TFL/tfl.ML
author wenzelm
Fri Oct 12 12:08:04 2001 +0200 (2001-10-12)
changeset 11729 a7da2e8b5762
parent 11632 6fc8de600f58
child 12902 a23dc0b7566f
permissions -rw-r--r--
removed read_inst', no longer export insts';
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(*  Title:      TFL/tfl.ML
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    ID:         $Id$
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    Author:     Konrad Slind, Cambridge University Computer Laboratory
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    Copyright   1997  University of Cambridge
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First part of main module.
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*)
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signature PRIM =
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sig
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  val trace: bool ref
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  type pattern
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  val mk_functional: theory -> term list -> {functional: term, pats: pattern list}
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  val wfrec_definition0: theory -> string -> term -> term -> theory * thm
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  val post_definition: thm list -> theory * (thm * pattern list) ->
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   {theory: theory,
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    rules: thm,
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    rows: int list,
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    TCs: term list list,
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    full_pats_TCs: (term * term list) list}
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  val wfrec_eqns: theory -> xstring -> thm list -> term list ->
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   {WFR: term,
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    SV: term list,
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    proto_def: term,
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    extracta: (thm * term list) list,
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    pats: pattern list}
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  val lazyR_def: theory -> xstring -> thm list -> term list ->
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   {theory: theory,
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    rules: thm,
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    R: term,
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    SV: term list,
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    full_pats_TCs: (term * term list) list,
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    patterns : pattern list}
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  val mk_induction: theory ->
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    {fconst: term, R: term, SV: term list, pat_TCs_list: (term * term list) list} -> thm
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  val postprocess: bool -> {wf_tac: tactic, terminator: tactic, simplifier: cterm -> thm}
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    -> theory -> {rules: thm, induction: thm, TCs: term list list}
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    -> {rules: thm, induction: thm, nested_tcs: thm list}
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end;
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structure Prim: PRIM =
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struct
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val trace = ref false;
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open BasisLibrary;
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structure R = Rules;
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structure S = USyntax;
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structure U = Utils;
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fun TFL_ERR func mesg = U.ERR {module = "Tfl", func = func, mesg = mesg};
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val concl = #2 o R.dest_thm;
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val hyp = #1 o R.dest_thm;
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val list_mk_type = U.end_itlist (curry (op -->));
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fun enumerate xs = ListPair.zip(xs, 0 upto (length xs - 1));
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fun front_last [] = raise TFL_ERR "front_last" "empty list"
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  | front_last [x] = ([],x)
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  | front_last (h::t) =
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     let val (pref,x) = front_last t
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     in
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        (h::pref,x)
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     end;
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(*---------------------------------------------------------------------------
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 * The next function is common to pattern-match translation and
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 * proof of completeness of cases for the induction theorem.
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 *
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 * The curried function "gvvariant" returns a function to generate distinct
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 * variables that are guaranteed not to be in names.  The names of
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 * the variables go u, v, ..., z, aa, ..., az, ...  The returned
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 * function contains embedded refs!
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 *---------------------------------------------------------------------------*)
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fun gvvariant names =
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  let val slist = ref names
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      val vname = ref "u"
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      fun new() =
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         if !vname mem_string (!slist)
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         then (vname := bump_string (!vname);  new())
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         else (slist := !vname :: !slist;  !vname)
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  in
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  fn ty => Free(new(), ty)
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  end;
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(*---------------------------------------------------------------------------
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 * Used in induction theorem production. This is the simple case of
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 * partitioning up pattern rows by the leading constructor.
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 *---------------------------------------------------------------------------*)
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fun ipartition gv (constructors,rows) =
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  let fun pfail s = raise TFL_ERR "partition.part" s
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      fun part {constrs = [],   rows = [],   A} = rev A
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        | part {constrs = [],   rows = _::_, A} = pfail"extra cases in defn"
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        | part {constrs = _::_, rows = [],   A} = pfail"cases missing in defn"
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        | part {constrs = c::crst, rows,     A} =
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          let val (Name,Ty) = dest_Const c
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              val L = binder_types Ty
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              val (in_group, not_in_group) =
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               U.itlist (fn (row as (p::rst, rhs)) =>
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                         fn (in_group,not_in_group) =>
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                  let val (pc,args) = S.strip_comb p
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                  in if (#1(dest_Const pc) = Name)
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                     then ((args@rst, rhs)::in_group, not_in_group)
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                     else (in_group, row::not_in_group)
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                  end)      rows ([],[])
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              val col_types = U.take type_of (length L, #1(hd in_group))
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          in
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          part{constrs = crst, rows = not_in_group,
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               A = {constructor = c,
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                    new_formals = map gv col_types,
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                    group = in_group}::A}
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          end
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  in part{constrs = constructors, rows = rows, A = []}
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  end;
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(*---------------------------------------------------------------------------
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 * Each pattern carries with it a tag (i,b) where
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 * i is the clause it came from and
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 * b=true indicates that clause was given by the user
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 * (or is an instantiation of a user supplied pattern)
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 * b=false --> i = ~1
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 *---------------------------------------------------------------------------*)
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type pattern = term * (int * bool)
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fun pattern_map f (tm,x) = (f tm, x);
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fun pattern_subst theta = pattern_map (subst_free theta);
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val pat_of = fst;
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fun row_of_pat x = fst (snd x);
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fun given x = snd (snd x);
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(*---------------------------------------------------------------------------
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 * Produce an instance of a constructor, plus genvars for its arguments.
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 *---------------------------------------------------------------------------*)
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fun fresh_constr ty_match colty gv c =
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  let val (_,Ty) = dest_Const c
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      val L = binder_types Ty
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      and ty = body_type Ty
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      val ty_theta = ty_match ty colty
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      val c' = S.inst ty_theta c
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      val gvars = map (S.inst ty_theta o gv) L
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  in (c', gvars)
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  end;
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(*---------------------------------------------------------------------------
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 * Goes through a list of rows and picks out the ones beginning with a
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 * pattern with constructor = Name.
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 *---------------------------------------------------------------------------*)
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fun mk_group Name rows =
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  U.itlist (fn (row as ((prfx, p::rst), rhs)) =>
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            fn (in_group,not_in_group) =>
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               let val (pc,args) = S.strip_comb p
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               in if ((#1 (Term.dest_Const pc) = Name) handle TERM _ => false)
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                  then (((prfx,args@rst), rhs)::in_group, not_in_group)
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                  else (in_group, row::not_in_group) end)
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      rows ([],[]);
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(*---------------------------------------------------------------------------
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 * Partition the rows. Not efficient: we should use hashing.
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 *---------------------------------------------------------------------------*)
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fun partition _ _ (_,_,_,[]) = raise TFL_ERR "partition" "no rows"
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  | partition gv ty_match
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              (constructors, colty, res_ty, rows as (((prfx,_),_)::_)) =
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let val fresh = fresh_constr ty_match colty gv
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     fun part {constrs = [],      rows, A} = rev A
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       | part {constrs = c::crst, rows, A} =
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         let val (c',gvars) = fresh c
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             val (Name,Ty) = dest_Const c'
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             val (in_group, not_in_group) = mk_group Name rows
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             val in_group' =
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                 if (null in_group)  (* Constructor not given *)
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                 then [((prfx, #2(fresh c)), (S.ARB res_ty, (~1,false)))]
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                 else in_group
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         in
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         part{constrs = crst,
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              rows = not_in_group,
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              A = {constructor = c',
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                   new_formals = gvars,
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                   group = in_group'}::A}
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         end
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in part{constrs=constructors, rows=rows, A=[]}
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end;
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(*---------------------------------------------------------------------------
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 * Misc. routines used in mk_case
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 *---------------------------------------------------------------------------*)
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fun mk_pat (c,l) =
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  let val L = length (binder_types (type_of c))
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      fun build (prfx,tag,plist) =
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          let val args   = take (L,plist)
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              and plist' = drop(L,plist)
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          in (prfx,tag,list_comb(c,args)::plist') end
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  in map build l end;
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fun v_to_prfx (prfx, v::pats) = (v::prfx,pats)
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  | v_to_prfx _ = raise TFL_ERR "mk_case" "v_to_prfx";
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fun v_to_pats (v::prfx,tag, pats) = (prfx, tag, v::pats)
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  | v_to_pats _ = raise TFL_ERR "mk_case" "v_to_pats";
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(*----------------------------------------------------------------------------
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 * Translation of pattern terms into nested case expressions.
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 *
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 * This performs the translation and also builds the full set of patterns.
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 * Thus it supports the construction of induction theorems even when an
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 * incomplete set of patterns is given.
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 *---------------------------------------------------------------------------*)
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fun mk_case ty_info ty_match usednames range_ty =
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 let
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 fun mk_case_fail s = raise TFL_ERR "mk_case" s
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 val fresh_var = gvvariant usednames
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 val divide = partition fresh_var ty_match
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 fun expand constructors ty ((_,[]), _) = mk_case_fail"expand_var_row"
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   | expand constructors ty (row as ((prfx, p::rst), rhs)) =
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       if (is_Free p)
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       then let val fresh = fresh_constr ty_match ty fresh_var
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                fun expnd (c,gvs) =
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                  let val capp = list_comb(c,gvs)
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                  in ((prfx, capp::rst), pattern_subst[(p,capp)] rhs)
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                  end
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            in map expnd (map fresh constructors)  end
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       else [row]
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 fun mk{rows=[],...} = mk_case_fail"no rows"
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   | mk{path=[], rows = ((prfx, []), (tm,tag))::_} =  (* Done *)
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        ([(prfx,tag,[])], tm)
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   | mk{path=[], rows = _::_} = mk_case_fail"blunder"
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   | mk{path as u::rstp, rows as ((prfx, []), rhs)::rst} =
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        mk{path = path,
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           rows = ((prfx, [fresh_var(type_of u)]), rhs)::rst}
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   | mk{path = u::rstp, rows as ((_, p::_), _)::_} =
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     let val (pat_rectangle,rights) = ListPair.unzip rows
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         val col0 = map(hd o #2) pat_rectangle
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     in
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     if (forall is_Free col0)
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     then let val rights' = map (fn(v,e) => pattern_subst[(v,u)] e)
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                                (ListPair.zip (col0, rights))
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              val pat_rectangle' = map v_to_prfx pat_rectangle
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              val (pref_patl,tm) = mk{path = rstp,
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                                      rows = ListPair.zip (pat_rectangle',
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                                                           rights')}
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          in (map v_to_pats pref_patl, tm)
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          end
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     else
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     let val pty as Type (ty_name,_) = type_of p
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     in
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     case (ty_info ty_name)
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     of None => mk_case_fail("Not a known datatype: "^ty_name)
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      | Some{case_const,constructors} =>
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        let
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            val case_const_name = #1(dest_Const case_const)
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            val nrows = List.concat (map (expand constructors pty) rows)
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            val subproblems = divide(constructors, pty, range_ty, nrows)
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            val groups      = map #group subproblems
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            and new_formals = map #new_formals subproblems
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            and constructors' = map #constructor subproblems
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            val news = map (fn (nf,rows) => {path = nf@rstp, rows=rows})
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                           (ListPair.zip (new_formals, groups))
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            val rec_calls = map mk news
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            val (pat_rect,dtrees) = ListPair.unzip rec_calls
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            val case_functions = map S.list_mk_abs
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                                  (ListPair.zip (new_formals, dtrees))
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            val types = map type_of (case_functions@[u]) @ [range_ty]
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            val case_const' = Const(case_const_name, list_mk_type types)
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            val tree = list_comb(case_const', case_functions@[u])
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            val pat_rect1 = List.concat
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                              (ListPair.map mk_pat (constructors', pat_rect))
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        in (pat_rect1,tree)
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        end
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     end end
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 in mk
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 end;
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(* Repeated variable occurrences in a pattern are not allowed. *)
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fun FV_multiset tm =
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   case (S.dest_term tm)
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     of S.VAR{Name,Ty} => [Free(Name,Ty)]
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      | S.CONST _ => []
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      | S.COMB{Rator, Rand} => FV_multiset Rator @ FV_multiset Rand
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      | S.LAMB _ => raise TFL_ERR "FV_multiset" "lambda";
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fun no_repeat_vars thy pat =
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 let fun check [] = true
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       | check (v::rst) =
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         if mem_term (v,rst) then
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            raise TFL_ERR "no_repeat_vars"
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                          (quote (#1 (dest_Free v)) ^
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                          " occurs repeatedly in the pattern " ^
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                          quote (string_of_cterm (Thry.typecheck thy pat)))
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         else check rst
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 in check (FV_multiset pat)
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 end;
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fun dest_atom (Free p) = p
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  | dest_atom (Const p) = p
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  | dest_atom  _ = raise TFL_ERR "dest_atom" "function name not an identifier";
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fun same_name (p,q) = #1(dest_atom p) = #1(dest_atom q);
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local fun mk_functional_err s = raise TFL_ERR "mk_functional" s
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      fun single [_$_] =
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              mk_functional_err "recdef does not allow currying"
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        | single [f] = f
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        | single fs  =
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              (*multiple function names?*)
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              if length (gen_distinct same_name fs) < length fs
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              then mk_functional_err
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                   "The function being declared appears with multiple types"
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              else mk_functional_err
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                   (Int.toString (length fs) ^
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                    " distinct function names being declared")
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in
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fun mk_functional thy clauses =
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 let val (L,R) = ListPair.unzip (map HOLogic.dest_eq clauses
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                   handle TERM _ => raise TFL_ERR "mk_functional"
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                        "recursion equations must use the = relation")
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     val (funcs,pats) = ListPair.unzip (map (fn (t$u) =>(t,u)) L)
wenzelm@10769
   332
     val atom = single (gen_distinct (op aconv) funcs)
wenzelm@10769
   333
     val (fname,ftype) = dest_atom atom
wenzelm@10769
   334
     val dummy = map (no_repeat_vars thy) pats
wenzelm@10769
   335
     val rows = ListPair.zip (map (fn x => ([]:term list,[x])) pats,
wenzelm@10769
   336
                              map (fn (t,i) => (t,(i,true))) (enumerate R))
wenzelm@10769
   337
     val names = foldr add_term_names (R,[])
wenzelm@10769
   338
     val atype = type_of(hd pats)
wenzelm@10769
   339
     and aname = variant names "a"
wenzelm@10769
   340
     val a = Free(aname,atype)
wenzelm@10769
   341
     val ty_info = Thry.match_info thy
wenzelm@10769
   342
     val ty_match = Thry.match_type thy
wenzelm@10769
   343
     val range_ty = type_of (hd R)
wenzelm@10769
   344
     val (patts, case_tm) = mk_case ty_info ty_match (aname::names) range_ty
wenzelm@10769
   345
                                    {path=[a], rows=rows}
wenzelm@10769
   346
     val patts1 = map (fn (_,tag,[pat]) => (pat,tag)) patts
wenzelm@10769
   347
          handle Match => mk_functional_err "error in pattern-match translation"
wenzelm@10769
   348
     val patts2 = Library.sort (Library.int_ord o Library.pairself row_of_pat) patts1
wenzelm@10769
   349
     val finals = map row_of_pat patts2
wenzelm@10769
   350
     val originals = map (row_of_pat o #2) rows
wenzelm@10769
   351
     val dummy = case (originals\\finals)
wenzelm@10769
   352
             of [] => ()
wenzelm@10769
   353
          | L => mk_functional_err
wenzelm@10769
   354
 ("The following clauses are redundant (covered by preceding clauses): " ^
wenzelm@10769
   355
                   commas (map (fn i => Int.toString (i + 1)) L))
wenzelm@10769
   356
 in {functional = Abs(Sign.base_name fname, ftype,
wenzelm@10769
   357
                      abstract_over (atom,
wenzelm@10769
   358
                                     absfree(aname,atype, case_tm))),
wenzelm@10769
   359
     pats = patts2}
wenzelm@10769
   360
end end;
wenzelm@10769
   361
wenzelm@10769
   362
wenzelm@10769
   363
(*----------------------------------------------------------------------------
wenzelm@10769
   364
 *
wenzelm@10769
   365
 *                    PRINCIPLES OF DEFINITION
wenzelm@10769
   366
 *
wenzelm@10769
   367
 *---------------------------------------------------------------------------*)
wenzelm@10769
   368
wenzelm@10769
   369
wenzelm@10769
   370
(*For Isabelle, the lhs of a definition must be a constant.*)
wenzelm@10769
   371
fun mk_const_def sign (Name, Ty, rhs) =
wenzelm@10769
   372
    Sign.infer_types sign (K None) (K None) [] false
wenzelm@10769
   373
               ([Const("==",dummyT) $ Const(Name,Ty) $ rhs], propT)
wenzelm@10769
   374
    |> #1;
wenzelm@10769
   375
wenzelm@10769
   376
(*Make all TVars available for instantiation by adding a ? to the front*)
wenzelm@10769
   377
fun poly_tvars (Type(a,Ts)) = Type(a, map (poly_tvars) Ts)
wenzelm@10769
   378
  | poly_tvars (TFree (a,sort)) = TVar (("?" ^ a, 0), sort)
wenzelm@10769
   379
  | poly_tvars (TVar ((a,i),sort)) = TVar (("?" ^ a, i+1), sort);
wenzelm@10769
   380
wenzelm@10769
   381
local val f_eq_wfrec_R_M =
wenzelm@10769
   382
           #ant(S.dest_imp(#2(S.strip_forall (concl Thms.WFREC_COROLLARY))))
wenzelm@10769
   383
      val {lhs=f, rhs} = S.dest_eq f_eq_wfrec_R_M
wenzelm@10769
   384
      val (fname,_) = dest_Free f
wenzelm@10769
   385
      val (wfrec,_) = S.strip_comb rhs
wenzelm@10769
   386
in
wenzelm@10769
   387
fun wfrec_definition0 thy fid R (functional as Abs(Name, Ty, _)) =
wenzelm@10769
   388
 let val def_name = if Name<>fid then
wenzelm@10769
   389
                        raise TFL_ERR "wfrec_definition0"
wenzelm@10769
   390
                                      ("Expected a definition of " ^
wenzelm@10769
   391
                                             quote fid ^ " but found one of " ^
wenzelm@10769
   392
                                      quote Name)
wenzelm@10769
   393
                    else Name ^ "_def"
wenzelm@10769
   394
     val wfrec_R_M =  map_term_types poly_tvars
wenzelm@10769
   395
                          (wfrec $ map_term_types poly_tvars R)
wenzelm@10769
   396
                      $ functional
wenzelm@10769
   397
     val def_term = mk_const_def (Theory.sign_of thy) (Name, Ty, wfrec_R_M)
wenzelm@10769
   398
     val (thy', [def]) = PureThy.add_defs_i false [Thm.no_attributes (def_name, def_term)] thy
wenzelm@10769
   399
 in (thy', def) end;
wenzelm@10769
   400
end;
wenzelm@10769
   401
wenzelm@10769
   402
wenzelm@10769
   403
wenzelm@10769
   404
(*---------------------------------------------------------------------------
wenzelm@10769
   405
 * This structure keeps track of congruence rules that aren't derived
wenzelm@10769
   406
 * from a datatype definition.
wenzelm@10769
   407
 *---------------------------------------------------------------------------*)
wenzelm@10769
   408
fun extraction_thms thy =
wenzelm@10769
   409
 let val {case_rewrites,case_congs} = Thry.extract_info thy
wenzelm@10769
   410
 in (case_rewrites, case_congs)
wenzelm@10769
   411
 end;
wenzelm@10769
   412
wenzelm@10769
   413
wenzelm@10769
   414
(*---------------------------------------------------------------------------
wenzelm@10769
   415
 * Pair patterns with termination conditions. The full list of patterns for
wenzelm@10769
   416
 * a definition is merged with the TCs arising from the user-given clauses.
wenzelm@10769
   417
 * There can be fewer clauses than the full list, if the user omitted some
wenzelm@10769
   418
 * cases. This routine is used to prepare input for mk_induction.
wenzelm@10769
   419
 *---------------------------------------------------------------------------*)
wenzelm@10769
   420
fun merge full_pats TCs =
wenzelm@10769
   421
let fun insert (p,TCs) =
wenzelm@10769
   422
      let fun insrt ((x as (h,[]))::rst) =
wenzelm@10769
   423
                 if (p aconv h) then (p,TCs)::rst else x::insrt rst
wenzelm@10769
   424
            | insrt (x::rst) = x::insrt rst
wenzelm@10769
   425
            | insrt[] = raise TFL_ERR "merge.insert" "pattern not found"
wenzelm@10769
   426
      in insrt end
wenzelm@10769
   427
    fun pass ([],ptcl_final) = ptcl_final
wenzelm@10769
   428
      | pass (ptcs::tcl, ptcl) = pass(tcl, insert ptcs ptcl)
wenzelm@10769
   429
in
wenzelm@10769
   430
  pass (TCs, map (fn p => (p,[])) full_pats)
wenzelm@10769
   431
end;
wenzelm@10769
   432
wenzelm@10769
   433
wenzelm@10769
   434
fun givens pats = map pat_of (filter given pats);
wenzelm@10769
   435
wenzelm@10769
   436
fun post_definition meta_tflCongs (theory, (def, pats)) =
wenzelm@10769
   437
 let val tych = Thry.typecheck theory
wenzelm@10769
   438
     val f = #lhs(S.dest_eq(concl def))
wenzelm@10769
   439
     val corollary = R.MATCH_MP Thms.WFREC_COROLLARY def
wenzelm@10769
   440
     val pats' = filter given pats
wenzelm@10769
   441
     val given_pats = map pat_of pats'
wenzelm@10769
   442
     val rows = map row_of_pat pats'
wenzelm@10769
   443
     val WFR = #ant(S.dest_imp(concl corollary))
wenzelm@10769
   444
     val R = #Rand(S.dest_comb WFR)
wenzelm@10769
   445
     val corollary' = R.UNDISCH corollary  (* put WF R on assums *)
wenzelm@10769
   446
     val corollaries = map (fn pat => R.SPEC (tych pat) corollary')
wenzelm@10769
   447
                           given_pats
wenzelm@10769
   448
     val (case_rewrites,context_congs) = extraction_thms theory
wenzelm@10769
   449
     val corollaries' = map(rewrite_rule case_rewrites) corollaries
wenzelm@10769
   450
     val extract = R.CONTEXT_REWRITE_RULE
wenzelm@10769
   451
                     (f, [R], cut_apply, meta_tflCongs@context_congs)
wenzelm@10769
   452
     val (rules, TCs) = ListPair.unzip (map extract corollaries')
wenzelm@10769
   453
     val rules0 = map (rewrite_rule [Thms.CUT_DEF]) rules
wenzelm@10769
   454
     val mk_cond_rule = R.FILTER_DISCH_ALL(not o curry (op aconv) WFR)
wenzelm@10769
   455
     val rules1 = R.LIST_CONJ(map mk_cond_rule rules0)
wenzelm@10769
   456
 in
wenzelm@10769
   457
 {theory = theory,
wenzelm@10769
   458
  rules = rules1,
wenzelm@10769
   459
  rows = rows,
wenzelm@10769
   460
  full_pats_TCs = merge (map pat_of pats) (ListPair.zip (given_pats, TCs)),
wenzelm@10769
   461
  TCs = TCs}
wenzelm@10769
   462
 end;
wenzelm@10769
   463
wenzelm@10769
   464
wenzelm@10769
   465
(*---------------------------------------------------------------------------
wenzelm@10769
   466
 * Perform the extraction without making the definition. Definition and
wenzelm@10769
   467
 * extraction commute for the non-nested case.  (Deferred recdefs)
wenzelm@10769
   468
 *
wenzelm@10769
   469
 * The purpose of wfrec_eqns is merely to instantiate the recursion theorem
wenzelm@10769
   470
 * and extract termination conditions: no definition is made.
wenzelm@10769
   471
 *---------------------------------------------------------------------------*)
wenzelm@10769
   472
wenzelm@10769
   473
fun wfrec_eqns thy fid tflCongs eqns =
wenzelm@10769
   474
 let val {lhs,rhs} = S.dest_eq (hd eqns)
wenzelm@10769
   475
     val (f,args) = S.strip_comb lhs
wenzelm@10769
   476
     val (fname,fty) = dest_atom f
wenzelm@10769
   477
     val (SV,a) = front_last args    (* SV = schematic variables *)
wenzelm@10769
   478
     val g = list_comb(f,SV)
wenzelm@10769
   479
     val h = Free(fname,type_of g)
wenzelm@10769
   480
     val eqns1 = map (subst_free[(g,h)]) eqns
wenzelm@10769
   481
     val {functional as Abs(Name, Ty, _),  pats} = mk_functional thy eqns1
wenzelm@10769
   482
     val given_pats = givens pats
wenzelm@10769
   483
     (* val f = Free(Name,Ty) *)
wenzelm@10769
   484
     val Type("fun", [f_dty, f_rty]) = Ty
wenzelm@10769
   485
     val dummy = if Name<>fid then
wenzelm@10769
   486
                        raise TFL_ERR "wfrec_eqns"
wenzelm@10769
   487
                                      ("Expected a definition of " ^
wenzelm@10769
   488
                                      quote fid ^ " but found one of " ^
wenzelm@10769
   489
                                      quote Name)
wenzelm@10769
   490
                 else ()
wenzelm@10769
   491
     val (case_rewrites,context_congs) = extraction_thms thy
wenzelm@10769
   492
     val tych = Thry.typecheck thy
wenzelm@10769
   493
     val WFREC_THM0 = R.ISPEC (tych functional) Thms.WFREC_COROLLARY
wenzelm@10769
   494
     val Const("All",_) $ Abs(Rname,Rtype,_) = concl WFREC_THM0
wenzelm@10769
   495
     val R = Free (variant (foldr add_term_names (eqns,[])) Rname,
wenzelm@10769
   496
                   Rtype)
wenzelm@10769
   497
     val WFREC_THM = R.ISPECL [tych R, tych g] WFREC_THM0
wenzelm@10769
   498
     val ([proto_def, WFR],_) = S.strip_imp(concl WFREC_THM)
wenzelm@10769
   499
     val dummy =
wenzelm@10769
   500
           if !trace then
wenzelm@10769
   501
               writeln ("ORIGINAL PROTO_DEF: " ^
wenzelm@10769
   502
                          Sign.string_of_term (Theory.sign_of thy) proto_def)
wenzelm@10769
   503
           else ()
wenzelm@10769
   504
     val R1 = S.rand WFR
wenzelm@10769
   505
     val corollary' = R.UNDISCH(R.UNDISCH WFREC_THM)
wenzelm@10769
   506
     val corollaries = map (fn pat => R.SPEC (tych pat) corollary') given_pats
wenzelm@10769
   507
     val corollaries' = map (rewrite_rule case_rewrites) corollaries
wenzelm@10769
   508
     fun extract X = R.CONTEXT_REWRITE_RULE
wenzelm@10769
   509
                       (f, R1::SV, cut_apply, tflCongs@context_congs) X
wenzelm@10769
   510
 in {proto_def = proto_def,
wenzelm@10769
   511
     SV=SV,
wenzelm@10769
   512
     WFR=WFR,
wenzelm@10769
   513
     pats=pats,
wenzelm@10769
   514
     extracta = map extract corollaries'}
wenzelm@10769
   515
 end;
wenzelm@10769
   516
wenzelm@10769
   517
wenzelm@10769
   518
(*---------------------------------------------------------------------------
wenzelm@10769
   519
 * Define the constant after extracting the termination conditions. The
wenzelm@10769
   520
 * wellfounded relation used in the definition is computed by using the
wenzelm@10769
   521
 * choice operator on the extracted conditions (plus the condition that
wenzelm@10769
   522
 * such a relation must be wellfounded).
wenzelm@10769
   523
 *---------------------------------------------------------------------------*)
wenzelm@10769
   524
wenzelm@10769
   525
fun lazyR_def thy fid tflCongs eqns =
wenzelm@10769
   526
 let val {proto_def,WFR,pats,extracta,SV} =
wenzelm@10769
   527
           wfrec_eqns thy fid tflCongs eqns
wenzelm@10769
   528
     val R1 = S.rand WFR
wenzelm@10769
   529
     val f = #lhs(S.dest_eq proto_def)
wenzelm@10769
   530
     val (extractants,TCl) = ListPair.unzip extracta
wenzelm@10769
   531
     val dummy = if !trace
wenzelm@10769
   532
                 then (writeln "Extractants = ";
wenzelm@10769
   533
                       prths extractants;
wenzelm@10769
   534
                       ())
wenzelm@10769
   535
                 else ()
wenzelm@10769
   536
     val TCs = foldr (gen_union (op aconv)) (TCl, [])
wenzelm@10769
   537
     val full_rqt = WFR::TCs
wenzelm@10769
   538
     val R' = S.mk_select{Bvar=R1, Body=S.list_mk_conj full_rqt}
wenzelm@10769
   539
     val R'abs = S.rand R'
wenzelm@10769
   540
     val proto_def' = subst_free[(R1,R')] proto_def
wenzelm@10769
   541
     val dummy = if !trace then writeln ("proto_def' = " ^
wenzelm@10769
   542
                                         Sign.string_of_term
wenzelm@10769
   543
                                         (Theory.sign_of thy) proto_def')
wenzelm@10769
   544
                           else ()
wenzelm@10769
   545
     val {lhs,rhs} = S.dest_eq proto_def'
wenzelm@10769
   546
     val (c,args) = S.strip_comb lhs
wenzelm@10769
   547
     val (Name,Ty) = dest_atom c
wenzelm@10769
   548
     val defn = mk_const_def (Theory.sign_of thy)
wenzelm@10769
   549
                 (Name, Ty, S.list_mk_abs (args,rhs))
wenzelm@10769
   550
     val (theory, [def0]) =
wenzelm@10769
   551
       thy
wenzelm@10769
   552
       |> PureThy.add_defs_i false
wenzelm@10769
   553
            [Thm.no_attributes (fid ^ "_def", defn)]
wenzelm@10769
   554
     val def = freezeT def0;
wenzelm@10769
   555
     val dummy = if !trace then writeln ("DEF = " ^ string_of_thm def)
wenzelm@10769
   556
                           else ()
wenzelm@10769
   557
     (* val fconst = #lhs(S.dest_eq(concl def))  *)
wenzelm@10769
   558
     val tych = Thry.typecheck theory
wenzelm@10769
   559
     val full_rqt_prop = map (Dcterm.mk_prop o tych) full_rqt
wenzelm@10769
   560
         (*lcp: a lot of object-logic inference to remove*)
wenzelm@10769
   561
     val baz = R.DISCH_ALL
wenzelm@10769
   562
                 (U.itlist R.DISCH full_rqt_prop
wenzelm@10769
   563
                  (R.LIST_CONJ extractants))
wenzelm@10769
   564
     val dum = if !trace then writeln ("baz = " ^ string_of_thm baz)
wenzelm@10769
   565
                           else ()
wenzelm@10769
   566
     val f_free = Free (fid, fastype_of f)  (*'cos f is a Const*)
wenzelm@10769
   567
     val SV' = map tych SV;
wenzelm@10769
   568
     val SVrefls = map reflexive SV'
wenzelm@10769
   569
     val def0 = (U.rev_itlist (fn x => fn th => R.rbeta(combination th x))
wenzelm@10769
   570
                   SVrefls def)
wenzelm@10769
   571
                RS meta_eq_to_obj_eq
wenzelm@10769
   572
     val def' = R.MP (R.SPEC (tych R') (R.GEN (tych R1) baz)) def0
wenzelm@10769
   573
     val body_th = R.LIST_CONJ (map R.ASSUME full_rqt_prop)
paulson@11455
   574
     val SELECT_AX = (*in this way we hope to avoid a STATIC dependence upon
paulson@11455
   575
                       theory Hilbert_Choice*)
paulson@11455
   576
         thm "Hilbert_Choice.tfl_some" 
paulson@11455
   577
         handle ERROR => error
paulson@11455
   578
    "defer_recdef requires theory Main or at least Hilbert_Choice as parent"
paulson@11455
   579
     val bar = R.MP (R.ISPECL[tych R'abs, tych R1] SELECT_AX) body_th
wenzelm@10769
   580
 in {theory = theory, R=R1, SV=SV,
wenzelm@10769
   581
     rules = U.rev_itlist (U.C R.MP) (R.CONJUNCTS bar) def',
wenzelm@10769
   582
     full_pats_TCs = merge (map pat_of pats) (ListPair.zip (givens pats, TCl)),
wenzelm@10769
   583
     patterns = pats}
wenzelm@10769
   584
 end;
wenzelm@10769
   585
wenzelm@10769
   586
wenzelm@10769
   587
wenzelm@10769
   588
(*----------------------------------------------------------------------------
wenzelm@10769
   589
 *
wenzelm@10769
   590
 *                           INDUCTION THEOREM
wenzelm@10769
   591
 *
wenzelm@10769
   592
 *---------------------------------------------------------------------------*)
wenzelm@10769
   593
wenzelm@10769
   594
wenzelm@10769
   595
(*------------------------  Miscellaneous function  --------------------------
wenzelm@10769
   596
 *
wenzelm@10769
   597
 *           [x_1,...,x_n]     ?v_1...v_n. M[v_1,...,v_n]
wenzelm@10769
   598
 *     -----------------------------------------------------------
wenzelm@10769
   599
 *     ( M[x_1,...,x_n], [(x_i,?v_1...v_n. M[v_1,...,v_n]),
wenzelm@10769
   600
 *                        ...
wenzelm@10769
   601
 *                        (x_j,?v_n. M[x_1,...,x_(n-1),v_n])] )
wenzelm@10769
   602
 *
wenzelm@10769
   603
 * This function is totally ad hoc. Used in the production of the induction
wenzelm@10769
   604
 * theorem. The nchotomy theorem can have clauses that look like
wenzelm@10769
   605
 *
wenzelm@10769
   606
 *     ?v1..vn. z = C vn..v1
wenzelm@10769
   607
 *
wenzelm@10769
   608
 * in which the order of quantification is not the order of occurrence of the
wenzelm@10769
   609
 * quantified variables as arguments to C. Since we have no control over this
wenzelm@10769
   610
 * aspect of the nchotomy theorem, we make the correspondence explicit by
wenzelm@10769
   611
 * pairing the incoming new variable with the term it gets beta-reduced into.
wenzelm@10769
   612
 *---------------------------------------------------------------------------*)
wenzelm@10769
   613
wenzelm@10769
   614
fun alpha_ex_unroll (xlist, tm) =
wenzelm@10769
   615
  let val (qvars,body) = S.strip_exists tm
wenzelm@10769
   616
      val vlist = #2(S.strip_comb (S.rhs body))
wenzelm@10769
   617
      val plist = ListPair.zip (vlist, xlist)
wenzelm@10769
   618
      val args = map (fn qv => the (gen_assoc (op aconv) (plist, qv))) qvars
wenzelm@10769
   619
                   handle Library.OPTION => sys_error
wenzelm@10769
   620
                       "TFL fault [alpha_ex_unroll]: no correspondence"
wenzelm@10769
   621
      fun build ex      []   = []
wenzelm@10769
   622
        | build (_$rex) (v::rst) =
wenzelm@10769
   623
           let val ex1 = betapply(rex, v)
wenzelm@10769
   624
           in  ex1 :: build ex1 rst
wenzelm@10769
   625
           end
wenzelm@10769
   626
     val (nex::exl) = rev (tm::build tm args)
wenzelm@10769
   627
  in
wenzelm@10769
   628
  (nex, ListPair.zip (args, rev exl))
wenzelm@10769
   629
  end;
wenzelm@10769
   630
wenzelm@10769
   631
wenzelm@10769
   632
wenzelm@10769
   633
(*----------------------------------------------------------------------------
wenzelm@10769
   634
 *
wenzelm@10769
   635
 *             PROVING COMPLETENESS OF PATTERNS
wenzelm@10769
   636
 *
wenzelm@10769
   637
 *---------------------------------------------------------------------------*)
wenzelm@10769
   638
wenzelm@10769
   639
fun mk_case ty_info usednames thy =
wenzelm@10769
   640
 let
wenzelm@10769
   641
 val divide = ipartition (gvvariant usednames)
wenzelm@10769
   642
 val tych = Thry.typecheck thy
wenzelm@10769
   643
 fun tych_binding(x,y) = (tych x, tych y)
wenzelm@10769
   644
 fun fail s = raise TFL_ERR "mk_case" s
wenzelm@10769
   645
 fun mk{rows=[],...} = fail"no rows"
wenzelm@10769
   646
   | mk{path=[], rows = [([], (thm, bindings))]} =
wenzelm@10769
   647
                         R.IT_EXISTS (map tych_binding bindings) thm
wenzelm@10769
   648
   | mk{path = u::rstp, rows as (p::_, _)::_} =
wenzelm@10769
   649
     let val (pat_rectangle,rights) = ListPair.unzip rows
wenzelm@10769
   650
         val col0 = map hd pat_rectangle
wenzelm@10769
   651
         val pat_rectangle' = map tl pat_rectangle
wenzelm@10769
   652
     in
wenzelm@10769
   653
     if (forall is_Free col0) (* column 0 is all variables *)
wenzelm@10769
   654
     then let val rights' = map (fn ((thm,theta),v) => (thm,theta@[(u,v)]))
wenzelm@10769
   655
                                (ListPair.zip (rights, col0))
wenzelm@10769
   656
          in mk{path = rstp, rows = ListPair.zip (pat_rectangle', rights')}
wenzelm@10769
   657
          end
wenzelm@10769
   658
     else                     (* column 0 is all constructors *)
wenzelm@10769
   659
     let val Type (ty_name,_) = type_of p
wenzelm@10769
   660
     in
wenzelm@10769
   661
     case (ty_info ty_name)
wenzelm@10769
   662
     of None => fail("Not a known datatype: "^ty_name)
wenzelm@10769
   663
      | Some{constructors,nchotomy} =>
wenzelm@10769
   664
        let val thm' = R.ISPEC (tych u) nchotomy
wenzelm@10769
   665
            val disjuncts = S.strip_disj (concl thm')
wenzelm@10769
   666
            val subproblems = divide(constructors, rows)
wenzelm@10769
   667
            val groups      = map #group subproblems
wenzelm@10769
   668
            and new_formals = map #new_formals subproblems
wenzelm@10769
   669
            val existentials = ListPair.map alpha_ex_unroll
wenzelm@10769
   670
                                   (new_formals, disjuncts)
wenzelm@10769
   671
            val constraints = map #1 existentials
wenzelm@10769
   672
            val vexl = map #2 existentials
wenzelm@10769
   673
            fun expnd tm (pats,(th,b)) = (pats,(R.SUBS[R.ASSUME(tych tm)]th,b))
wenzelm@10769
   674
            val news = map (fn (nf,rows,c) => {path = nf@rstp,
wenzelm@10769
   675
                                               rows = map (expnd c) rows})
wenzelm@10769
   676
                           (U.zip3 new_formals groups constraints)
wenzelm@10769
   677
            val recursive_thms = map mk news
wenzelm@10769
   678
            val build_exists = foldr
wenzelm@10769
   679
                                (fn((x,t), th) =>
wenzelm@10769
   680
                                 R.CHOOSE (tych x, R.ASSUME (tych t)) th)
wenzelm@10769
   681
            val thms' = ListPair.map build_exists (vexl, recursive_thms)
wenzelm@10769
   682
            val same_concls = R.EVEN_ORS thms'
wenzelm@10769
   683
        in R.DISJ_CASESL thm' same_concls
wenzelm@10769
   684
        end
wenzelm@10769
   685
     end end
wenzelm@10769
   686
 in mk
wenzelm@10769
   687
 end;
wenzelm@10769
   688
wenzelm@10769
   689
wenzelm@10769
   690
fun complete_cases thy =
wenzelm@10769
   691
 let val tych = Thry.typecheck thy
wenzelm@10769
   692
     val ty_info = Thry.induct_info thy
wenzelm@10769
   693
 in fn pats =>
wenzelm@10769
   694
 let val names = foldr add_term_names (pats,[])
wenzelm@10769
   695
     val T = type_of (hd pats)
wenzelm@10769
   696
     val aname = Term.variant names "a"
wenzelm@10769
   697
     val vname = Term.variant (aname::names) "v"
wenzelm@10769
   698
     val a = Free (aname, T)
wenzelm@10769
   699
     val v = Free (vname, T)
wenzelm@10769
   700
     val a_eq_v = HOLogic.mk_eq(a,v)
wenzelm@10769
   701
     val ex_th0 = R.EXISTS (tych (S.mk_exists{Bvar=v,Body=a_eq_v}), tych a)
wenzelm@10769
   702
                           (R.REFL (tych a))
wenzelm@10769
   703
     val th0 = R.ASSUME (tych a_eq_v)
wenzelm@10769
   704
     val rows = map (fn x => ([x], (th0,[]))) pats
wenzelm@10769
   705
 in
wenzelm@10769
   706
 R.GEN (tych a)
wenzelm@10769
   707
       (R.RIGHT_ASSOC
wenzelm@10769
   708
          (R.CHOOSE(tych v, ex_th0)
wenzelm@10769
   709
                (mk_case ty_info (vname::aname::names)
wenzelm@10769
   710
                 thy {path=[v], rows=rows})))
wenzelm@10769
   711
 end end;
wenzelm@10769
   712
wenzelm@10769
   713
wenzelm@10769
   714
(*---------------------------------------------------------------------------
wenzelm@10769
   715
 * Constructing induction hypotheses: one for each recursive call.
wenzelm@10769
   716
 *
wenzelm@10769
   717
 * Note. R will never occur as a variable in the ind_clause, because
wenzelm@10769
   718
 * to do so, it would have to be from a nested definition, and we don't
wenzelm@10769
   719
 * allow nested defns to have R variable.
wenzelm@10769
   720
 *
wenzelm@10769
   721
 * Note. When the context is empty, there can be no local variables.
wenzelm@10769
   722
 *---------------------------------------------------------------------------*)
wenzelm@10769
   723
(*
wenzelm@10769
   724
local infix 5 ==>
wenzelm@10769
   725
      fun (tm1 ==> tm2) = S.mk_imp{ant = tm1, conseq = tm2}
wenzelm@10769
   726
in
wenzelm@10769
   727
fun build_ih f P (pat,TCs) =
wenzelm@10769
   728
 let val globals = S.free_vars_lr pat
wenzelm@10769
   729
     fun nested tm = is_some (S.find_term (curry (op aconv) f) tm)
wenzelm@10769
   730
     fun dest_TC tm =
wenzelm@10769
   731
         let val (cntxt,R_y_pat) = S.strip_imp(#2(S.strip_forall tm))
wenzelm@10769
   732
             val (R,y,_) = S.dest_relation R_y_pat
wenzelm@10769
   733
             val P_y = if (nested tm) then R_y_pat ==> P$y else P$y
wenzelm@10769
   734
         in case cntxt
wenzelm@10769
   735
              of [] => (P_y, (tm,[]))
wenzelm@10769
   736
               | _  => let
wenzelm@10769
   737
                    val imp = S.list_mk_conj cntxt ==> P_y
wenzelm@10769
   738
                    val lvs = gen_rems (op aconv) (S.free_vars_lr imp, globals)
wenzelm@10769
   739
                    val locals = #2(U.pluck (curry (op aconv) P) lvs) handle U.ERR _ => lvs
wenzelm@10769
   740
                    in (S.list_mk_forall(locals,imp), (tm,locals)) end
wenzelm@10769
   741
         end
wenzelm@10769
   742
 in case TCs
wenzelm@10769
   743
    of [] => (S.list_mk_forall(globals, P$pat), [])
wenzelm@10769
   744
     |  _ => let val (ihs, TCs_locals) = ListPair.unzip(map dest_TC TCs)
wenzelm@10769
   745
                 val ind_clause = S.list_mk_conj ihs ==> P$pat
wenzelm@10769
   746
             in (S.list_mk_forall(globals,ind_clause), TCs_locals)
wenzelm@10769
   747
             end
wenzelm@10769
   748
 end
wenzelm@10769
   749
end;
wenzelm@10769
   750
*)
wenzelm@10769
   751
wenzelm@10769
   752
local infix 5 ==>
wenzelm@10769
   753
      fun (tm1 ==> tm2) = S.mk_imp{ant = tm1, conseq = tm2}
wenzelm@10769
   754
in
wenzelm@10769
   755
fun build_ih f (P,SV) (pat,TCs) =
wenzelm@10769
   756
 let val pat_vars = S.free_vars_lr pat
wenzelm@10769
   757
     val globals = pat_vars@SV
wenzelm@10769
   758
     fun nested tm = is_some (S.find_term (curry (op aconv) f) tm)
wenzelm@10769
   759
     fun dest_TC tm =
wenzelm@10769
   760
         let val (cntxt,R_y_pat) = S.strip_imp(#2(S.strip_forall tm))
wenzelm@10769
   761
             val (R,y,_) = S.dest_relation R_y_pat
wenzelm@10769
   762
             val P_y = if (nested tm) then R_y_pat ==> P$y else P$y
wenzelm@10769
   763
         in case cntxt
wenzelm@10769
   764
              of [] => (P_y, (tm,[]))
wenzelm@10769
   765
               | _  => let
wenzelm@10769
   766
                    val imp = S.list_mk_conj cntxt ==> P_y
wenzelm@10769
   767
                    val lvs = gen_rems (op aconv) (S.free_vars_lr imp, globals)
wenzelm@10769
   768
                    val locals = #2(U.pluck (curry (op aconv) P) lvs) handle U.ERR _ => lvs
wenzelm@10769
   769
                    in (S.list_mk_forall(locals,imp), (tm,locals)) end
wenzelm@10769
   770
         end
wenzelm@10769
   771
 in case TCs
wenzelm@10769
   772
    of [] => (S.list_mk_forall(pat_vars, P$pat), [])
wenzelm@10769
   773
     |  _ => let val (ihs, TCs_locals) = ListPair.unzip(map dest_TC TCs)
wenzelm@10769
   774
                 val ind_clause = S.list_mk_conj ihs ==> P$pat
wenzelm@10769
   775
             in (S.list_mk_forall(pat_vars,ind_clause), TCs_locals)
wenzelm@10769
   776
             end
wenzelm@10769
   777
 end
wenzelm@10769
   778
end;
wenzelm@10769
   779
wenzelm@10769
   780
(*---------------------------------------------------------------------------
wenzelm@10769
   781
 * This function makes good on the promise made in "build_ih".
wenzelm@10769
   782
 *
wenzelm@10769
   783
 * Input  is tm = "(!y. R y pat ==> P y) ==> P pat",
wenzelm@10769
   784
 *           TCs = TC_1[pat] ... TC_n[pat]
wenzelm@10769
   785
 *           thm = ih1 /\ ... /\ ih_n |- ih[pat]
wenzelm@10769
   786
 *---------------------------------------------------------------------------*)
wenzelm@10769
   787
fun prove_case f thy (tm,TCs_locals,thm) =
wenzelm@10769
   788
 let val tych = Thry.typecheck thy
wenzelm@10769
   789
     val antc = tych(#ant(S.dest_imp tm))
wenzelm@10769
   790
     val thm' = R.SPEC_ALL thm
wenzelm@10769
   791
     fun nested tm = is_some (S.find_term (curry (op aconv) f) tm)
wenzelm@10769
   792
     fun get_cntxt TC = tych(#ant(S.dest_imp(#2(S.strip_forall(concl TC)))))
wenzelm@10769
   793
     fun mk_ih ((TC,locals),th2,nested) =
wenzelm@10769
   794
         R.GENL (map tych locals)
wenzelm@10769
   795
            (if nested then R.DISCH (get_cntxt TC) th2 handle U.ERR _ => th2
wenzelm@10769
   796
             else if S.is_imp (concl TC) then R.IMP_TRANS TC th2
wenzelm@10769
   797
             else R.MP th2 TC)
wenzelm@10769
   798
 in
wenzelm@10769
   799
 R.DISCH antc
wenzelm@10769
   800
 (if S.is_imp(concl thm') (* recursive calls in this clause *)
wenzelm@10769
   801
  then let val th1 = R.ASSUME antc
wenzelm@10769
   802
           val TCs = map #1 TCs_locals
wenzelm@10769
   803
           val ylist = map (#2 o S.dest_relation o #2 o S.strip_imp o
wenzelm@10769
   804
                            #2 o S.strip_forall) TCs
wenzelm@10769
   805
           val TClist = map (fn(TC,lvs) => (R.SPEC_ALL(R.ASSUME(tych TC)),lvs))
wenzelm@10769
   806
                            TCs_locals
wenzelm@10769
   807
           val th2list = map (U.C R.SPEC th1 o tych) ylist
wenzelm@10769
   808
           val nlist = map nested TCs
wenzelm@10769
   809
           val triples = U.zip3 TClist th2list nlist
wenzelm@10769
   810
           val Pylist = map mk_ih triples
wenzelm@10769
   811
       in R.MP thm' (R.LIST_CONJ Pylist) end
wenzelm@10769
   812
  else thm')
wenzelm@10769
   813
 end;
wenzelm@10769
   814
wenzelm@10769
   815
wenzelm@10769
   816
(*---------------------------------------------------------------------------
wenzelm@10769
   817
 *
wenzelm@10769
   818
 *         x = (v1,...,vn)  |- M[x]
wenzelm@10769
   819
 *    ---------------------------------------------
wenzelm@10769
   820
 *      ?v1 ... vn. x = (v1,...,vn) |- M[x]
wenzelm@10769
   821
 *
wenzelm@10769
   822
 *---------------------------------------------------------------------------*)
wenzelm@10769
   823
fun LEFT_ABS_VSTRUCT tych thm =
wenzelm@10769
   824
  let fun CHOOSER v (tm,thm) =
wenzelm@10769
   825
        let val ex_tm = S.mk_exists{Bvar=v,Body=tm}
wenzelm@10769
   826
        in (ex_tm, R.CHOOSE(tych v, R.ASSUME (tych ex_tm)) thm)
wenzelm@10769
   827
        end
wenzelm@10769
   828
      val [veq] = filter (can S.dest_eq) (#1 (R.dest_thm thm))
wenzelm@10769
   829
      val {lhs,rhs} = S.dest_eq veq
wenzelm@10769
   830
      val L = S.free_vars_lr rhs
wenzelm@10769
   831
  in  #2 (U.itlist CHOOSER L (veq,thm))  end;
wenzelm@10769
   832
wenzelm@10769
   833
wenzelm@10769
   834
(*----------------------------------------------------------------------------
wenzelm@10769
   835
 * Input : f, R,  and  [(pat1,TCs1),..., (patn,TCsn)]
wenzelm@10769
   836
 *
wenzelm@10769
   837
 * Instantiates WF_INDUCTION_THM, getting Sinduct and then tries to prove
wenzelm@10769
   838
 * recursion induction (Rinduct) by proving the antecedent of Sinduct from
wenzelm@10769
   839
 * the antecedent of Rinduct.
wenzelm@10769
   840
 *---------------------------------------------------------------------------*)
wenzelm@10769
   841
fun mk_induction thy {fconst, R, SV, pat_TCs_list} =
wenzelm@10769
   842
let val tych = Thry.typecheck thy
wenzelm@10769
   843
    val Sinduction = R.UNDISCH (R.ISPEC (tych R) Thms.WF_INDUCTION_THM)
wenzelm@10769
   844
    val (pats,TCsl) = ListPair.unzip pat_TCs_list
wenzelm@10769
   845
    val case_thm = complete_cases thy pats
wenzelm@10769
   846
    val domain = (type_of o hd) pats
wenzelm@10769
   847
    val Pname = Term.variant (foldr (foldr add_term_names)
wenzelm@10769
   848
                              (pats::TCsl, [])) "P"
wenzelm@10769
   849
    val P = Free(Pname, domain --> HOLogic.boolT)
wenzelm@10769
   850
    val Sinduct = R.SPEC (tych P) Sinduction
wenzelm@10769
   851
    val Sinduct_assumf = S.rand ((#ant o S.dest_imp o concl) Sinduct)
wenzelm@10769
   852
    val Rassums_TCl' = map (build_ih fconst (P,SV)) pat_TCs_list
wenzelm@10769
   853
    val (Rassums,TCl') = ListPair.unzip Rassums_TCl'
wenzelm@10769
   854
    val Rinduct_assum = R.ASSUME (tych (S.list_mk_conj Rassums))
wenzelm@10769
   855
    val cases = map (fn pat => betapply (Sinduct_assumf, pat)) pats
wenzelm@10769
   856
    val tasks = U.zip3 cases TCl' (R.CONJUNCTS Rinduct_assum)
wenzelm@10769
   857
    val proved_cases = map (prove_case fconst thy) tasks
wenzelm@10769
   858
    val v = Free (variant (foldr add_term_names (map concl proved_cases, []))
wenzelm@10769
   859
                    "v",
wenzelm@10769
   860
                  domain)
wenzelm@10769
   861
    val vtyped = tych v
wenzelm@10769
   862
    val substs = map (R.SYM o R.ASSUME o tych o (curry HOLogic.mk_eq v)) pats
wenzelm@10769
   863
    val proved_cases1 = ListPair.map (fn (th,th') => R.SUBS[th]th')
wenzelm@10769
   864
                          (substs, proved_cases)
wenzelm@10769
   865
    val abs_cases = map (LEFT_ABS_VSTRUCT tych) proved_cases1
wenzelm@10769
   866
    val dant = R.GEN vtyped (R.DISJ_CASESL (R.ISPEC vtyped case_thm) abs_cases)
wenzelm@10769
   867
    val dc = R.MP Sinduct dant
wenzelm@10769
   868
    val Parg_ty = type_of(#Bvar(S.dest_forall(concl dc)))
wenzelm@10769
   869
    val vars = map (gvvariant[Pname]) (S.strip_prod_type Parg_ty)
wenzelm@10769
   870
    val dc' = U.itlist (R.GEN o tych) vars
wenzelm@10769
   871
                       (R.SPEC (tych(S.mk_vstruct Parg_ty vars)) dc)
wenzelm@10769
   872
in
wenzelm@10769
   873
   R.GEN (tych P) (R.DISCH (tych(concl Rinduct_assum)) dc')
wenzelm@10769
   874
end
wenzelm@10769
   875
handle U.ERR _ => raise TFL_ERR "mk_induction" "failed derivation";
wenzelm@10769
   876
wenzelm@10769
   877
wenzelm@10769
   878
wenzelm@10769
   879
wenzelm@10769
   880
(*---------------------------------------------------------------------------
wenzelm@10769
   881
 *
wenzelm@10769
   882
 *                        POST PROCESSING
wenzelm@10769
   883
 *
wenzelm@10769
   884
 *---------------------------------------------------------------------------*)
wenzelm@10769
   885
wenzelm@10769
   886
wenzelm@10769
   887
fun simplify_induction thy hth ind =
wenzelm@10769
   888
  let val tych = Thry.typecheck thy
wenzelm@10769
   889
      val (asl,_) = R.dest_thm ind
wenzelm@10769
   890
      val (_,tc_eq_tc') = R.dest_thm hth
wenzelm@10769
   891
      val tc = S.lhs tc_eq_tc'
wenzelm@10769
   892
      fun loop [] = ind
wenzelm@10769
   893
        | loop (asm::rst) =
wenzelm@10769
   894
          if (can (Thry.match_term thy asm) tc)
wenzelm@10769
   895
          then R.UNDISCH
wenzelm@10769
   896
                 (R.MATCH_MP
wenzelm@10769
   897
                     (R.MATCH_MP Thms.simp_thm (R.DISCH (tych asm) ind))
wenzelm@10769
   898
                     hth)
wenzelm@10769
   899
         else loop rst
wenzelm@10769
   900
  in loop asl
wenzelm@10769
   901
end;
wenzelm@10769
   902
wenzelm@10769
   903
wenzelm@10769
   904
(*---------------------------------------------------------------------------
wenzelm@10769
   905
 * The termination condition is an antecedent to the rule, and an
wenzelm@10769
   906
 * assumption to the theorem.
wenzelm@10769
   907
 *---------------------------------------------------------------------------*)
wenzelm@10769
   908
fun elim_tc tcthm (rule,induction) =
wenzelm@10769
   909
   (R.MP rule tcthm, R.PROVE_HYP tcthm induction)
wenzelm@10769
   910
wenzelm@10769
   911
wenzelm@11632
   912
fun postprocess strict {wf_tac, terminator, simplifier} theory {rules,induction,TCs} =
wenzelm@10769
   913
let val tych = Thry.typecheck theory
wenzelm@11632
   914
    val prove = R.prove strict;
wenzelm@10769
   915
wenzelm@10769
   916
   (*---------------------------------------------------------------------
wenzelm@10769
   917
    * Attempt to eliminate WF condition. It's the only assumption of rules
wenzelm@10769
   918
    *---------------------------------------------------------------------*)
wenzelm@10769
   919
   val (rules1,induction1)  =
wenzelm@11632
   920
       let val thm = prove(tych(HOLogic.mk_Trueprop
wenzelm@10769
   921
                                  (hd(#1(R.dest_thm rules)))),
wenzelm@10769
   922
                             wf_tac)
wenzelm@10769
   923
       in (R.PROVE_HYP thm rules,  R.PROVE_HYP thm induction)
wenzelm@10769
   924
       end handle U.ERR _ => (rules,induction);
wenzelm@10769
   925
wenzelm@10769
   926
   (*----------------------------------------------------------------------
wenzelm@10769
   927
    * The termination condition (tc) is simplified to |- tc = tc' (there
wenzelm@10769
   928
    * might not be a change!) and then 3 attempts are made:
wenzelm@10769
   929
    *
wenzelm@10769
   930
    *   1. if |- tc = T, then eliminate it with eqT; otherwise,
wenzelm@10769
   931
    *   2. apply the terminator to tc'. If |- tc' = T then eliminate; else
wenzelm@10769
   932
    *   3. replace tc by tc' in both the rules and the induction theorem.
wenzelm@10769
   933
    *---------------------------------------------------------------------*)
wenzelm@10769
   934
wenzelm@10769
   935
   fun print_thms s L =
wenzelm@10769
   936
     if !trace then writeln (cat_lines (s :: map string_of_thm L))
wenzelm@10769
   937
     else ();
wenzelm@10769
   938
wenzelm@10769
   939
   fun print_cterms s L =
wenzelm@10769
   940
     if !trace then writeln (cat_lines (s :: map string_of_cterm L))
wenzelm@10769
   941
     else ();;
wenzelm@10769
   942
wenzelm@10769
   943
   fun simplify_tc tc (r,ind) =
wenzelm@10769
   944
       let val tc1 = tych tc
wenzelm@10769
   945
           val _ = print_cterms "TC before simplification: " [tc1]
wenzelm@10769
   946
           val tc_eq = simplifier tc1
wenzelm@10769
   947
           val _ = print_thms "result: " [tc_eq]
wenzelm@10769
   948
       in
wenzelm@10769
   949
       elim_tc (R.MATCH_MP Thms.eqT tc_eq) (r,ind)
wenzelm@10769
   950
       handle U.ERR _ =>
wenzelm@10769
   951
        (elim_tc (R.MATCH_MP(R.MATCH_MP Thms.rev_eq_mp tc_eq)
wenzelm@11632
   952
                  (prove(tych(HOLogic.mk_Trueprop(S.rhs(concl tc_eq))),
wenzelm@10769
   953
                           terminator)))
wenzelm@10769
   954
                 (r,ind)
wenzelm@10769
   955
         handle U.ERR _ =>
wenzelm@10769
   956
          (R.UNDISCH(R.MATCH_MP (R.MATCH_MP Thms.simp_thm r) tc_eq),
wenzelm@10769
   957
           simplify_induction theory tc_eq ind))
wenzelm@10769
   958
       end
wenzelm@10769
   959
wenzelm@10769
   960
   (*----------------------------------------------------------------------
wenzelm@10769
   961
    * Nested termination conditions are harder to get at, since they are
wenzelm@10769
   962
    * left embedded in the body of the function (and in induction
wenzelm@10769
   963
    * theorem hypotheses). Our "solution" is to simplify them, and try to
wenzelm@10769
   964
    * prove termination, but leave the application of the resulting theorem
wenzelm@10769
   965
    * to a higher level. So things go much as in "simplify_tc": the
wenzelm@10769
   966
    * termination condition (tc) is simplified to |- tc = tc' (there might
wenzelm@10769
   967
    * not be a change) and then 2 attempts are made:
wenzelm@10769
   968
    *
wenzelm@10769
   969
    *   1. if |- tc = T, then return |- tc; otherwise,
wenzelm@10769
   970
    *   2. apply the terminator to tc'. If |- tc' = T then return |- tc; else
wenzelm@10769
   971
    *   3. return |- tc = tc'
wenzelm@10769
   972
    *---------------------------------------------------------------------*)
wenzelm@10769
   973
   fun simplify_nested_tc tc =
wenzelm@10769
   974
      let val tc_eq = simplifier (tych (#2 (S.strip_forall tc)))
wenzelm@10769
   975
      in
wenzelm@10769
   976
      R.GEN_ALL
wenzelm@10769
   977
       (R.MATCH_MP Thms.eqT tc_eq
wenzelm@10769
   978
        handle U.ERR _ =>
wenzelm@10769
   979
          (R.MATCH_MP(R.MATCH_MP Thms.rev_eq_mp tc_eq)
wenzelm@11632
   980
                      (prove(tych(HOLogic.mk_Trueprop (S.rhs(concl tc_eq))),
wenzelm@10769
   981
                               terminator))
wenzelm@10769
   982
            handle U.ERR _ => tc_eq))
wenzelm@10769
   983
      end
wenzelm@10769
   984
wenzelm@10769
   985
   (*-------------------------------------------------------------------
wenzelm@10769
   986
    * Attempt to simplify the termination conditions in each rule and
wenzelm@10769
   987
    * in the induction theorem.
wenzelm@10769
   988
    *-------------------------------------------------------------------*)
wenzelm@10769
   989
   fun strip_imp tm = if S.is_neg tm then ([],tm) else S.strip_imp tm
wenzelm@10769
   990
   fun loop ([],extras,R,ind) = (rev R, ind, extras)
wenzelm@10769
   991
     | loop ((r,ftcs)::rst, nthms, R, ind) =
wenzelm@10769
   992
        let val tcs = #1(strip_imp (concl r))
wenzelm@10769
   993
            val extra_tcs = gen_rems (op aconv) (ftcs, tcs)
wenzelm@10769
   994
            val extra_tc_thms = map simplify_nested_tc extra_tcs
wenzelm@10769
   995
            val (r1,ind1) = U.rev_itlist simplify_tc tcs (r,ind)
wenzelm@10769
   996
            val r2 = R.FILTER_DISCH_ALL(not o S.is_WFR) r1
wenzelm@10769
   997
        in loop(rst, nthms@extra_tc_thms, r2::R, ind1)
wenzelm@10769
   998
        end
wenzelm@10769
   999
   val rules_tcs = ListPair.zip (R.CONJUNCTS rules1, TCs)
wenzelm@10769
  1000
   val (rules2,ind2,extras) = loop(rules_tcs,[],[],induction1)
wenzelm@10769
  1001
in
wenzelm@10769
  1002
  {induction = ind2, rules = R.LIST_CONJ rules2, nested_tcs = extras}
wenzelm@10769
  1003
end;
wenzelm@10769
  1004
wenzelm@10769
  1005
wenzelm@10769
  1006
end;