 |
| dups => ["Duplicate type variables on lhs: " ^ show_names dups]); |
|
197 |
||
198 |
val extra_rhs_tfrees = |
|
199 |
(case gen_rems (op =) (rhs_tfrees, lhs_tfrees) of [] => [] |
|
200 |
| extras => ["Extra type variables on rhs: " ^ show_names extras]); |
|
201 |
||
202 |
val illegal_frees = |
|
203 |
(case term_frees set of [] => [] |
|
204 |
| xs => ["Illegal variables on rhs: " ^ show_names (map dest_Free xs)]); |
|
205 |
||
206 |
val errs = illegal_vars @ dup_lhs_tfrees @ extra_rhs_tfrees @ illegal_frees; |
|
11426
f280d4b29a2c
abtract non-emptiness statements (no longer use Eps);
wenzelm
parents:
10697
diff
changeset
|
207 |
val _ = if null errs then () else error (cat_lines errs); |
f280d4b29a2c
abtract non-emptiness statements (no longer use Eps);
wenzelm
parents:
10697
diff
changeset
|
208 |
|
f280d4b29a2c
abtract non-emptiness statements (no longer use Eps);
wenzelm
parents:
10697
diff
changeset
|
209 |
(*test theory errors now!*) |
f280d4b29a2c
abtract non-emptiness statements (no longer use Eps);
wenzelm
parents:
10697
diff
changeset
|
210 |
val test_thy = Theory.copy thy; |
11727
a27150cc8fa5
test: use SkipProof.make_thm instead of Thm.assume;
wenzelm
parents:
11608
diff
changeset
|
211 |
val _ = (test_thy, |
11822 | 212 |
setmp quick_and_dirty true (SkipProof.make_thm test_thy) goal) |> typedef_result; |
11426
f280d4b29a2c
abtract non-emptiness statements (no longer use Eps);
wenzelm
parents:
10697
diff
changeset
|
213 |
|
11822 | 214 |
in (cset, goal, goal_pat, typedef_result) end |
11426
f280d4b29a2c
abtract non-emptiness statements (no longer use Eps);
wenzelm
parents:
10697
diff
changeset
|
215 |
handle ERROR => err_in_typedef name; |
4866 | 216 |
|
217 |
||
6383 | 218 |
(* add_typedef interfaces *) |
4866 | 219 |
|
11827 | 220 |
fun gen_typedef prep_term def name typ set opt_morphs tac1 names thms tac2 thy = |
6383 | 221 |
let |
11822 | 222 |
val (cset, goal, _, typedef_result) = |
223 |
prepare_typedef prep_term def name typ set opt_morphs thy; |
|
11827 | 224 |
val non_empty = prove_nonempty thy cset goal (tac1, names, thms, tac2); |
11822 | 225 |
val ((thy', _), result) = (thy, non_empty) |> typedef_result; |
226 |
in (thy', result) end; |
|
4866 | 227 |
|
11827 | 228 |
fun sane_typedef prep_term def opt_name typ set opt_morphs tac = |
229 |
gen_typedef prep_term def |
|
230 |
(if_none opt_name (#1 typ)) typ set opt_morphs all_tac [] [] (Some tac); |
|
11822 | 231 |
|
232 |
fun add_typedef_x name typ set names thms tac = |
|
11827 | 233 |
#1 o gen_typedef read_term true name typ set None (Tactic.rtac exI 1) names thms tac; |
11822 | 234 |
|
235 |
val add_typedef = sane_typedef read_term; |
|
236 |
val add_typedef_i = sane_typedef cert_term; |
|
4866 | 237 |
|
238 |
||
6383 | 239 |
(* typedef_proof interface *) |
240 |
||
11744 | 241 |
fun gen_typedef_proof prep_term ((name, typ, set, opt_morphs), comment) int thy = |
11822 | 242 |
let |
243 |
val (_, goal, goal_pat, att_result) = |
|
244 |
prepare_typedef prep_term true name typ set opt_morphs thy; |
|
245 |
val att = #1 o att_result; |
|
246 |
in |
|
247 |
thy |> IsarThy.theorem_i Drule.internalK ((("", [att]), (goal, ([goal_pat], []))), comment) int |
|
11740 | 248 |
end; |
6383 | 249 |
|
250 |
val typedef_proof = gen_typedef_proof read_term; |
|
251 |
val typedef_proof_i = gen_typedef_proof cert_term; |
|
6357 | 252 |
|
253 |
||
6383 | 254 |
|
255 |
(** outer syntax **) |
|
256 |
||
6723 | 257 |
local structure P = OuterParse and K = OuterSyntax.Keyword in |
6383 | 258 |
|
6357 | 259 |
val typedeclP = |
6723 | 260 |
OuterSyntax.command "typedecl" "HOL type declaration" K.thy_decl |
7152 | 261 |
(P.type_args -- P.name -- P.opt_infix --| P.marg_comment >> (fn ((vs, t), mx) => |
6357 | 262 |
Toplevel.theory (add_typedecls [(t, vs, mx)]))); |
263 |
||
6723 | 264 |
|
6383 | 265 |
val typedef_proof_decl = |
6723 | 266 |
Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") -- |
11744 | 267 |
(P.type_args -- P.name) -- P.opt_infix -- (P.$$$ "=" |-- P.term) -- |
268 |
Scan.option (P.$$$ "morphisms" |-- P.!!! (P.name -- P.name)) -- |
|
269 |
P.marg_comment; |
|
6357 | 270 |
|
11744 | 271 |
fun mk_typedef_proof (((((opt_name, (vs, t)), mx), A), morphs), comment) = |
272 |
typedef_proof ((if_none opt_name (Syntax.type_name t mx), (t, vs, mx), A, morphs), comment); |
|
6357 | 273 |
|
274 |
val typedefP = |
|
6723 | 275 |
OuterSyntax.command "typedef" "HOL type definition (requires non-emptiness proof)" K.thy_goal |
6383 | 276 |
(typedef_proof_decl >> (Toplevel.print oo (Toplevel.theory_to_proof o mk_typedef_proof))); |
6357 | 277 |
|
6723 | 278 |
|
11744 | 279 |
val _ = OuterSyntax.add_keywords ["morphisms"]; |
6357 | 280 |
val _ = OuterSyntax.add_parsers [typedeclP, typedefP]; |
281 |
||
4866 | 282 |
end; |
6383 | 283 |
|
284 |
||
285 |
end; |