author | haftmann |
Fri, 07 Dec 2007 15:07:59 +0100 | |
changeset 25571 | c9e39eafc7a0 |
parent 24558 | 419f7cde7f59 |
child 26337 | 44473c957672 |
permissions | -rw-r--r-- |
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(* Title: HOL/Nominal/nominal_fresh_fun.ML |
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ID: $Id$ |
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Authors: Stefan Berghofer, Julien Narboux, TU Muenchen |
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Provides a tactic to generate fresh names and |
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a tactic to analyse instances of the fresh_fun. |
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*) |
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(* First some functions that should be in the library *) |
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(* A tactical which applies a list of int -> tactic to the *) |
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(* corresponding subgoals present after the application of *) |
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(* another tactic. *) |
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(* *) |
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(* T THENL [A,B,C] is equivalent to T THEN (C 3 THEN B 2 THEN A 1) *) |
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infix 1 THENL |
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fun tac THENL tacs = |
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tac THEN |
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(EVERY (map (fn (tac,i) => tac i) (rev tacs ~~ (length tacs downto 1)))) |
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(* A tactic which only succeeds when the argument *) |
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(* tactic solves completely the specified subgoal *) |
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fun SOLVEI t = t THEN_ALL_NEW (fn i => no_tac); |
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(* A version of TRY for int -> tactic *) |
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fun TRY' tac i = TRY (tac i); |
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fun gen_res_inst_tac_term instf tyinst tinst elim th i st = |
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let |
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val thy = theory_of_thm st; |
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val cgoal = nth (cprems_of st) (i - 1); |
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val {maxidx, ...} = rep_cterm cgoal; |
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val j = maxidx + 1; |
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val tyinst' = map (apfst (Logic.incr_tvar j)) tyinst; |
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val ps = Logic.strip_params (term_of cgoal); |
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val Ts = map snd ps; |
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val tinst' = map (fn (t, u) => |
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(head_of (Logic.incr_indexes (Ts, j) t), |
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list_abs (ps, u))) tinst; |
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val th' = instf |
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(map (pairself (ctyp_of thy)) tyinst') |
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(map (pairself (cterm_of thy)) tinst') |
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(Thm.lift_rule cgoal th) |
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in |
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compose_tac (elim, th', nprems_of th) i st |
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end handle Subscript => Seq.empty; |
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val res_inst_tac_term = |
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gen_res_inst_tac_term (curry Thm.instantiate); |
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val res_inst_tac_term' = |
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gen_res_inst_tac_term (K Drule.cterm_instantiate) []; |
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fun cut_inst_tac_term' tinst th = |
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res_inst_tac_term' tinst false (Tactic.make_elim_preserve th); |
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fun get_dyn_thm thy name atom_name = (PureThy.get_thm thy (Name name)) handle _ => |
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raise ERROR ("The atom type "^atom_name^" is not defined."); |
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(* End of function waiting to be in the library :o) *) |
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(* The theorems needed that are known at compile time. *) |
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val at_exists_fresh' = @{thm "at_exists_fresh'"}; |
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val fresh_fun_app' = @{thm "fresh_fun_app'"}; |
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val fresh_prod = @{thm "fresh_prod"}; |
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(* A tactic to generate a name fresh for all the free *) |
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(* variables and parameters of the goal *) |
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fun generate_fresh_tac atom_name i thm = |
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let |
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val thy = theory_of_thm thm; |
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(* the parsing function returns a qualified name, we get back the base name *) |
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val atom_basename = Sign.base_name atom_name; |
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val goal = List.nth(prems_of thm, i-1); |
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val ps = Logic.strip_params goal; |
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val Ts = rev (map snd ps); |
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fun is_of_fs_name T = Sign.of_sort thy (T, Sign.intern_sort thy ["fs_"^atom_basename]); |
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(* rebuild de bruijn indices *) |
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val bvs = map_index (Bound o fst) ps; |
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(* select variables of the right class *) |
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val vs = filter (fn t => is_of_fs_name (fastype_of1 (Ts, t))) |
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(term_frees goal @ bvs); |
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(* build the tuple *) |
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val s = (Library.foldr1 (fn (v, s) => |
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HOLogic.pair_const (fastype_of1 (Ts, v)) (fastype_of1 (Ts, s)) $ v $ s) vs) handle _ => HOLogic.unit ; |
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val fs_name_thm = get_dyn_thm thy ("fs_"^atom_basename^"1") atom_basename; |
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val at_name_inst_thm = get_dyn_thm thy ("at_"^atom_basename^"_inst") atom_basename; |
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val exists_fresh' = at_name_inst_thm RS at_exists_fresh'; |
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(* find the variable we want to instantiate *) |
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val x = hd (term_vars (prop_of exists_fresh')); |
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in |
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(cut_inst_tac_term' [(x,s)] exists_fresh' 1 THEN |
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rtac fs_name_thm 1 THEN |
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etac exE 1) thm |
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handle Empty => all_tac thm (* if we collected no variables then we do nothing *) |
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end; |
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fun get_inner_fresh_fun (Bound j) = NONE |
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| get_inner_fresh_fun (v as Free _) = NONE |
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| get_inner_fresh_fun (v as Var _) = NONE |
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| get_inner_fresh_fun (Const _) = NONE |
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| get_inner_fresh_fun (Abs (_, _, t)) = get_inner_fresh_fun t |
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| get_inner_fresh_fun (Const ("Nominal.fresh_fun",Type("fun",[Type ("fun",[Type (T,_),_]),_])) $ u) |
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= SOME T |
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| get_inner_fresh_fun (t $ u) = |
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let val a = get_inner_fresh_fun u in |
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if a = NONE then get_inner_fresh_fun t else a |
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end; |
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(* This tactic generates a fresh name of the atom type *) |
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(* given by the innermost fresh_fun *) |
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fun generate_fresh_fun_tac i thm = |
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let |
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val goal = List.nth(prems_of thm, i-1); |
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val atom_name_opt = get_inner_fresh_fun goal; |
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in |
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case atom_name_opt of |
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NONE => all_tac thm |
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| SOME atom_name => generate_fresh_tac atom_name i thm |
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end |
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(* Two substitution tactics which looks for the innermost occurence in |
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one assumption or in the conclusion *) |
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val search_fun = curry (Seq.flat o (uncurry EqSubst.searchf_bt_unify_valid)); |
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val search_fun_asm = EqSubst.skip_first_asm_occs_search EqSubst.searchf_bt_unify_valid; |
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fun subst_inner_tac ctx = EqSubst.eqsubst_tac' ctx search_fun; |
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fun subst_inner_asm_tac_aux i ctx = EqSubst.eqsubst_asm_tac' ctx search_fun_asm i; |
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(* A tactic to substitute in the first assumption |
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which contains an occurence. *) |
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fun subst_inner_asm_tac ctx th = |
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curry (curry (FIRST' (map uncurry (map uncurry (map subst_inner_asm_tac_aux |
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(1 upto Thm.nprems_of th)))))) ctx th; |
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fun fresh_fun_tac no_asm i thm = |
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(* Find the variable we instantiate *) |
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let |
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val thy = theory_of_thm thm; |
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val ctx = Context.init_proof thy; |
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val ss = simpset_of thy; |
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val abs_fresh = PureThy.get_thms thy (Name "abs_fresh"); |
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val fresh_perm_app = PureThy.get_thms thy (Name "fresh_perm_app"); |
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val ss' = ss addsimps fresh_prod::abs_fresh; |
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val ss'' = ss' addsimps fresh_perm_app; |
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val x = hd (tl (term_vars (prop_of exI))); |
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val goal = nth (prems_of thm) (i-1); |
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val atom_name_opt = get_inner_fresh_fun goal; |
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val n = List.length (Logic.strip_params goal); |
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(* Here we rely on the fact that the variable introduced by generate_fresh_tac *) |
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(* is the last one in the list, the inner one *) |
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in |
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case atom_name_opt of |
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NONE => all_tac thm |
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| SOME atom_name => |
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let |
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val atom_basename = Sign.base_name atom_name; |
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val pt_name_inst = get_dyn_thm thy ("pt_"^atom_basename^"_inst") atom_basename; |
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val at_name_inst = get_dyn_thm thy ("at_"^atom_basename^"_inst") atom_basename; |
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fun inst_fresh vars params i st = |
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let val vars' = term_vars (prop_of st); |
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val thy = theory_of_thm st; |
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in case vars' \\ vars of |
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[x] => Seq.single (Thm.instantiate ([],[(cterm_of thy x,cterm_of thy (list_abs (params,Bound 0)))]) st) |
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| _ => error "fresh_fun_simp: Too many variables, please report." |
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end |
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in |
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((fn st => |
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let |
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val vars = term_vars (prop_of st); |
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val params = Logic.strip_params (nth (prems_of st) (i-1)) |
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(* The tactics which solve the subgoals generated |
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by the conditionnal rewrite rule. *) |
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val post_rewrite_tacs = |
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[rtac pt_name_inst, |
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rtac at_name_inst, |
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TRY' (SOLVEI (NominalPermeq.finite_guess_tac ss'')), |
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inst_fresh vars params THEN' |
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(TRY' (SOLVEI (NominalPermeq.fresh_guess_tac ss''))) THEN' |
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(TRY' (SOLVEI (asm_full_simp_tac ss'')))] |
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in |
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((if no_asm then no_tac else |
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(subst_inner_asm_tac ctx fresh_fun_app' i THENL post_rewrite_tacs)) |
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ORELSE |
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(subst_inner_tac ctx fresh_fun_app' i THENL post_rewrite_tacs)) st |
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end)) thm |
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end |
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end |
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(* syntax for options, given "(no_asm)" will give back true, without |
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gives back false *) |
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val options_syntax = |
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(Args.parens (Args.$$$ "no_asm") >> (K true)) || |
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(Scan.succeed false); |
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val setup_generate_fresh = |
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Method.goal_args_ctxt' Args.tyname (fn ctxt => generate_fresh_tac) |
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val setup_fresh_fun_simp = |
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Method.simple_args options_syntax |
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(fn b => fn _ => Method.SIMPLE_METHOD (fresh_fun_tac b 1)) |