author | haftmann |
Thu, 08 Jul 2010 16:19:24 +0200 | |
changeset 37744 | 3daaf23b9ab4 |
parent 37530 | 70d03844b2f9 |
child 38387 | f31678522745 |
permissions | -rw-r--r-- |
37744 | 1 |
(* Title: HOL/Tools/Quotient/quotient_typ.ML |
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Author: Cezary Kaliszyk and Christian Urban |
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Initial version of HOL quotient package.
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|
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rollback of local typedef until problem with type-variables can be sorted out; fixed header
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parents:
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Definition of a quotient type. |
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|
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Initial version of HOL quotient package.
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*) |
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Initial version of HOL quotient package.
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parents:
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|
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Initial version of HOL quotient package.
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signature QUOTIENT_TYPE = |
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Initial version of HOL quotient package.
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sig |
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parents:
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val add_quotient_type: ((string list * binding * mixfix) * (typ * term * bool)) * thm |
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-> Proof.context -> Quotient_Info.quotdata_info * local_theory |
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export add_quotient_type.
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|
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parents:
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val quotient_type: ((string list * binding * mixfix) * (typ * term * bool)) list |
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Initial version of HOL quotient package.
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-> Proof.context -> Proof.state |
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Initial version of HOL quotient package.
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parents:
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|
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Quotient package now uses Partial Equivalence instead place of equivalence
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parents:
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val quotient_type_cmd: ((((string list * binding) * mixfix) * string) * (bool * string)) list |
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Initial version of HOL quotient package.
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-> Proof.context -> Proof.state |
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Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
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end; |
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Initial version of HOL quotient package.
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parents:
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|
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Initial version of HOL quotient package.
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structure Quotient_Type: QUOTIENT_TYPE = |
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Initial version of HOL quotient package.
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struct |
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Initial version of HOL quotient package.
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parents:
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|
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Initial version of HOL quotient package.
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open Quotient_Info; |
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Initial version of HOL quotient package.
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|
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Initial version of HOL quotient package.
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(* wrappers for define, note, Attrib.internal and theorem_i *) |
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Initial version of HOL quotient package.
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fun define (name, mx, rhs) lthy = |
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Initial version of HOL quotient package.
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parents:
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let |
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Initial version of HOL quotient package.
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val ((rhs, (_ , thm)), lthy') = |
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Initial version of HOL quotient package.
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Local_Theory.define ((name, mx), (Attrib.empty_binding, rhs)) lthy |
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Initial version of HOL quotient package.
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in |
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((rhs, thm), lthy') |
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Initial version of HOL quotient package.
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end |
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Initial version of HOL quotient package.
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parents:
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|
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Initial version of HOL quotient package.
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fun note (name, thm, attrs) lthy = |
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Local_Theory.note ((name, attrs), [thm]) lthy |> snd |
70d03844b2f9
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parents:
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|
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Initial version of HOL quotient package.
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fun intern_attr at = Attrib.internal (K at) |
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Initial version of HOL quotient package.
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|
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Initial version of HOL quotient package.
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fun theorem after_qed goals ctxt = |
4f1fba00f66d
Initial version of HOL quotient package.
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let |
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Initial version of HOL quotient package.
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val goals' = map (rpair []) goals |
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Initial version of HOL quotient package.
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fun after_qed' thms = after_qed (the_single thms) |
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Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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in |
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Proof.theorem NONE after_qed' [goals'] ctxt |
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Initial version of HOL quotient package.
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end |
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Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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|
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Initial version of HOL quotient package.
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parents:
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|
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Initial version of HOL quotient package.
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parents:
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Initial version of HOL quotient package.
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(*** definition of quotient types ***) |
4f1fba00f66d
Initial version of HOL quotient package.
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|
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Initial version of HOL quotient package.
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parents:
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val mem_def1 = @{lemma "y : S ==> S y" by (simp add: mem_def)} |
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Initial version of HOL quotient package.
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val mem_def2 = @{lemma "S y ==> y : S" by (simp add: mem_def)} |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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|
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Initial version of HOL quotient package.
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parents:
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(* constructs the term lambda (c::rty => bool). EX (x::rty). c = rel x *) |
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Initial version of HOL quotient package.
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fun typedef_term rel rty lthy = |
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Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
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let |
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Initial version of HOL quotient package.
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parents:
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val [x, c] = |
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Initial version of HOL quotient package.
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[("x", rty), ("c", HOLogic.mk_setT rty)] |
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Initial version of HOL quotient package.
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|> Variable.variant_frees lthy [rel] |
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Initial version of HOL quotient package.
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|> map Free |
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Initial version of HOL quotient package.
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in |
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Initial version of HOL quotient package.
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lambda c (HOLogic.exists_const rty $ |
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parents:
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lambda x (HOLogic.mk_conj (rel $ x $ x, HOLogic.mk_eq (c, rel $ x)))) |
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Initial version of HOL quotient package.
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end |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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|
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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Initial version of HOL quotient package.
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parents:
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(* makes the new type definitions and proves non-emptyness *) |
37493
2377d246a631
Quotient package now uses Partial Equivalence instead place of equivalence
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parents:
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fun typedef_make (vs, qty_name, mx, rel, rty) equiv_thm lthy = |
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Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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let |
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Initial version of HOL quotient package.
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parents:
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val typedef_tac = |
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parents:
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EVERY1 (map rtac [@{thm part_equivp_typedef}, equiv_thm]) |
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Initial version of HOL quotient package.
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parents:
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in |
35806
a814cccce0b8
rollback of local typedef until problem with type-variables can be sorted out; fixed header
Christian Urban <urbanc@in.tum.de>
parents:
35790
diff
changeset
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(* FIXME: purely local typedef causes at the moment |
a814cccce0b8
rollback of local typedef until problem with type-variables can be sorted out; fixed header
Christian Urban <urbanc@in.tum.de>
parents:
35790
diff
changeset
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75 |
problems with type variables |
a814cccce0b8
rollback of local typedef until problem with type-variables can be sorted out; fixed header
Christian Urban <urbanc@in.tum.de>
parents:
35790
diff
changeset
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|
35790
a9507cd84326
removed Local_Theory.theory_result by using local Typedef.add_typedef
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parents:
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Typedef.add_typedef false NONE (qty_name, vs, mx) |
a9507cd84326
removed Local_Theory.theory_result by using local Typedef.add_typedef
Christian Urban <urbanc@in.tum.de>
parents:
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diff
changeset
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(typedef_term rel rty lthy) NONE typedef_tac lthy |
35806
a814cccce0b8
rollback of local typedef until problem with type-variables can be sorted out; fixed header
Christian Urban <urbanc@in.tum.de>
parents:
35790
diff
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*) |
a814cccce0b8
rollback of local typedef until problem with type-variables can be sorted out; fixed header
Christian Urban <urbanc@in.tum.de>
parents:
35790
diff
changeset
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80 |
Local_Theory.theory_result |
a814cccce0b8
rollback of local typedef until problem with type-variables can be sorted out; fixed header
Christian Urban <urbanc@in.tum.de>
parents:
35790
diff
changeset
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(Typedef.add_typedef_global false NONE |
35842 | 82 |
(qty_name, map (rpair dummyS) vs, mx) |
35806
a814cccce0b8
rollback of local typedef until problem with type-variables can be sorted out; fixed header
Christian Urban <urbanc@in.tum.de>
parents:
35790
diff
changeset
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83 |
(typedef_term rel rty lthy) |
a814cccce0b8
rollback of local typedef until problem with type-variables can be sorted out; fixed header
Christian Urban <urbanc@in.tum.de>
parents:
35790
diff
changeset
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NONE typedef_tac) lthy |
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85 |
end |
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Initial version of HOL quotient package.
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parents:
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|
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Initial version of HOL quotient package.
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parents:
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|
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Initial version of HOL quotient package.
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parents:
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(* tactic to prove the quot_type theorem for the new type *) |
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fun typedef_quot_type_tac equiv_thm ((_, typedef_info): Typedef.info) = |
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Initial version of HOL quotient package.
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parents:
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let |
4f1fba00f66d
Initial version of HOL quotient package.
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parents:
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val rep_thm = #Rep typedef_info RS mem_def1 |
4f1fba00f66d
Initial version of HOL quotient package.
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parents:
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val rep_inv = #Rep_inverse typedef_info |
37493
2377d246a631
Quotient package now uses Partial Equivalence instead place of equivalence
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parents:
36960
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val abs_inv = #Abs_inverse typedef_info |
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Initial version of HOL quotient package.
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parents:
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val rep_inj = #Rep_inject typedef_info |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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in |
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Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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(rtac @{thm quot_type.intro} THEN' RANGE [ |
4f1fba00f66d
Initial version of HOL quotient package.
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parents:
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rtac equiv_thm, |
4f1fba00f66d
Initial version of HOL quotient package.
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parents:
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rtac rep_thm, |
4f1fba00f66d
Initial version of HOL quotient package.
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parents:
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rtac rep_inv, |
37493
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parents:
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rtac abs_inv THEN' rtac mem_def2 THEN' atac, |
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rtac rep_inj]) 1 |
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102 |
end |
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parents:
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|
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Initial version of HOL quotient package.
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parents:
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|
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Initial version of HOL quotient package.
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parents:
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(* proves the quot_type theorem for the new type *) |
4f1fba00f66d
Initial version of HOL quotient package.
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parents:
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106 |
fun typedef_quot_type_thm (rel, abs, rep, equiv_thm, typedef_info) lthy = |
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Initial version of HOL quotient package.
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parents:
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let |
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Initial version of HOL quotient package.
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parents:
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val quot_type_const = Const (@{const_name "quot_type"}, dummyT) |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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val goal = |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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HOLogic.mk_Trueprop (quot_type_const $ rel $ abs $ rep) |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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111 |
|> Syntax.check_term lthy |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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112 |
in |
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Initial version of HOL quotient package.
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parents:
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113 |
Goal.prove lthy [] [] goal |
4f1fba00f66d
Initial version of HOL quotient package.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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(K (typedef_quot_type_tac equiv_thm typedef_info)) |
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115 |
end |
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116 |
|
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(* proves the quotient theorem for the new type *) |
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118 |
fun typedef_quotient_thm (rel, abs, rep, abs_def, rep_def, quot_type_thm) lthy = |
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119 |
let |
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val quotient_const = Const (@{const_name "Quotient"}, dummyT) |
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val goal = |
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HOLogic.mk_Trueprop (quotient_const $ rel $ abs $ rep) |
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|> Syntax.check_term lthy |
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124 |
|
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val typedef_quotient_thm_tac = |
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126 |
EVERY1 [ |
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K (rewrite_goals_tac [abs_def, rep_def]), |
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rtac @{thm quot_type.Quotient}, |
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rtac quot_type_thm] |
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130 |
in |
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Goal.prove lthy [] [] goal |
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(K typedef_quotient_thm_tac) |
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133 |
end |
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134 |
|
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135 |
|
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136 |
(* main function for constructing a quotient type *) |
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137 |
fun add_quotient_type (((vs, qty_name, mx), (rty, rel, partial)), equiv_thm) lthy = |
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138 |
let |
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139 |
val part_equiv = |
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140 |
if partial |
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141 |
then equiv_thm |
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else equiv_thm RS @{thm equivp_implies_part_equivp} |
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143 |
|
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144 |
(* generates the typedef *) |
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145 |
val ((qty_full_name, typedef_info), lthy1) = typedef_make (vs, qty_name, mx, rel, rty) part_equiv lthy |
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146 |
|
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(* abs and rep functions from the typedef *) |
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val Abs_ty = #abs_type (#1 typedef_info) |
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val Rep_ty = #rep_type (#1 typedef_info) |
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val Abs_name = #Abs_name (#1 typedef_info) |
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val Rep_name = #Rep_name (#1 typedef_info) |
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val Abs_const = Const (Abs_name, Rep_ty --> Abs_ty) |
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val Rep_const = Const (Rep_name, Abs_ty --> Rep_ty) |
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154 |
|
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155 |
(* more useful abs and rep definitions *) |
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Initial version of HOL quotient package.
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156 |
val abs_const = Const (@{const_name "quot_type.abs"}, dummyT ) |
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157 |
val rep_const = Const (@{const_name "quot_type.rep"}, dummyT ) |
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Initial version of HOL quotient package.
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158 |
val abs_trm = Syntax.check_term lthy1 (abs_const $ rel $ Abs_const) |
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Initial version of HOL quotient package.
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159 |
val rep_trm = Syntax.check_term lthy1 (rep_const $ Rep_const) |
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Initial version of HOL quotient package.
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160 |
val abs_name = Binding.prefix_name "abs_" qty_name |
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Initial version of HOL quotient package.
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161 |
val rep_name = Binding.prefix_name "rep_" qty_name |
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Initial version of HOL quotient package.
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162 |
|
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163 |
val ((abs, abs_def), lthy2) = define (abs_name, NoSyn, abs_trm) lthy1 |
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Initial version of HOL quotient package.
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164 |
val ((rep, rep_def), lthy3) = define (rep_name, NoSyn, rep_trm) lthy2 |
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Initial version of HOL quotient package.
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165 |
|
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166 |
(* quot_type theorem *) |
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167 |
val quot_thm = typedef_quot_type_thm (rel, Abs_const, Rep_const, part_equiv, typedef_info) lthy3 |
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168 |
|
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169 |
(* quotient theorem *) |
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Initial version of HOL quotient package.
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170 |
val quotient_thm = typedef_quotient_thm (rel, abs, rep, abs_def, rep_def, quot_thm) lthy3 |
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Initial version of HOL quotient package.
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171 |
val quotient_thm_name = Binding.prefix_name "Quotient_" qty_name |
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Initial version of HOL quotient package.
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172 |
|
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Initial version of HOL quotient package.
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173 |
(* name equivalence theorem *) |
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Initial version of HOL quotient package.
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174 |
val equiv_thm_name = Binding.suffix_name "_equivp" qty_name |
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Initial version of HOL quotient package.
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175 |
|
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176 |
(* storing the quotdata *) |
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177 |
val quotdata = {qtyp = Abs_ty, rtyp = rty, equiv_rel = rel, equiv_thm = equiv_thm} |
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178 |
|
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179 |
fun qinfo phi = transform_quotdata phi quotdata |
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180 |
|
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181 |
val lthy4 = lthy3 |
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182 |
|> Local_Theory.declaration true (fn phi => quotdata_update_gen qty_full_name (qinfo phi)) |
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183 |
|> note (equiv_thm_name, equiv_thm, if partial then [] else [intern_attr equiv_rules_add]) |
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184 |
|> note (quotient_thm_name, quotient_thm, [intern_attr quotient_rules_add]) |
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185 |
in |
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186 |
(quotdata, lthy4) |
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187 |
end |
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Initial version of HOL quotient package.
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188 |
|
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Initial version of HOL quotient package.
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189 |
|
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Initial version of HOL quotient package.
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190 |
(* sanity checks for the quotient type specifications *) |
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191 |
fun sanity_check ((vs, qty_name, _), (rty, rel, _)) = |
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192 |
let |
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193 |
val rty_tfreesT = map fst (Term.add_tfreesT rty []) |
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Initial version of HOL quotient package.
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194 |
val rel_tfrees = map fst (Term.add_tfrees rel []) |
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Initial version of HOL quotient package.
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195 |
val rel_frees = map fst (Term.add_frees rel []) |
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Initial version of HOL quotient package.
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196 |
val rel_vars = Term.add_vars rel [] |
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Initial version of HOL quotient package.
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197 |
val rel_tvars = Term.add_tvars rel [] |
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Initial version of HOL quotient package.
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198 |
val qty_str = Binding.str_of qty_name ^ ": " |
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Initial version of HOL quotient package.
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199 |
|
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Initial version of HOL quotient package.
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200 |
val illegal_rel_vars = |
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Initial version of HOL quotient package.
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201 |
if null rel_vars andalso null rel_tvars then [] |
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Initial version of HOL quotient package.
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202 |
else [qty_str ^ "illegal schematic variable(s) in the relation."] |
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Initial version of HOL quotient package.
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203 |
|
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Initial version of HOL quotient package.
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204 |
val dup_vs = |
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Initial version of HOL quotient package.
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205 |
(case duplicates (op =) vs of |
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Initial version of HOL quotient package.
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206 |
[] => [] |
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Initial version of HOL quotient package.
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207 |
| dups => [qty_str ^ "duplicate type variable(s) on the lhs: " ^ commas_quote dups]) |
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Initial version of HOL quotient package.
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208 |
|
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Initial version of HOL quotient package.
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209 |
val extra_rty_tfrees = |
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Initial version of HOL quotient package.
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210 |
(case subtract (op =) vs rty_tfreesT of |
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Initial version of HOL quotient package.
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211 |
[] => [] |
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Initial version of HOL quotient package.
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212 |
| extras => [qty_str ^ "extra type variable(s) on the lhs: " ^ commas_quote extras]) |
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Initial version of HOL quotient package.
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213 |
|
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Initial version of HOL quotient package.
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214 |
val extra_rel_tfrees = |
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Initial version of HOL quotient package.
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|
215 |
(case subtract (op =) vs rel_tfrees of |
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Initial version of HOL quotient package.
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216 |
[] => [] |
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Initial version of HOL quotient package.
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217 |
| extras => [qty_str ^ "extra type variable(s) in the relation: " ^ commas_quote extras]) |
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Initial version of HOL quotient package.
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218 |
|
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Initial version of HOL quotient package.
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219 |
val illegal_rel_frees = |
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Initial version of HOL quotient package.
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220 |
(case rel_frees of |
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Initial version of HOL quotient package.
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221 |
[] => [] |
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Initial version of HOL quotient package.
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222 |
| xs => [qty_str ^ "illegal variable(s) in the relation: " ^ commas_quote xs]) |
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Initial version of HOL quotient package.
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223 |
|
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Initial version of HOL quotient package.
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224 |
val errs = illegal_rel_vars @ dup_vs @ extra_rty_tfrees @ extra_rel_tfrees @ illegal_rel_frees |
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in |
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if null errs then () else error (cat_lines errs) |
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end |
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(* check for existence of map functions *) |
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fun map_check ctxt (_, (rty, _, _)) = |
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let |
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val thy = ProofContext.theory_of ctxt |
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fun map_check_aux rty warns = |
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case rty of |
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Type (_, []) => warns |
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| Type (s, _) => if maps_defined thy s then warns else s::warns |
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| _ => warns |
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val warns = map_check_aux rty [] |
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in |
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if null warns then () |
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else warning ("No map function defined for " ^ commas warns ^ |
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". This will cause problems later on.") |
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end |
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|
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(*** interface and syntax setup ***) |
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(* the ML-interface takes a list of 5-tuples consisting of: |
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|
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- the name of the quotient type |
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- its free type variables (first argument) |
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- its mixfix annotation |
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- the type to be quotient |
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- the partial flag (a boolean) |
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- the relation according to which the type is quotient |
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|
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it opens a proof-state in which one has to show that the |
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Initial version of HOL quotient package.
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relations are equivalence relations |
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*) |
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|
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Initial version of HOL quotient package.
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fun quotient_type quot_list lthy = |
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let |
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Initial version of HOL quotient package.
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(* sanity check *) |
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Initial version of HOL quotient package.
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val _ = List.app sanity_check quot_list |
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Initial version of HOL quotient package.
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val _ = List.app (map_check lthy) quot_list |
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Initial version of HOL quotient package.
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|
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fun mk_goal (rty, rel, partial) = |
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let |
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val equivp_ty = ([rty, rty] ---> @{typ bool}) --> @{typ bool} |
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val const = |
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if partial then @{const_name part_equivp} else @{const_name equivp} |
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in |
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HOLogic.mk_Trueprop (Const (const, equivp_ty) $ rel) |
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end |
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|
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val goals = map (mk_goal o snd) quot_list |
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|
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fun after_qed thms lthy = |
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fold_map add_quotient_type (quot_list ~~ thms) lthy |> snd |
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in |
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theorem after_qed goals lthy |
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end |
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Initial version of HOL quotient package.
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|
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Initial version of HOL quotient package.
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fun quotient_type_cmd specs lthy = |
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let |
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fun parse_spec ((((vs, qty_name), mx), rty_str), (partial, rel_str)) lthy = |
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let |
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val rty = Syntax.read_typ lthy rty_str |
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Initial version of HOL quotient package.
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val lthy1 = Variable.declare_typ rty lthy |
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val rel = |
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Syntax.parse_term lthy1 rel_str |
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|> Syntax.type_constraint (rty --> rty --> @{typ bool}) |
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|> Syntax.check_term lthy1 |
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val lthy2 = Variable.declare_term rel lthy1 |
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in |
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(((vs, qty_name, mx), (rty, rel, partial)), lthy2) |
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end |
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|
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Initial version of HOL quotient package.
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val (spec', lthy') = fold_map parse_spec specs lthy |
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Initial version of HOL quotient package.
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in |
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Initial version of HOL quotient package.
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quotient_type spec' lthy' |
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Initial version of HOL quotient package.
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306 |
end |
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Initial version of HOL quotient package.
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307 |
|
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parents:
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308 |
val partial = Scan.optional (Parse.reserved "partial" -- Parse.$$$ ":" >> K true) false |
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|
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val quotspec_parser = |
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311 |
Parse.and_list1 |
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312 |
((Parse.type_args -- Parse.binding) -- |
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Parse.opt_mixfix -- (Parse.$$$ "=" |-- Parse.typ) -- |
2377d246a631
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314 |
(Parse.$$$ "/" |-- (partial -- Parse.term))) |
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|
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prefer structure Keyword, Parse, Parse_Spec, Outer_Syntax;
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316 |
val _ = Keyword.keyword "/" |
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|
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Initial version of HOL quotient package.
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val _ = |
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319 |
Outer_Syntax.local_theory_to_proof "quotient_type" |
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Initial version of HOL quotient package.
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"quotient type definitions (require equivalence proofs)" |
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321 |
Keyword.thy_goal (quotspec_parser >> quotient_type_cmd) |
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Initial version of HOL quotient package.
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|
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Initial version of HOL quotient package.
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323 |
end; (* structure *) |