src/Provers/ind.ML
author nipkow
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(*  Title: 	Provers/ind
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    ID:         $Id$
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    Author: 	Tobias Nipkow
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    Copyright   1991  University of Cambridge
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Generic induction package -- for use with simplifier
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*)
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signature IND_DATA =
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  sig
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  val spec: thm (* All(?P) ==> ?P(?a) *)
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  end;
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signature IND =
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  sig
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  val all_frees_tac: string -> int -> tactic
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  val ALL_IND_TAC: thm -> (int -> tactic) -> (int -> tactic)
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  val IND_TAC: thm -> (int -> tactic) -> string -> (int -> tactic)
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  end;
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functor InductionFun(Ind_Data: IND_DATA):IND =
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struct
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local open Ind_Data in
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val _$(_$Var(a_ixname,aT)) = concl_of spec;
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val a_name = implode(tl(explode(Syntax.string_of_vname a_ixname)));
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fun add_term_frees tsig =
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let fun add(tm, vars) = case tm of
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	Free(v,T) => if Type.typ_instance(tsig,T,aT) then v ins vars
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		     else vars
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      | Abs (_,_,body) => add(body,vars)
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      | rator$rand => add(rator, add(rand, vars))
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      | _ => vars
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in add end;
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fun qnt_tac i = fn (tac,var) => tac THEN res_inst_tac [(a_name,var)] spec i;
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(*Generalizes over all free variables, with the named var outermost.*)
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fun all_frees_tac (var:string) i thm = 
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    let val tsig = #tsig(Sign.rep_sg(#sign(rep_thm thm)));
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        val frees = add_term_frees tsig (nth_elem(i-1,prems_of thm),[var]);
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        val frees' = sort (rev_order o string_ord) (frees \ var) @ [var]
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    in foldl (qnt_tac i) (all_tac,frees') thm end;
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fun REPEAT_SIMP_TAC simp_tac n i =
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let fun repeat thm = 
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        (COND (has_fewer_prems n) all_tac
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	 let val k = nprems_of thm
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	 in simp_tac i THEN COND (has_fewer_prems k) repeat all_tac end)
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	thm
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in repeat end;
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fun ALL_IND_TAC sch simp_tac i thm = 
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	(resolve_tac [sch] i THEN
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	 REPEAT_SIMP_TAC simp_tac (nprems_of thm) i) thm;
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fun IND_TAC sch simp_tac var =
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	all_frees_tac var THEN' ALL_IND_TAC sch simp_tac;
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end
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end;