--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Tools/pcpodef.ML Sun Jun 21 15:45:57 2009 +0200
@@ -0,0 +1,201 @@
+(* Title: HOLCF/Tools/pcpodef.ML
+ Author: Brian Huffman
+
+Primitive domain definitions for HOLCF, similar to Gordon/HOL-style
+typedef (see also ~~/src/HOL/Tools/typedef.ML).
+*)
+
+signature PCPODEF =
+sig
+ val pcpodef_proof: (bool * binding) * (binding * string list * mixfix) * term
+ * (binding * binding) option -> theory -> Proof.state
+ val pcpodef_proof_cmd: (bool * binding) * (binding * string list * mixfix) * string
+ * (binding * binding) option -> theory -> Proof.state
+ val cpodef_proof: (bool * binding) * (binding * string list * mixfix) * term
+ * (binding * binding) option -> theory -> Proof.state
+ val cpodef_proof_cmd: (bool * binding) * (binding * string list * mixfix) * string
+ * (binding * binding) option -> theory -> Proof.state
+end;
+
+structure Pcpodef :> PCPODEF =
+struct
+
+(** type definitions **)
+
+(* prepare_cpodef *)
+
+fun declare_type_name a = Variable.declare_constraints (Logic.mk_type (TFree (a, dummyS)));
+
+fun adm_const T = Const (@{const_name adm}, (T --> HOLogic.boolT) --> HOLogic.boolT);
+fun mk_adm (x, T, P) = adm_const T $ absfree (x, T, P);
+
+fun prepare_pcpodef prep_term pcpo def name (t, vs, mx) raw_set opt_morphs thy =
+ let
+ val _ = Theory.requires thy "Pcpodef" "pcpodefs";
+ val ctxt = ProofContext.init thy;
+
+ val full = Sign.full_name thy;
+ val full_name = full name;
+ val bname = Binding.name_of name;
+
+ (*rhs*)
+ val set = prep_term (ctxt |> fold declare_type_name vs) raw_set;
+ val setT = Term.fastype_of set;
+ val rhs_tfrees = Term.add_tfrees set [];
+ val oldT = HOLogic.dest_setT setT handle TYPE _ =>
+ error ("Not a set type: " ^ quote (Syntax.string_of_typ ctxt setT));
+
+ (*goal*)
+ val goal_UU_mem = HOLogic.mk_Trueprop (HOLogic.mk_mem (Const (@{const_name UU}, oldT), set));
+ val goal_nonempty =
+ HOLogic.mk_Trueprop (HOLogic.mk_exists ("x", oldT, HOLogic.mk_mem (Free ("x", oldT), set)));
+ val goal_admissible =
+ HOLogic.mk_Trueprop (mk_adm ("x", oldT, HOLogic.mk_mem (Free ("x", oldT), set)));
+
+ (*lhs*)
+ val defS = Sign.defaultS thy;
+ val lhs_tfrees = map (fn v => (v, the_default defS (AList.lookup (op =) rhs_tfrees v))) vs;
+ val lhs_sorts = map snd lhs_tfrees;
+
+ val tname = Binding.map_name (Syntax.type_name mx) t;
+ val full_tname = full tname;
+ val newT = Type (full_tname, map TFree lhs_tfrees);
+
+ val (Rep_name, Abs_name) =
+ (case opt_morphs of
+ NONE => (Binding.prefix_name "Rep_" name, Binding.prefix_name "Abs_" name)
+ | SOME morphs => morphs);
+ val RepC = Const (full Rep_name, newT --> oldT);
+ fun belowC T = Const (@{const_name below}, T --> T --> HOLogic.boolT);
+ val below_def = Logic.mk_equals (belowC newT,
+ Abs ("x", newT, Abs ("y", newT, belowC oldT $ (RepC $ Bound 1) $ (RepC $ Bound 0))));
+
+ fun make_po tac thy1 =
+ let
+ val ((_, {type_definition, set_def, ...}), thy2) = thy1
+ |> Typedef.add_typedef def (SOME name) (t, vs, mx) set opt_morphs tac;
+ val lthy3 = thy2
+ |> TheoryTarget.instantiation ([full_tname], lhs_tfrees, @{sort po});
+ val below_def' = Syntax.check_term lthy3 below_def;
+ val ((_, (_, below_definition')), lthy4) = lthy3
+ |> Specification.definition (NONE,
+ ((Binding.prefix_name "below_" (Binding.suffix_name "_def" name), []), below_def'));
+ val ctxt_thy = ProofContext.init (ProofContext.theory_of lthy4);
+ val below_definition = singleton (ProofContext.export lthy4 ctxt_thy) below_definition';
+ val thy5 = lthy4
+ |> Class.prove_instantiation_instance
+ (K (Tactic.rtac (@{thm typedef_po} OF [type_definition, below_definition]) 1))
+ |> LocalTheory.exit_global;
+ in ((type_definition, below_definition, set_def), thy5) end;
+
+ fun make_cpo admissible (type_def, below_def, set_def) theory =
+ let
+ val admissible' = fold_rule (the_list set_def) admissible;
+ val cpo_thms = map (Thm.transfer theory) [type_def, below_def, admissible'];
+ val theory' = theory
+ |> AxClass.prove_arity (full_tname, lhs_sorts, @{sort cpo})
+ (Tactic.rtac (@{thm typedef_cpo} OF cpo_thms) 1);
+ val cpo_thms' = map (Thm.transfer theory') cpo_thms;
+ in
+ theory'
+ |> Sign.add_path (Binding.name_of name)
+ |> PureThy.add_thms
+ ([((Binding.prefix_name "adm_" name, admissible'), []),
+ ((Binding.prefix_name "cont_" Rep_name, @{thm typedef_cont_Rep} OF cpo_thms'), []),
+ ((Binding.prefix_name "cont_" Abs_name, @{thm typedef_cont_Abs} OF cpo_thms'), []),
+ ((Binding.prefix_name "lub_" name, @{thm typedef_lub} OF cpo_thms'), []),
+ ((Binding.prefix_name "thelub_" name, @{thm typedef_thelub} OF cpo_thms'), []),
+ ((Binding.prefix_name "compact_" name, @{thm typedef_compact} OF cpo_thms'), [])])
+ |> snd
+ |> Sign.parent_path
+ end;
+
+ fun make_pcpo UU_mem (type_def, below_def, set_def) theory =
+ let
+ val UU_mem' = fold_rule (the_list set_def) UU_mem;
+ val pcpo_thms = map (Thm.transfer theory) [type_def, below_def, UU_mem'];
+ val theory' = theory
+ |> AxClass.prove_arity (full_tname, lhs_sorts, @{sort pcpo})
+ (Tactic.rtac (@{thm typedef_pcpo} OF pcpo_thms) 1);
+ val pcpo_thms' = map (Thm.transfer theory') pcpo_thms;
+ in
+ theory'
+ |> Sign.add_path (Binding.name_of name)
+ |> PureThy.add_thms
+ ([((Binding.suffix_name "_strict" Rep_name, @{thm typedef_Rep_strict} OF pcpo_thms'), []),
+ ((Binding.suffix_name "_strict" Abs_name, @{thm typedef_Abs_strict} OF pcpo_thms'), []),
+ ((Binding.suffix_name "_strict_iff" Rep_name, @{thm typedef_Rep_strict_iff} OF pcpo_thms'), []),
+ ((Binding.suffix_name "_strict_iff" Abs_name, @{thm typedef_Abs_strict_iff} OF pcpo_thms'), []),
+ ((Binding.suffix_name "_defined" Rep_name, @{thm typedef_Rep_defined} OF pcpo_thms'), []),
+ ((Binding.suffix_name "_defined" Abs_name, @{thm typedef_Abs_defined} OF pcpo_thms'), [])])
+ |> snd
+ |> Sign.parent_path
+ end;
+
+ fun pcpodef_result UU_mem admissible =
+ make_po (Tactic.rtac exI 1 THEN Tactic.rtac UU_mem 1)
+ #-> (fn defs => make_cpo admissible defs #> make_pcpo UU_mem defs);
+
+ fun cpodef_result nonempty admissible =
+ make_po (Tactic.rtac nonempty 1)
+ #-> make_cpo admissible;
+ in
+ if pcpo
+ then (goal_UU_mem, goal_admissible, pcpodef_result)
+ else (goal_nonempty, goal_admissible, cpodef_result)
+ end
+ handle ERROR msg =>
+ cat_error msg ("The error(s) above occurred in cpodef " ^ quote (Binding.str_of name));
+
+
+(* proof interface *)
+
+local
+
+fun gen_pcpodef_proof prep_term pcpo ((def, name), typ, set, opt_morphs) thy =
+ let
+ val (goal1, goal2, make_result) =
+ prepare_pcpodef prep_term pcpo def name typ set opt_morphs thy;
+ fun after_qed [[th1, th2]] = ProofContext.theory (make_result th1 th2);
+ in Proof.theorem_i NONE after_qed [[(goal1, []), (goal2, [])]] (ProofContext.init thy) end;
+
+in
+
+fun pcpodef_proof x = gen_pcpodef_proof Syntax.check_term true x;
+fun pcpodef_proof_cmd x = gen_pcpodef_proof Syntax.read_term true x;
+
+fun cpodef_proof x = gen_pcpodef_proof Syntax.check_term false x;
+fun cpodef_proof_cmd x = gen_pcpodef_proof Syntax.read_term false x;
+
+end;
+
+
+
+(** outer syntax **)
+
+local structure P = OuterParse and K = OuterKeyword in
+
+val typedef_proof_decl =
+ Scan.optional (P.$$$ "(" |--
+ ((P.$$$ "open" >> K false) -- Scan.option P.binding || P.binding >> (fn s => (true, SOME s)))
+ --| P.$$$ ")") (true, NONE) --
+ (P.type_args -- P.binding) -- P.opt_infix -- (P.$$$ "=" |-- P.term) --
+ Scan.option (P.$$$ "morphisms" |-- P.!!! (P.binding -- P.binding));
+
+fun mk_pcpodef_proof pcpo ((((((def, opt_name), (vs, t)), mx), A), morphs)) =
+ (if pcpo then pcpodef_proof_cmd else cpodef_proof_cmd)
+ ((def, the_default (Binding.map_name (Syntax.type_name mx) t) opt_name), (t, vs, mx), A, morphs);
+
+val _ =
+ OuterSyntax.command "pcpodef" "HOLCF type definition (requires admissibility proof)" K.thy_goal
+ (typedef_proof_decl >>
+ (Toplevel.print oo (Toplevel.theory_to_proof o mk_pcpodef_proof true)));
+
+val _ =
+ OuterSyntax.command "cpodef" "HOLCF type definition (requires admissibility proof)" K.thy_goal
+ (typedef_proof_decl >>
+ (Toplevel.print oo (Toplevel.theory_to_proof o mk_pcpodef_proof false)));
+
+end;
+
+end;