renamed Variable.import_thms to Variable.import (back again cf. ed7aa5a350ef -- Alice is no longer supported);
renamed Variable.importT_thms to Variable.importT (again);
1 (* Title: Pure/Isar/local_defs.ML
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 -> cterm * thm
21 val trans_terms: Proof.context -> thm list -> thm
22 val trans_props: Proof.context -> thm list -> thm
23 val print_rules: Proof.context -> unit
24 val defn_add: attribute
25 val defn_del: attribute
26 val meta_rewrite_conv: Proof.context -> conv
27 val meta_rewrite_rule: Proof.context -> thm -> thm
28 val unfold: Proof.context -> thm list -> thm -> thm
29 val unfold_goals: Proof.context -> thm list -> thm -> thm
30 val unfold_tac: Proof.context -> thm list -> tactic
31 val fold: Proof.context -> thm list -> thm -> thm
32 val fold_tac: Proof.context -> thm list -> tactic
33 val derived_def: Proof.context -> bool -> term ->
34 ((string * typ) * term) * (Proof.context -> thm -> thm)
37 structure LocalDefs: LOCAL_DEFS =
40 (** primitive definitions **)
44 fun cert_def ctxt eq =
46 fun err msg = cat_error msg ("The error(s) above occurred in definition: " ^
47 quote (Syntax.string_of_term ctxt eq));
48 val ((lhs, _), eq') = eq
49 |> Sign.no_vars (Syntax.pp ctxt)
50 |> PrimitiveDefs.dest_def ctxt Term.is_Free (Variable.is_fixed ctxt) (K true)
51 handle TERM (msg, _) => err msg | ERROR msg => err msg;
52 in (Term.dest_Free (Term.head_of lhs), eq') end;
54 val abs_def = PrimitiveDefs.abs_def #>> Term.dest_Free;
56 fun mk_def ctxt args =
58 val (xs, rhss) = split_list args;
59 val (bind, _) = ProofContext.bind_fixes xs ctxt;
60 val lhss = map (fn (x, rhs) => bind (Free (x, Term.fastype_of rhs))) args;
61 in map Logic.mk_equals (lhss ~~ rhss) end;
67 #1 o Term.dest_Free o Term.head_of o #1 o Logic.dest_equals o Term.strip_all_body;
78 Drule.implies_intr_list defs
79 #> Drule.generalize ([], map (head_of_def o Thm.term_of) defs)
80 #> funpow (length defs) (fn th => Drule.reflexive_thm RS th);
82 val expand_term = Envir.expand_term_frees o map (abs_def o Thm.term_of);
84 fun def_export _ defs = (expand defs, expand_term defs);
89 fun add_defs defs ctxt =
91 val ((bvars, mxs), specs) = defs |> split_list |>> split_list;
92 val ((bfacts, atts), rhss) = specs |> split_list |>> split_list;
93 val xs = map Name.of_binding bvars;
94 val names = map2 Thm.def_binding_optional bvars bfacts;
95 val eqs = mk_def ctxt (xs ~~ rhss);
96 val lhss = map (fst o Logic.dest_equals) eqs;
99 |> ProofContext.add_fixes (map2 (fn x => fn mx => (x, NONE, mx)) bvars mxs) |> #2
100 |> fold Variable.declare_term eqs
101 |> ProofContext.add_assms_i def_export
102 (map2 (fn a => fn eq => (a, [(eq, [])])) (names ~~ atts) eqs)
103 |>> map2 (fn lhs => fn (name, [th]) => (lhs, (name, th))) lhss
106 fun add_def (var, rhs) ctxt =
107 let val ([(lhs, (_, th))], ctxt') = add_defs [(var, (Thm.empty_binding, rhs))] ctxt
108 in ((lhs, th), ctxt') end;
113 fun fixed_abbrev ((x, mx), rhs) ctxt =
115 val T = Term.fastype_of rhs;
116 val ([x'], ctxt') = ctxt
117 |> Variable.declare_term rhs
118 |> ProofContext.add_fixes [(x, SOME T, mx)];
119 val lhs = Free (x', T);
120 val _ = cert_def ctxt' (Logic.mk_equals (lhs, rhs));
121 fun abbrev_export _ _ = (I, Envir.expand_term_frees [((x', T), rhs)]);
122 val (_, ctxt'') = Assumption.add_assms abbrev_export [] ctxt';
123 in ((lhs, rhs), ctxt'') end;
126 (* specific export -- result based on educated guessing *)
135 fun export inner outer = (*beware of closure sizes*)
137 val exp = Assumption.export false inner outer;
138 val prems = Assumption.all_prems_of inner;
142 val still_fixed = map #1 (Thm.fold_terms Term.add_frees th' []);
143 val defs = prems |> filter_out (fn prem =>
144 (case try (head_of_def o Thm.prop_of) prem of
145 SOME x => member (op =) still_fixed x
147 in (map Drule.abs_def defs, th') end
154 -------------- and --------------
155 TERM b as b xs == b as
157 fun export_cterm inner outer ct =
158 let val (defs, ct') = export inner outer (Drule.mk_term ct) ||> Drule.dest_term
159 in (ct', MetaSimplifier.rewrite true defs ct) end;
162 (* basic transitivity reasoning -- modulo beta-eta *)
166 val is_trivial = Pattern.aeconv o Logic.dest_equals o Thm.prop_of;
168 fun trans_list _ _ [] = raise Empty
169 | trans_list trans ctxt (th :: raw_eqs) =
170 (case filter_out is_trivial raw_eqs of
173 let val ((_, th' :: eqs'), ctxt') = Variable.import true (th :: eqs) ctxt
174 in singleton (Variable.export ctxt' ctxt) (fold trans eqs' th') end);
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));
185 (** defived definitions **)
187 (* transformation rules *)
189 structure Rules = GenericDataFun
194 fun merge _ = Thm.merge_thms;
197 fun print_rules ctxt =
198 Pretty.writeln (Pretty.big_list "definitional transformations:"
199 (map (ProofContext.pretty_thm ctxt) (Rules.get (Context.Proof ctxt))));
201 val defn_add = Thm.declaration_attribute (Rules.map o Thm.add_thm);
202 val defn_del = Thm.declaration_attribute (Rules.map o Thm.del_thm);
205 (* meta rewrite rules *)
207 fun meta_rewrite_conv ctxt =
208 MetaSimplifier.rewrite_cterm (false, false, false) (K (K NONE))
209 (MetaSimplifier.context ctxt MetaSimplifier.empty_ss
210 addeqcongs [Drule.equals_cong] (*protect meta-level equality*)
211 addsimps (Rules.get (Context.Proof ctxt)));
213 val meta_rewrite_rule = Conv.fconv_rule o meta_rewrite_conv;
216 (* rewriting with object-level rules *)
218 fun meta f ctxt = f o map (meta_rewrite_rule ctxt);
220 val unfold = meta MetaSimplifier.rewrite_rule;
221 val unfold_goals = meta MetaSimplifier.rewrite_goals_rule;
222 val unfold_tac = meta MetaSimplifier.rewrite_goals_tac;
223 val fold = meta MetaSimplifier.fold_rule;
224 val fold_tac = meta MetaSimplifier.fold_goals_tac;
227 (* derived defs -- potentially within the object-logic *)
229 fun derived_def ctxt conditional prop =
231 val ((c, T), rhs) = prop
232 |> Thm.cterm_of (ProofContext.theory_of ctxt)
233 |> meta_rewrite_conv ctxt
234 |> (snd o Logic.dest_equals o Thm.prop_of)
235 |> conditional ? Logic.strip_imp_concl
236 |> (abs_def o #2 o cert_def ctxt);
237 fun prove ctxt' def =
239 val frees = Term.fold_aterms (fn Free (x, _) =>
240 if Variable.is_fixed ctxt' x then I else insert (op =) x | _ => I) prop [];
242 Goal.prove ctxt' frees [] prop (K (ALLGOALS
243 (CONVERSION (meta_rewrite_conv ctxt') THEN'
244 MetaSimplifier.rewrite_goal_tac [def] THEN'
245 resolve_tac [Drule.reflexive_thm])))
246 handle ERROR msg => cat_error msg "Failed to prove definitional specification."
248 in (((c, T), rhs), prove) end;