--- a/Quot/quotient.ML Fri Dec 11 19:22:30 2009 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,226 +0,0 @@
-signature QUOTIENT =
-sig
- exception LIFT_MATCH of string
-
- val quotient_type: ((binding * mixfix) * (typ * term)) list -> Proof.context -> Proof.state
- val quotient_type_cmd: (((bstring * mixfix) * string) * string) list -> Proof.context -> Proof.state
-
-end;
-
-structure Quotient: QUOTIENT =
-struct
-
-exception LIFT_MATCH of string
-
-(* wrappers for define, note and theorem_i *)
-fun define (name, mx, rhs) lthy =
-let
- val ((rhs, (_ , thm)), lthy') =
- Local_Theory.define ((name, mx), (Attrib.empty_binding, rhs)) lthy
-in
- ((rhs, thm), lthy')
-end
-
-fun note (name, thm, attrs) lthy =
-let
- val ((_,[thm']), lthy') = Local_Theory.note ((name, attrs), [thm]) lthy
-in
- (thm', lthy')
-end
-
-fun internal_attr at = Attrib.internal (K at)
-
-fun theorem after_qed goals ctxt =
-let
- val goals' = map (rpair []) goals
- fun after_qed' thms = after_qed (the_single thms)
-in
- Proof.theorem_i NONE after_qed' [goals'] ctxt
-end
-
-
-(* definition of quotient types *)
-(********************************)
-
-(* constructs the term lambda (c::rty => bool). EX (x::rty). c = rel x *)
-fun typedef_term rel rty lthy =
-let
- val [x, c] = [("x", rty), ("c", HOLogic.mk_setT rty)]
- |> Variable.variant_frees lthy [rel]
- |> map Free
-in
- lambda c
- (HOLogic.exists_const rty $
- lambda x (HOLogic.mk_eq (c, (rel $ x))))
-end
-
-(* makes the new type definitions and proves non-emptyness*)
-fun typedef_make (qty_name, mx, rel, rty) lthy =
-let
- val typedef_tac =
- EVERY1 [rewrite_goal_tac @{thms mem_def},
- rtac @{thm exI},
- rtac @{thm exI},
- rtac @{thm refl}]
- val tfrees = map fst (Term.add_tfreesT rty [])
-in
- Local_Theory.theory_result
- (Typedef.add_typedef false NONE
- (qty_name, tfrees, mx)
- (typedef_term rel rty lthy)
- NONE typedef_tac) lthy
-end
-
-(* tactic to prove the QUOT_TYPE theorem for the new type *)
-fun typedef_quot_type_tac equiv_thm (typedef_info: Typedef.info) =
-let
- val unfold_mem = MetaSimplifier.rewrite_rule [@{thm mem_def}]
- val rep_thm = #Rep typedef_info |> unfold_mem
- val rep_inv = #Rep_inverse typedef_info
- val abs_inv = #Abs_inverse typedef_info |> unfold_mem
- val rep_inj = #Rep_inject typedef_info
-in
- EVERY1 [rtac @{thm QUOT_TYPE.intro},
- rtac equiv_thm,
- rtac rep_thm,
- rtac rep_inv,
- rtac abs_inv,
- rtac @{thm exI},
- rtac @{thm refl},
- rtac rep_inj]
-end
-
-(* proves the QUOT_TYPE theorem *)
-fun typedef_quot_type_thm (rel, abs, rep, equiv_thm, typedef_info) lthy =
-let
- val quot_type_const = Const (@{const_name "QUOT_TYPE"}, dummyT)
- val goal = HOLogic.mk_Trueprop (quot_type_const $ rel $ abs $ rep)
- |> Syntax.check_term lthy
-in
- Goal.prove lthy [] [] goal
- (K (typedef_quot_type_tac equiv_thm typedef_info))
-end
-
-(* proves the quotient theorem *)
-fun typedef_quotient_thm (rel, abs, rep, abs_def, rep_def, quot_type_thm) lthy =
-let
- val quotient_const = Const (@{const_name "Quotient"}, dummyT)
- val goal = HOLogic.mk_Trueprop (quotient_const $ rel $ abs $ rep)
- |> Syntax.check_term lthy
-
- val typedef_quotient_thm_tac =
- EVERY1 [K (rewrite_goals_tac [abs_def, rep_def]),
- rtac @{thm QUOT_TYPE.Quotient},
- rtac quot_type_thm]
-in
- Goal.prove lthy [] [] goal
- (K typedef_quotient_thm_tac)
-end
-
-(* main function for constructing the quotient type *)
-fun mk_typedef_main (((qty_name, mx), (rty, rel)), equiv_thm) lthy =
-let
- (* generates typedef *)
- val ((_, typedef_info), lthy1) = typedef_make (qty_name, mx, rel, rty) lthy
-
- (* abs and rep functions *)
- val abs_ty = #abs_type typedef_info
- val rep_ty = #rep_type typedef_info
- val abs_name = #Abs_name typedef_info
- val rep_name = #Rep_name typedef_info
- val abs = Const (abs_name, rep_ty --> abs_ty)
- val rep = Const (rep_name, abs_ty --> rep_ty)
-
- (* ABS and REP definitions *)
- val ABS_const = Const (@{const_name "QUOT_TYPE.abs"}, dummyT )
- val REP_const = Const (@{const_name "QUOT_TYPE.rep"}, dummyT )
- val ABS_trm = Syntax.check_term lthy1 (ABS_const $ rel $ abs)
- val REP_trm = Syntax.check_term lthy1 (REP_const $ rep)
- val ABS_name = Binding.prefix_name "abs_" qty_name
- val REP_name = Binding.prefix_name "rep_" qty_name
- val (((ABS, ABS_def), (REP, REP_def)), lthy2) =
- lthy1 |> define (ABS_name, NoSyn, ABS_trm)
- ||>> define (REP_name, NoSyn, REP_trm)
-
- (* quot_type theorem *)
- val quot_thm = typedef_quot_type_thm (rel, abs, rep, equiv_thm, typedef_info) lthy2
- val quot_thm_name = Binding.prefix_name "QUOT_TYPE_" qty_name
-
- (* quotient theorem *)
- val quotient_thm = typedef_quotient_thm (rel, ABS, REP, ABS_def, REP_def, quot_thm) lthy2
- val quotient_thm_name = Binding.prefix_name "Quotient_" qty_name
-
- (* storing the quot-info *)
- val qty_str = fst (Term.dest_Type abs_ty)
- val lthy3 = quotdata_update qty_str
- (Logic.varifyT abs_ty, Logic.varifyT rty, rel, equiv_thm) lthy2
- (* FIXME: varifyT should not be used *)
- (* FIXME: the relation needs to be a string, since its type needs *)
- (* FIXME: to recalculated in for example REGULARIZE *)
-
-in
- lthy3
- |> note (quot_thm_name, quot_thm, [])
- ||>> note (quotient_thm_name, quotient_thm, [internal_attr quotient_rules_add])
- ||>> note (Binding.suffix_name "_equivp" qty_name, equiv_thm, [internal_attr equiv_rules_add])
-end
-
-
-
-
-(* interface and syntax setup *)
-
-(* the ML-interface takes a list of 4-tuples consisting of *)
-(* *)
-(* - the name of the quotient type *)
-(* - its mixfix annotation *)
-(* - the type to be quotient *)
-(* - the relation according to which the type is quotient *)
-
-fun quotient_type quot_list lthy =
-let
- fun mk_goal (rty, rel) =
- let
- val equivp_ty = ([rty, rty] ---> @{typ bool}) --> @{typ bool}
- in
- HOLogic.mk_Trueprop (Const (@{const_name equivp}, equivp_ty) $ rel)
- end
-
- val goals = map (mk_goal o snd) quot_list
-
- fun after_qed thms lthy =
- fold_map mk_typedef_main (quot_list ~~ thms) lthy |> snd
-in
- theorem after_qed goals lthy
-end
-
-fun quotient_type_cmd spec lthy =
-let
- fun parse_spec (((qty_str, mx), rty_str), rel_str) =
- let
- val qty_name = Binding.name qty_str
- val rty = Syntax.read_typ lthy rty_str
- val rel = Syntax.read_term lthy rel_str
- in
- ((qty_name, mx), (rty, rel))
- end
-in
- quotient_type (map parse_spec spec) lthy
-end
-
-val quotspec_parser =
- OuterParse.and_list1
- (OuterParse.short_ident -- OuterParse.opt_infix --
- (OuterParse.$$$ "=" |-- OuterParse.typ) --
- (OuterParse.$$$ "/" |-- OuterParse.term))
-
-val _ = OuterKeyword.keyword "/"
-
-val _ =
- OuterSyntax.local_theory_to_proof "quotient"
- "quotient type definitions (requires equivalence proofs)"
- OuterKeyword.thy_goal (quotspec_parser >> quotient_type_cmd)
-
-end; (* structure *)
-
-open Quotient