--- a/Nominal-General/nominal_eqvt.ML Sun Nov 14 12:09:14 2010 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,142 +0,0 @@
-(* Title: nominal_eqvt.ML
- Author: Stefan Berghofer (original code)
- Author: Christian Urban
-
- Automatic proofs for equivariance of inductive predicates.
-*)
-
-signature NOMINAL_EQVT =
-sig
- val eqvt_rel_tac: Proof.context -> string list -> term -> thm -> thm list -> int -> tactic
- val eqvt_rel_single_case_tac: Proof.context -> string list -> term -> thm -> int -> tactic
-
- val equivariance: bool -> term list -> thm -> thm list -> Proof.context -> thm list * local_theory
- val equivariance_cmd: string -> Proof.context -> local_theory
-end
-
-structure Nominal_Eqvt : NOMINAL_EQVT =
-struct
-
-open Nominal_Permeq;
-open Nominal_ThmDecls;
-
-val atomize_conv =
- MetaSimplifier.rewrite_cterm (true, false, false) (K (K NONE))
- (HOL_basic_ss addsimps @{thms induct_atomize});
-val atomize_intr = Conv.fconv_rule (Conv.prems_conv ~1 atomize_conv);
-fun atomize_induct ctxt = Conv.fconv_rule (Conv.prems_conv ~1
- (Conv.params_conv ~1 (K (Conv.prems_conv ~1 atomize_conv)) ctxt));
-
-
-(** equivariance tactics **)
-
-val perm_boolE = @{thm permute_boolE}
-val perm_cancel = @{thms permute_minus_cancel(2)}
-
-fun eqvt_rel_single_case_tac ctxt pred_names pi intro =
- let
- val thy = ProofContext.theory_of ctxt
- val cpi = Thm.cterm_of thy (mk_minus pi)
- val pi_intro_rule = Drule.instantiate' [] [SOME cpi] perm_boolE
- val simps1 = HOL_basic_ss addsimps @{thms permute_fun_def minus_minus split_paired_all}
- val simps2 = HOL_basic_ss addsimps @{thms permute_bool_def}
- in
- eqvt_strict_tac ctxt [] pred_names THEN'
- SUBPROOF (fn {prems, context as ctxt, ...} =>
- let
- val prems' = map (transform_prem2 ctxt pred_names) prems
- val tac1 = resolve_tac prems'
- val tac2 = EVERY' [ rtac pi_intro_rule,
- eqvt_strict_tac ctxt perm_cancel pred_names, resolve_tac prems' ]
- val tac3 = EVERY' [ rtac pi_intro_rule,
- eqvt_strict_tac ctxt perm_cancel pred_names, simp_tac simps1,
- simp_tac simps2, resolve_tac prems']
- in
- (rtac intro THEN_ALL_NEW FIRST' [tac1, tac2, tac3]) 1
- end) ctxt
- end
-
-fun eqvt_rel_tac ctxt pred_names pi induct intros =
- let
- val cases = map (eqvt_rel_single_case_tac ctxt pred_names pi) intros
- in
- EVERY' (rtac induct :: cases)
- end
-
-
-(** equivariance procedure *)
-
-fun prepare_goal pi pred =
- let
- val (c, xs) = strip_comb pred;
- in
- HOLogic.mk_imp (pred, list_comb (c, map (mk_perm pi) xs))
- end
-
-(* stores thm under name.eqvt and adds [eqvt]-attribute *)
-
-fun note_named_thm (name, thm) ctxt =
- let
- val thm_name = Binding.qualified_name
- (Long_Name.qualify (Long_Name.base_name name) "eqvt")
- val attr = Attrib.internal (K eqvt_add)
- val ((_, [thm']), ctxt') = Local_Theory.note ((thm_name, [attr]), [thm]) ctxt
- in
- (thm', ctxt')
- end
-
-fun equivariance note_flag pred_trms raw_induct intrs ctxt =
- let
- val is_already_eqvt =
- filter (is_eqvt ctxt) pred_trms
- |> map (Syntax.string_of_term ctxt)
- val _ = if null is_already_eqvt then ()
- else error ("Already equivariant: " ^ commas is_already_eqvt)
-
- val pred_names = map (fst o dest_Const) pred_trms
- val raw_induct' = atomize_induct ctxt raw_induct
- val intrs' = map atomize_intr intrs
-
- val (([raw_concl], [raw_pi]), ctxt') =
- ctxt
- |> Variable.import_terms false [concl_of raw_induct']
- ||>> Variable.variant_fixes ["p"]
- val pi = Free (raw_pi, @{typ perm})
-
- val preds = map (fst o HOLogic.dest_imp)
- (HOLogic.dest_conj (HOLogic.dest_Trueprop raw_concl));
-
- val goal = HOLogic.mk_Trueprop
- (foldr1 HOLogic.mk_conj (map (prepare_goal pi) preds))
-
- val thms = Goal.prove ctxt' [] [] goal
- (fn {context,...} => eqvt_rel_tac context pred_names pi raw_induct' intrs' 1)
- |> Datatype_Aux.split_conj_thm
- |> ProofContext.export ctxt' ctxt
- |> map (fn th => th RS mp)
- |> map zero_var_indexes
- in
- if note_flag
- then fold_map note_named_thm (pred_names ~~ thms) ctxt
- else (thms, ctxt)
- end
-
-fun equivariance_cmd pred_name ctxt =
- let
- val thy = ProofContext.theory_of ctxt
- val (_, {preds, raw_induct, intrs, ...}) =
- Inductive.the_inductive ctxt (Sign.intern_const thy pred_name)
- in
- equivariance true preds raw_induct intrs ctxt |> snd
- end
-
-local structure P = Parse and K = Keyword in
-
-val _ =
- Outer_Syntax.local_theory "equivariance"
- "Proves equivariance for inductive predicate involving nominal datatypes."
- K.thy_decl (P.xname >> equivariance_cmd);
-
-end;
-
-end (* structure *)