src/Pure/Isar/local_defs.ML
author wenzelm
Mon May 03 14:25:56 2010 +0200 (2010-05-03)
changeset 36610 bafd82950e24
parent 35739 35a3b3721ffb
child 39133 70d3915c92f0
permissions -rw-r--r--
renamed ProofContext.init to ProofContext.init_global to emphasize that this is not the real thing;
     1 (*  Title:      Pure/Isar/local_defs.ML
     2     Author:     Makarius
     3 
     4 Local definitions.
     5 *)
     6 
     7 signature LOCAL_DEFS =
     8 sig
     9   val cert_def: Proof.context -> term -> (string * typ) * term
    10   val abs_def: term -> (string * typ) * term
    11   val mk_def: Proof.context -> (string * term) list -> term list
    12   val expand: cterm list -> thm -> thm
    13   val def_export: Assumption.export
    14   val add_defs: ((binding * mixfix) * (Thm.binding * term)) list -> Proof.context ->
    15     (term * (string * thm)) list * Proof.context
    16   val add_def: (binding * mixfix) * term -> Proof.context -> (term * thm) * Proof.context
    17   val fixed_abbrev: (binding * mixfix) * term -> Proof.context ->
    18     (term * term) * Proof.context
    19   val export: Proof.context -> Proof.context -> thm -> thm list * thm
    20   val export_cterm: Proof.context -> Proof.context -> cterm -> thm list * cterm
    21   val trans_terms: Proof.context -> thm list -> thm
    22   val trans_props: Proof.context -> thm list -> thm
    23   val contract: Proof.context -> thm list -> cterm -> thm -> thm
    24   val print_rules: Proof.context -> unit
    25   val defn_add: attribute
    26   val defn_del: attribute
    27   val meta_rewrite_conv: Proof.context -> conv
    28   val meta_rewrite_rule: Proof.context -> thm -> thm
    29   val unfold: Proof.context -> thm list -> thm -> thm
    30   val unfold_goals: Proof.context -> thm list -> thm -> thm
    31   val unfold_tac: Proof.context -> thm list -> tactic
    32   val fold: Proof.context -> thm list -> thm -> thm
    33   val fold_tac: Proof.context -> thm list -> tactic
    34   val derived_def: Proof.context -> bool -> term ->
    35     ((string * typ) * term) * (Proof.context -> thm -> thm)
    36 end;
    37 
    38 structure Local_Defs: LOCAL_DEFS =
    39 struct
    40 
    41 (** primitive definitions **)
    42 
    43 (* prepare defs *)
    44 
    45 fun cert_def ctxt eq =
    46   let
    47     fun err msg = cat_error msg ("The error(s) above occurred in definition: " ^
    48       quote (Syntax.string_of_term ctxt eq));
    49     val ((lhs, _), eq') = eq
    50       |> Sign.no_vars (Syntax.pp ctxt)
    51       |> Primitive_Defs.dest_def ctxt Term.is_Free (Variable.is_fixed ctxt) (K true)
    52       handle TERM (msg, _) => err msg | ERROR msg => err msg;
    53   in (Term.dest_Free (Term.head_of lhs), eq') end;
    54 
    55 val abs_def = Primitive_Defs.abs_def #>> Term.dest_Free;
    56 
    57 fun mk_def ctxt args =
    58   let
    59     val (xs, rhss) = split_list args;
    60     val (bind, _) = ProofContext.bind_fixes xs ctxt;
    61     val lhss = map (fn (x, rhs) => bind (Free (x, Term.fastype_of rhs))) args;
    62   in map Logic.mk_equals (lhss ~~ rhss) end;
    63 
    64 
    65 (* export defs *)
    66 
    67 val head_of_def =
    68   #1 o Term.dest_Free o Term.head_of o #1 o Logic.dest_equals o Term.strip_all_body;
    69 
    70 
    71 (*
    72   [x, x == a]
    73        :
    74       B x
    75   -----------
    76       B a
    77 *)
    78 fun expand defs =
    79   Drule.implies_intr_list defs
    80   #> Drule.generalize ([], map (head_of_def o Thm.term_of) defs)
    81   #> funpow (length defs) (fn th => Drule.reflexive_thm RS th);
    82 
    83 val expand_term = Envir.expand_term_frees o map (abs_def o Thm.term_of);
    84 
    85 fun def_export _ defs = (expand defs, expand_term defs);
    86 
    87 
    88 (* add defs *)
    89 
    90 fun add_defs defs ctxt =
    91   let
    92     val ((bvars, mxs), specs) = defs |> split_list |>> split_list;
    93     val ((bfacts, atts), rhss) = specs |> split_list |>> split_list;
    94     val xs = map Name.of_binding bvars;
    95     val names = map2 Thm.def_binding_optional bvars bfacts;
    96     val eqs = mk_def ctxt (xs ~~ rhss);
    97     val lhss = map (fst o Logic.dest_equals) eqs;
    98   in
    99     ctxt
   100     |> ProofContext.add_fixes (map2 (fn x => fn mx => (x, NONE, mx)) bvars mxs) |> #2
   101     |> fold Variable.declare_term eqs
   102     |> ProofContext.add_assms_i def_export
   103       (map2 (fn a => fn eq => (a, [(eq, [])])) (names ~~ atts) eqs)
   104     |>> map2 (fn lhs => fn (name, [th]) => (lhs, (name, th))) lhss
   105   end;
   106 
   107 fun add_def (var, rhs) ctxt =
   108   let val ([(lhs, (_, th))], ctxt') = add_defs [(var, (Thm.empty_binding, rhs))] ctxt
   109   in ((lhs, th), ctxt') end;
   110 
   111 
   112 (* fixed_abbrev *)
   113 
   114 fun fixed_abbrev ((x, mx), rhs) ctxt =
   115   let
   116     val T = Term.fastype_of rhs;
   117     val ([x'], ctxt') = ctxt
   118       |> Variable.declare_term rhs
   119       |> ProofContext.add_fixes [(x, SOME T, mx)];
   120     val lhs = Free (x', T);
   121     val _ = cert_def ctxt' (Logic.mk_equals (lhs, rhs));
   122     fun abbrev_export _ _ = (I, Envir.expand_term_frees [((x', T), rhs)]);
   123     val (_, ctxt'') = Assumption.add_assms abbrev_export [] ctxt';
   124   in ((lhs, rhs), ctxt'') end;
   125 
   126 
   127 (* specific export -- result based on educated guessing *)
   128 
   129 (*
   130   [xs, xs == as]
   131         :
   132        B xs
   133   --------------
   134        B as
   135 *)
   136 fun export inner outer =    (*beware of closure sizes*)
   137   let
   138     val exp = Assumption.export false inner outer;
   139     val prems = Assumption.all_prems_of inner;
   140   in fn th =>
   141     let
   142       val th' = exp th;
   143       val still_fixed = map #1 (Thm.fold_terms Term.add_frees th' []);
   144       val defs = prems |> filter_out (fn prem =>
   145         (case try (head_of_def o Thm.prop_of) prem of
   146           SOME x => member (op =) still_fixed x
   147         | NONE => true));
   148     in (map Drule.abs_def defs, th') end
   149   end;
   150 
   151 (*
   152   [xs, xs == as]
   153         :
   154      TERM b xs
   155   --------------  and  --------------
   156      TERM b as          b xs == b as
   157 *)
   158 fun export_cterm inner outer ct =
   159   export inner outer (Drule.mk_term ct) ||> Drule.dest_term;
   160 
   161 
   162 (* basic transitivity reasoning -- modulo beta-eta *)
   163 
   164 local
   165 
   166 val is_trivial = Pattern.aeconv o Logic.dest_equals o Thm.prop_of;
   167 
   168 fun trans_list _ _ [] = raise Empty
   169   | trans_list trans ctxt (th :: raw_eqs) =
   170       (case filter_out is_trivial raw_eqs of
   171         [] => th
   172       | eqs =>
   173           let val ((_, th' :: eqs'), ctxt') = Variable.import true (th :: eqs) ctxt
   174           in singleton (Variable.export ctxt' ctxt) (fold trans eqs' th') end);
   175 
   176 in
   177 
   178 val trans_terms = trans_list (fn eq2 => fn eq1 => eq2 COMP (eq1 COMP Drule.transitive_thm));
   179 val trans_props = trans_list (fn eq => fn th => th COMP (eq COMP Drule.equal_elim_rule1));
   180 
   181 end;
   182 
   183 fun contract ctxt defs ct th =
   184   trans_props ctxt [th, Thm.symmetric (MetaSimplifier.rewrite true defs ct)];
   185 
   186 
   187 (** defived definitions **)
   188 
   189 (* transformation rules *)
   190 
   191 structure Rules = Generic_Data
   192 (
   193   type T = thm list;
   194   val empty = [];
   195   val extend = I;
   196   val merge = Thm.merge_thms;
   197 );
   198 
   199 fun print_rules ctxt =
   200   Pretty.writeln (Pretty.big_list "definitional transformations:"
   201     (map (Display.pretty_thm ctxt) (Rules.get (Context.Proof ctxt))));
   202 
   203 val defn_add = Thm.declaration_attribute (Rules.map o Thm.add_thm);
   204 val defn_del = Thm.declaration_attribute (Rules.map o Thm.del_thm);
   205 
   206 
   207 (* meta rewrite rules *)
   208 
   209 fun meta_rewrite_conv ctxt =
   210   MetaSimplifier.rewrite_cterm (false, false, false) (K (K NONE))
   211     (MetaSimplifier.context ctxt MetaSimplifier.empty_ss
   212       addeqcongs [Drule.equals_cong]    (*protect meta-level equality*)
   213       addsimps (Rules.get (Context.Proof ctxt)));
   214 
   215 val meta_rewrite_rule = Conv.fconv_rule o meta_rewrite_conv;
   216 
   217 
   218 (* rewriting with object-level rules *)
   219 
   220 fun meta f ctxt = f o map (meta_rewrite_rule ctxt);
   221 
   222 val unfold       = meta MetaSimplifier.rewrite_rule;
   223 val unfold_goals = meta MetaSimplifier.rewrite_goals_rule;
   224 val unfold_tac   = meta MetaSimplifier.rewrite_goals_tac;
   225 val fold         = meta MetaSimplifier.fold_rule;
   226 val fold_tac     = meta MetaSimplifier.fold_goals_tac;
   227 
   228 
   229 (* derived defs -- potentially within the object-logic *)
   230 
   231 fun derived_def ctxt conditional prop =
   232   let
   233     val ((c, T), rhs) = prop
   234       |> Thm.cterm_of (ProofContext.theory_of ctxt)
   235       |> meta_rewrite_conv ctxt
   236       |> (snd o Logic.dest_equals o Thm.prop_of)
   237       |> conditional ? Logic.strip_imp_concl
   238       |> (abs_def o #2 o cert_def ctxt);
   239     fun prove ctxt' def =
   240       let
   241         val frees = Term.fold_aterms (fn Free (x, _) =>
   242           if Variable.is_fixed ctxt' x then I else insert (op =) x | _ => I) prop [];
   243       in
   244         Goal.prove ctxt' frees [] prop (K (ALLGOALS
   245           (CONVERSION (meta_rewrite_conv ctxt') THEN'
   246             MetaSimplifier.rewrite_goal_tac [def] THEN'
   247             resolve_tac [Drule.reflexive_thm])))
   248         handle ERROR msg => cat_error msg "Failed to prove definitional specification."
   249       end;
   250   in (((c, T), rhs), prove) end;
   251 
   252 end;