author | wenzelm |
Fri, 16 Mar 2012 18:20:12 +0100 | |
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parent 46949 | 94aa7b81bcf6 |
child 49759 | ecf1d5d87e5e |
permissions | -rw-r--r-- |
42151 | 1 |
(* Title: HOL/HOLCF/Tools/domaindef.ML |
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Author: Brian Huffman |
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Defining representable domains using algebraic deflations. |
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*) |
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signature DOMAINDEF = |
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sig |
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type rep_info = |
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{ |
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emb_def : thm, |
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prj_def : thm, |
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defl_def : thm, |
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liftemb_def : thm, |
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liftprj_def : thm, |
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liftdefl_def : thm, |
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DEFL : thm |
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} |
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val add_domaindef: bool -> binding option -> binding * (string * sort) list * mixfix -> |
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term -> (binding * binding) option -> theory -> |
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(Typedef.info * Cpodef.cpo_info * Cpodef.pcpo_info * rep_info) * theory |
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val domaindef_cmd: (bool * binding) * (binding * (string * string option) list * mixfix) * string |
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* (binding * binding) option -> theory -> theory |
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end |
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structure Domaindef : DOMAINDEF = |
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struct |
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open HOLCF_Library |
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infixr 6 ->> |
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infix -->> |
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(** type definitions **) |
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type rep_info = |
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{ |
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emb_def : thm, |
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prj_def : thm, |
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defl_def : thm, |
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liftemb_def : thm, |
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liftprj_def : thm, |
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liftdefl_def : thm, |
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DEFL : thm |
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} |
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(* building types and terms *) |
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val udomT = @{typ udom} |
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val deflT = @{typ "udom defl"} |
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val udeflT = @{typ "udom u defl"} |
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fun emb_const T = Const (@{const_name emb}, T ->> udomT) |
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fun prj_const T = Const (@{const_name prj}, udomT ->> T) |
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fun defl_const T = Const (@{const_name defl}, Term.itselfT T --> deflT) |
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fun liftemb_const T = Const (@{const_name liftemb}, mk_upT T ->> mk_upT udomT) |
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fun liftprj_const T = Const (@{const_name liftprj}, mk_upT udomT ->> mk_upT T) |
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fun liftdefl_const T = Const (@{const_name liftdefl}, Term.itselfT T --> udeflT) |
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fun mk_u_map t = |
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let |
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val (T, U) = dest_cfunT (fastype_of t) |
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val u_map_type = (T ->> U) ->> (mk_upT T ->> mk_upT U) |
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val u_map_const = Const (@{const_name u_map}, u_map_type) |
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in |
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mk_capply (u_map_const, t) |
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end |
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fun mk_cast (t, x) = |
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capply_const (udomT, udomT) |
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$ (capply_const (deflT, udomT ->> udomT) $ @{term "cast :: udom defl -> udom -> udom"} $ t) |
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$ x |
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(* manipulating theorems *) |
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(* proving class instances *) |
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fun gen_add_domaindef |
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(prep_term: Proof.context -> 'a -> term) |
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(def: bool) |
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(name: binding) |
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(typ as (tname, raw_args, _) : binding * (string * sort) list * mixfix) |
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(raw_defl: 'a) |
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(opt_morphs: (binding * binding) option) |
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(thy: theory) |
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: (Typedef.info * Cpodef.cpo_info * Cpodef.pcpo_info * rep_info) * theory = |
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let |
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val _ = Theory.requires thy "Domain" "domaindefs" |
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(*rhs*) |
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val tmp_ctxt = |
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Proof_Context.init_global thy |
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|> fold (Variable.declare_typ o TFree) raw_args |
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val defl = prep_term tmp_ctxt raw_defl |
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val tmp_ctxt = tmp_ctxt |> Variable.declare_constraints defl |
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val deflT = Term.fastype_of defl |
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val _ = if deflT = @{typ "udom defl"} then () |
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else error ("Not type defl: " ^ quote (Syntax.string_of_typ tmp_ctxt deflT)) |
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(*lhs*) |
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val lhs_tfrees = map (Proof_Context.check_tfree tmp_ctxt) raw_args |
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val full_tname = Sign.full_name thy tname |
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val newT = Type (full_tname, map TFree lhs_tfrees) |
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(*morphisms*) |
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val morphs = opt_morphs |
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|> the_default (Binding.prefix_name "Rep_" name, Binding.prefix_name "Abs_" name) |
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(*set*) |
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val set = @{term "defl_set :: udom defl => udom set"} $ defl |
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(*pcpodef*) |
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val tac1 = rtac @{thm defl_set_bottom} 1 |
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val tac2 = rtac @{thm adm_defl_set} 1 |
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val ((info, cpo_info, pcpo_info), thy) = thy |
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|> Cpodef.add_pcpodef def (SOME name) typ set (SOME morphs) (tac1, tac2) |
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(*definitions*) |
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val Rep_const = Const (#Rep_name (#1 info), newT --> udomT) |
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val Abs_const = Const (#Abs_name (#1 info), udomT --> newT) |
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val emb_eqn = Logic.mk_equals (emb_const newT, cabs_const (newT, udomT) $ Rep_const) |
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val prj_eqn = Logic.mk_equals (prj_const newT, cabs_const (udomT, newT) $ |
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Abs ("x", udomT, Abs_const $ mk_cast (defl, Bound 0))) |
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val defl_eqn = Logic.mk_equals (defl_const newT, |
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Abs ("x", Term.itselfT newT, defl)) |
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val liftemb_eqn = |
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Logic.mk_equals (liftemb_const newT, mk_u_map (emb_const newT)) |
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val liftprj_eqn = |
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Logic.mk_equals (liftprj_const newT, mk_u_map (prj_const newT)) |
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val liftdefl_eqn = |
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Logic.mk_equals (liftdefl_const newT, |
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Abs ("t", Term.itselfT newT, |
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mk_capply (@{const liftdefl_of}, defl_const newT $ Logic.mk_type newT))) |
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val name_def = Thm.def_binding name |
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val emb_bind = (Binding.prefix_name "emb_" name_def, []) |
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val prj_bind = (Binding.prefix_name "prj_" name_def, []) |
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val defl_bind = (Binding.prefix_name "defl_" name_def, []) |
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val liftemb_bind = (Binding.prefix_name "liftemb_" name_def, []) |
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val liftprj_bind = (Binding.prefix_name "liftprj_" name_def, []) |
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val liftdefl_bind = (Binding.prefix_name "liftdefl_" name_def, []) |
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(*instantiate class rep*) |
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val lthy = thy |
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|> Class.instantiation ([full_tname], lhs_tfrees, @{sort domain}) |
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val ((_, (_, emb_ldef)), lthy) = |
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Specification.definition (NONE, (emb_bind, emb_eqn)) lthy |
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val ((_, (_, prj_ldef)), lthy) = |
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Specification.definition (NONE, (prj_bind, prj_eqn)) lthy |
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val ((_, (_, defl_ldef)), lthy) = |
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Specification.definition (NONE, (defl_bind, defl_eqn)) lthy |
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val ((_, (_, liftemb_ldef)), lthy) = |
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Specification.definition (NONE, (liftemb_bind, liftemb_eqn)) lthy |
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val ((_, (_, liftprj_ldef)), lthy) = |
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Specification.definition (NONE, (liftprj_bind, liftprj_eqn)) lthy |
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val ((_, (_, liftdefl_ldef)), lthy) = |
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Specification.definition (NONE, (liftdefl_bind, liftdefl_eqn)) lthy |
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val ctxt_thy = Proof_Context.init_global (Proof_Context.theory_of lthy) |
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val emb_def = singleton (Proof_Context.export lthy ctxt_thy) emb_ldef |
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val prj_def = singleton (Proof_Context.export lthy ctxt_thy) prj_ldef |
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val defl_def = singleton (Proof_Context.export lthy ctxt_thy) defl_ldef |
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val liftemb_def = singleton (Proof_Context.export lthy ctxt_thy) liftemb_ldef |
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val liftprj_def = singleton (Proof_Context.export lthy ctxt_thy) liftprj_ldef |
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val liftdefl_def = singleton (Proof_Context.export lthy ctxt_thy) liftdefl_ldef |
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val type_definition_thm = |
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Raw_Simplifier.rewrite_rule |
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Typedef.info: separate global and local part, only the latter is transformed by morphisms;
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(the_list (#set_def (#2 info))) |
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(#type_definition (#2 info)) |
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val typedef_thms = |
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[type_definition_thm, #below_def cpo_info, emb_def, prj_def, defl_def, |
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liftemb_def, liftprj_def, liftdefl_def] |
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val thy = lthy |
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|> Class.prove_instantiation_instance |
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(K (Tactic.rtac (@{thm typedef_domain_class} OF typedef_thms) 1)) |
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|> Local_Theory.exit_global |
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|
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(*other theorems*) |
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val defl_thm' = Thm.transfer thy defl_def |
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val (DEFL_thm, thy) = thy |
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|> Sign.add_path (Binding.name_of name) |
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|> Global_Theory.add_thm |
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((Binding.prefix_name "DEFL_" name, |
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Drule.zero_var_indexes (@{thm typedef_DEFL} OF [defl_thm'])), []) |
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||> Sign.restore_naming thy |
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|
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val rep_info = |
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{ emb_def = emb_def, prj_def = prj_def, defl_def = defl_def, |
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liftemb_def = liftemb_def, liftprj_def = liftprj_def, |
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liftdefl_def = liftdefl_def, DEFL = DEFL_thm } |
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in |
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((info, cpo_info, pcpo_info, rep_info), thy) |
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end |
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handle ERROR msg => |
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cat_error msg ("The error(s) above occurred in domaindef " ^ Binding.print name) |
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|
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fun add_domaindef def opt_name typ defl opt_morphs thy = |
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let |
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val name = the_default (#1 typ) opt_name |
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in |
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gen_add_domaindef Syntax.check_term def name typ defl opt_morphs thy |
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end |
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|
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fun domaindef_cmd ((def, name), (b, raw_args, mx), A, morphs) thy = |
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let |
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val ctxt = Proof_Context.init_global thy |
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val args = map (apsnd (Typedecl.read_constraint ctxt)) raw_args |
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in snd (gen_add_domaindef Syntax.read_term def name (b, args, mx) A morphs thy) end |
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|
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(** outer syntax **) |
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|
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val domaindef_decl = |
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Scan.optional (@{keyword "("} |-- |
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((@{keyword "open"} >> K false) -- Scan.option Parse.binding || |
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Parse.binding >> (fn s => (true, SOME s))) |
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--| @{keyword ")"}) (true, NONE) -- |
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(Parse.type_args_constrained -- Parse.binding) -- |
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Parse.opt_mixfix -- (@{keyword "="} |-- Parse.term) -- |
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Scan.option (@{keyword "morphisms"} |-- Parse.!!! (Parse.binding -- Parse.binding)) |
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222 |
|
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fun mk_domaindef ((((((def, opt_name), (args, t)), mx), A), morphs)) = |
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domaindef_cmd ((def, the_default t opt_name), (t, args, mx), A, morphs) |
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|
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val _ = |
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outer syntax command definitions based on formal command_spec derived from theory header declarations;
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Outer_Syntax.command @{command_spec "domaindef"} "HOLCF definition of domains from deflations" |
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(domaindef_decl >> |
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(Toplevel.print oo (Toplevel.theory o mk_domaindef))) |
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230 |
|
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end |