/usr/share/hol88-2.02.19940316/contrib/quotient/quotientfns.ml is in hol88-contrib-source 2.02.19940316-19.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 | %
This file defines functions needed for constructing
quotient types.
%
%
AUTHOR: TON KALKER
DATE : 2 JUNE 1989
%
let check_quotient_def =
set_fail_prefix `not equivalence theorem!: `
(\thm.
let asl,w = dest_thm thm in
let t1,t2 = dest_comb w in
let name,ty = (dest_const t1 ? failwith `operator`) in
let base_type = ((hd o snd o dest_type o
hd o snd o dest_type) ty ? failwith `types`) in
if not (asl = []) then failwith `assumptions`
if not (name = `EQUIVALENCE`) then failwith `not EQUIVALENCE`
if not (is_const t2) then failwith `operand`
else t2,base_type);;
% <name>_ISO_DEF added for new define_new_type_bijections. %
% TFM 90.04.11 HOL88 Version 1.12 %
let construct_quot_ty(name,thm) =
let equi, base_type = check_quotient_def thm in
let exists_thm = MATCH_MP (DISCH_ALL EXISTS_CLASS) thm and
is_mk_class_thm = MATCH_MP (DISCH_ALL IS_MK_CLASS) thm in
let w = concl exists_thm in
let tm = (fst o dest_comb o snd o dest_exists) w in
let thm1 = new_type_definition(name,tm,exists_thm) in
let ISO =
define_new_type_bijections
(name ^ `_ISO_DEF`) (`ABS_` ^ name) (`REP_` ^ name) thm1 in
let thml =
[prove_abs_fn_one_one ISO; prove_abs_fn_onto ISO] in
let thm3 = ( GEN_ALL o
(REWRITE_RULE[is_mk_class_thm]) o
(SPEC "MK_CLASS ^equi (x':^base_type)") o
(SPEC "MK_CLASS ^equi (x:^base_type)"))(el 1 thml) in
let thm4 = (el 2 thml) in
let current = current_theory() in
let [ABS_name] = filter
(\tm.((fst o dest_const) tm) = (`ABS_` ^ name))
(constants current) in
let quot_ty = ((el 2) o snd o dest_type o type_of) ABS_name in
let PROJ_name = mk_var(`PROJ_` ^ name,":^base_type ->^quot_ty") in
let proj = new_definition(`PROJ_` ^name,
"^PROJ_name x = ^ABS_name (MK_CLASS ^equi x)") in
proj,thm3,thm4,base_type,quot_ty,equi;;
let prove_proj_onto name thm proj thm4 base_type quot_ty=
let surjective_thm = MATCH_MP (DISCH_ALL SURJECTIVE_LEMMA) thm in
let PROJ_name = mk_const(`PROJ_` ^ name,":^base_type ->^quot_ty") in
let tm = "ONTO ^PROJ_name" in
TAC_PROOF(
([],tm),
REWRITE_TAC[ONTO_DEF;proj] THEN
STRIP_TAC THEN
STRIP_ASSUME_TAC (SPEC "y:^quot_ty" thm4) THEN
ASSUM_LIST
(\asl.STRIP_ASSUME_TAC (MATCH_MP surjective_thm (hd asl))) THEN
EXISTS_TAC "x:^base_type" THEN
ASM_REWRITE_TAC[]);;
let prove_proj_universal name thm proj thm3 base_type quot_ty equi =
let universal_thm = MATCH_MP (DISCH_ALL UNIVERSAL_LEMMA) thm in
let PROJ_name = mk_const(`PROJ_` ^ name,":^base_type ->^quot_ty") in
let tm = "!x y.((^PROJ_name x = ^PROJ_name y) = (^equi x y))" in
TAC_PROOF(
([],tm),
REWRITE_TAC[proj;thm3;universal_thm]);;
let prove_proj_factor name base_type quot_ty thml =
let thm1 = INST_TYPE[(base_type,":*");(quot_ty,":***")] FACTOR_THM in
let thm2 = SPEC "f:^base_type -> **" thm1 in
let PROJ_name = mk_const(`PROJ_` ^ name,":^base_type ->^quot_ty") in
let thm3 = SPEC "^PROJ_name" thm2 in
let thm4 = GEN_ALL thm3 in
REWRITE_RULE thml thm4;;
let define_quotient_type(name,thm) =
let proj,thm3,thm4,base_type,quot_ty,equi = construct_quot_ty(name,thm)
in
let string1 = `SURJ_PROJ_` ^ name ^ `_THM` and
string2 = `UNIV_PROJ_` ^ name ^ `_THM` and
string3 = `FACTOR_PROJ_` ^ name ^ `_THM`
in
let thm1 = save_thm(string1,
prove_proj_onto name thm proj thm4 base_type quot_ty) and
thm2 = save_thm(string2,
prove_proj_universal name thm proj thm3 base_type quot_ty equi)
in
let thm3 = save_thm(string3,
prove_proj_factor name base_type quot_ty [thm1;thm2])
in [thm1;thm2;thm3];;
let FACTOR_TAC surj_thml univ_thml =
MATCH_MP_TAC FACTOR_THM THEN
REWRITE_TAC([ONTO_SURJ_THM;P;]@surj_thml) THEN
CONV_TAC (RAND_CONV (ABS_CONV PROD_CONV)) THEN
CONV_TAC PROD_CONV THEN
BETA_TAC THEN
REWRITE_TAC([PAIR_EQ]@univ_thml);;
let new_unique_specification =
set_fail_prefix `new_unique_specification`
(\name [flag,c] thm.
(
let thm1 = (BETA_RULE o (CONV_RULE EXISTS_UNIQUE_CONV)) thm
in
let ex_thm,uniq_thm = CONJ_PAIR thm1
in
let thm2 = (new_specification name [flag,c] ex_thm ?
(print_string (name ^ ` already defined`);
print_newline();
definition (current_theory()) name))
in
let [newconst] =
filter
(\d.(c = (fst o dest_const) d))
(constants (current_theory()))
in
let thm3 = SPEC newconst uniq_thm
in
let thm4 = REWRITE_RULE[thm2] thm3
in
let x = fst(dest_forall(concl thm4))
in
let thm5 = CONV_RULE (GEN_ALPHA_CONV "f:^(type_of x)") thm4
in
let thm6 = (save_thm((name ^ `_UNIQUE`), thm5) ?
(print_string (name ^ `_UNIQUE already present`);
print_newline();
theorem (current_theory()) (name ^ `_UNIQUE`)))
in
[thm2;thm6]
));;
|