src/Tools/misc_legacy.ML
author blanchet
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(*  Title:      Tools/misc_legacy.ML
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Misc legacy stuff -- to be phased out eventually.
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*)
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signature MISC_LEGACY =
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sig
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  val add_term_names: term * string list -> string list
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  val add_typ_tvars: typ * (indexname * sort) list -> (indexname * sort) list
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  val add_typ_tfree_names: typ * string list -> string list
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  val add_typ_tfrees: typ * (string * sort) list -> (string * sort) list
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  val add_term_tvars: term * (indexname * sort) list -> (indexname * sort) list
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  val add_term_tfrees: term * (string * sort) list -> (string * sort) list
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  val add_term_tfree_names: term * string list -> string list
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  val typ_tfrees: typ -> (string * sort) list
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  val typ_tvars: typ -> (indexname * sort) list
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  val term_tfrees: term -> (string * sort) list
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  val term_tvars: term -> (indexname * sort) list
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  val add_term_vars: term * term list -> term list
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  val term_vars: term -> term list
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  val add_term_frees: term * term list -> term list
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  val term_frees: term -> term list
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  val mk_defpair: term * term -> string * term
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  val get_def: theory -> xstring -> thm
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  val METAHYPS: (thm list -> tactic) -> int -> tactic
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  val freeze_thaw_robust: thm -> thm * (int -> thm -> thm)
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  val freeze_thaw: thm -> thm * (thm -> thm)
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end;
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structure Misc_Legacy: MISC_LEGACY =
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struct
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(*iterate a function over all types in a term*)
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fun it_term_types f =
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let fun iter(Const(_,T), a) = f(T,a)
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      | iter(Free(_,T), a) = f(T,a)
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      | iter(Var(_,T), a) = f(T,a)
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      | iter(Abs(_,T,t), a) = iter(t,f(T,a))
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      | iter(f$u, a) = iter(f, iter(u, a))
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      | iter(Bound _, a) = a
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in iter end
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(*Accumulates the names in the term, suppressing duplicates.
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  Includes Frees and Consts.  For choosing unambiguous bound var names.*)
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fun add_term_names (Const(a,_), bs) = insert (op =) (Long_Name.base_name a) bs
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  | add_term_names (Free(a,_), bs) = insert (op =) a bs
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  | add_term_names (f$u, bs) = add_term_names (f, add_term_names(u, bs))
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  | add_term_names (Abs(_,_,t), bs) = add_term_names(t,bs)
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  | add_term_names (_, bs) = bs;
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(*Accumulates the TVars in a type, suppressing duplicates.*)
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fun add_typ_tvars(Type(_,Ts),vs) = List.foldr add_typ_tvars vs Ts
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  | add_typ_tvars(TFree(_),vs) = vs
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  | add_typ_tvars(TVar(v),vs) = insert (op =) v vs;
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(*Accumulates the TFrees in a type, suppressing duplicates.*)
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fun add_typ_tfree_names(Type(_,Ts),fs) = List.foldr add_typ_tfree_names fs Ts
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  | add_typ_tfree_names(TFree(f,_),fs) = insert (op =) f fs
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  | add_typ_tfree_names(TVar(_),fs) = fs;
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fun add_typ_tfrees(Type(_,Ts),fs) = List.foldr add_typ_tfrees fs Ts
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  | add_typ_tfrees(TFree(f),fs) = insert (op =) f fs
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  | add_typ_tfrees(TVar(_),fs) = fs;
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(*Accumulates the TVars in a term, suppressing duplicates.*)
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val add_term_tvars = it_term_types add_typ_tvars;
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(*Accumulates the TFrees in a term, suppressing duplicates.*)
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val add_term_tfrees = it_term_types add_typ_tfrees;
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val add_term_tfree_names = it_term_types add_typ_tfree_names;
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(*Non-list versions*)
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fun typ_tfrees T = add_typ_tfrees(T,[]);
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fun typ_tvars T = add_typ_tvars(T,[]);
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fun term_tfrees t = add_term_tfrees(t,[]);
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fun term_tvars t = add_term_tvars(t,[]);
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(*Accumulates the Vars in the term, suppressing duplicates.*)
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fun add_term_vars (t, vars: term list) = case t of
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    Var   _ => Ord_List.insert Term_Ord.term_ord t vars
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  | Abs (_,_,body) => add_term_vars(body,vars)
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  | f$t =>  add_term_vars (f, add_term_vars(t, vars))
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  | _ => vars;
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fun term_vars t = add_term_vars(t,[]);
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(*Accumulates the Frees in the term, suppressing duplicates.*)
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fun add_term_frees (t, frees: term list) = case t of
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    Free   _ => Ord_List.insert Term_Ord.term_ord t frees
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  | Abs (_,_,body) => add_term_frees(body,frees)
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  | f$t =>  add_term_frees (f, add_term_frees(t, frees))
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  | _ => frees;
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fun term_frees t = add_term_frees(t,[]);
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fun mk_defpair (lhs, rhs) =
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  (case Term.head_of lhs of
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    Const (name, _) =>
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      (Thm.def_name (Long_Name.base_name name), Logic.mk_equals (lhs, rhs))
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  | _ => raise TERM ("Malformed definition: head of lhs not a constant", [lhs, rhs]));
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fun get_def thy = Thm.axiom thy o Name_Space.intern (Theory.axiom_space thy) o Thm.def_name;
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(**** METAHYPS -- tactical for using hypotheses as meta-level assumptions
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       METAHYPS (fn prems => tac prems) i
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converts subgoal i, of the form !!x1...xm. [| A1;...;An] ==> A into a new
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proof state A==>A, supplying A1,...,An as meta-level assumptions (in
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"prems").  The parameters x1,...,xm become free variables.  If the
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resulting proof state is [| B1;...;Bk] ==> C (possibly assuming A1,...,An)
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then it is lifted back into the original context, yielding k subgoals.
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Replaces unknowns in the context by Frees having the prefix METAHYP_
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New unknowns in [| B1;...;Bk] ==> C are lifted over x1,...,xm.
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DOES NOT HANDLE TYPE UNKNOWNS.
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NOTE: This version does not observe the proof context, and thus cannot
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work reliably.  See also Subgoal.SUBPROOF and Subgoal.FOCUS for
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properly localized variants of the same idea.
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****)
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local
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(*Strips assumptions in goal yielding  ( [x1,...,xm], [H1,...,Hn], B )
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    H1,...,Hn are the hypotheses;  x1...xm are variants of the parameters.
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  Main difference from strip_assums concerns parameters:
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    it replaces the bound variables by free variables.  *)
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fun strip_context_aux (params, Hs, Const (@{const_name Pure.imp}, _) $ H $ B) =
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      strip_context_aux (params, H :: Hs, B)
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  | strip_context_aux (params, Hs, Const (@{const_name Pure.all},_) $ Abs (a, T, t)) =
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      let val (b, u) = Syntax_Trans.variant_abs (a, T, t)
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      in strip_context_aux ((b, T) :: params, Hs, u) end
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  | strip_context_aux (params, Hs, B) = (rev params, rev Hs, B);
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fun strip_context A = strip_context_aux ([], [], A);
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(*Left-to-right replacements: ctpairs = [...,(vi,ti),...].
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  Instantiates distinct free variables by terms of same type.*)
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fun free_instantiate ctpairs =
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  forall_elim_list (map snd ctpairs) o forall_intr_list (map fst ctpairs);
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fun free_of s ((a, i), T) =
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  Free (s ^ (case i of 0 => a | _ => a ^ "_" ^ string_of_int i), T)
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fun mk_inst v = (Var v, free_of "METAHYP1_" v)
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fun metahyps_split_prem prem =
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  let (*find all vars in the hyps -- should find tvars also!*)
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      val hyps_vars = fold Term.add_vars (Logic.strip_assums_hyp prem) []
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      val insts = map mk_inst hyps_vars
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      (*replace the hyps_vars by Frees*)
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      val prem' = subst_atomic insts prem
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      val (params,hyps,concl) = strip_context prem'
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  in (insts,params,hyps,concl)  end;
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fun metahyps_aux_tac tacf (prem,gno) state =
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  let val (insts,params,hyps,concl) = metahyps_split_prem prem
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      val maxidx = Thm.maxidx_of state
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      val cterm = Thm.cterm_of (Thm.theory_of_thm state)
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      val chyps = map cterm hyps
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      val hypths = map Thm.assume chyps
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      val subprems = map (Thm.forall_elim_vars 0) hypths
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      val fparams = map Free params
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      val cparams = map cterm fparams
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      fun swap_ctpair (t,u) = (cterm u, cterm t)
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      (*Subgoal variables: make Free; lift type over params*)
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      fun mk_subgoal_inst concl_vars (v, T) =
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          if member (op =) concl_vars (v, T)
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          then ((v, T), true, free_of "METAHYP2_" (v, T))
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          else ((v, T), false, free_of "METAHYP2_" (v, map #2 params ---> T))
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      (*Instantiate subgoal vars by Free applied to params*)
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      fun mk_ctpair (v, in_concl, u) =
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          if in_concl then (cterm (Var v), cterm u)
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          else (cterm (Var v), cterm (list_comb (u, fparams)))
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      (*Restore Vars with higher type and index*)
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      fun mk_subgoal_swap_ctpair (((a, i), T), in_concl, u as Free (_, U)) =
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          if in_concl then (cterm u, cterm (Var ((a, i), T)))
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          else (cterm u, cterm (Var ((a, i + maxidx), U)))
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      (*Embed B in the original context of params and hyps*)
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      fun embed B = fold_rev Logic.all fparams (Logic.list_implies (hyps, B))
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      (*Strip the context using elimination rules*)
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      fun elim Bhyp = implies_elim_list (forall_elim_list cparams Bhyp) hypths
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      (*A form of lifting that discharges assumptions.*)
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      fun relift st =
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        let val prop = Thm.prop_of st
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            val subgoal_vars = (*Vars introduced in the subgoals*)
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              fold Term.add_vars (Logic.strip_imp_prems prop) []
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            and concl_vars = Term.add_vars (Logic.strip_imp_concl prop) []
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            val subgoal_insts = map (mk_subgoal_inst concl_vars) subgoal_vars
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            val st' = Thm.instantiate ([], map mk_ctpair subgoal_insts) st
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            val emBs = map (cterm o embed) (prems_of st')
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            val Cth  = implies_elim_list st' (map (elim o Thm.assume) emBs)
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        in  (*restore the unknowns to the hypotheses*)
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            free_instantiate (map swap_ctpair insts @
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                              map mk_subgoal_swap_ctpair subgoal_insts)
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                (*discharge assumptions from state in same order*)
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                (implies_intr_list emBs
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                  (forall_intr_list cparams (implies_intr_list chyps Cth)))
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        end
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      (*function to replace the current subgoal*)
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      fun next st =
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        Thm.bicompose {flatten = true, match = false, incremented = false}
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          (false, relift st, nprems_of st) gno state
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  in Seq.maps next (tacf subprems (Thm.trivial (cterm concl))) end;
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fun print_vars_terms n thm =
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  let
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    val thy = theory_of_thm thm
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    fun typed s ty =
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      "  " ^ s ^ " has type: " ^ Syntax.string_of_typ_global thy ty;
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    fun find_vars (Const (c, ty)) =
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          if null (Term.add_tvarsT ty []) then I
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          else insert (op =) (typed c ty)
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      | find_vars (Var (xi, ty)) =
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          insert (op =) (typed (Term.string_of_vname xi) ty)
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      | find_vars (Free _) = I
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      | find_vars (Bound _) = I
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      | find_vars (Abs (_, _, t)) = find_vars t
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      | find_vars (t1 $ t2) = find_vars t1 #> find_vars t2;
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    val prem = Logic.nth_prem (n, Thm.prop_of thm)
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    val tms = find_vars prem []
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  in warning (cat_lines ("Found schematic vars in assumptions:" :: tms)) end;
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in
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fun METAHYPS tacf n thm = SUBGOAL (metahyps_aux_tac tacf) n thm
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  handle THM("assume: variables",_,_) => (print_vars_terms n thm; Seq.empty)
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end;
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(* generating identifiers -- often fresh *)
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local
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(*Maps 0-61 to A-Z, a-z, 0-9; exclude _ or ' to avoid clash with internal/unusual indentifiers*)
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fun gensym_char i =
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  if i<26 then chr (ord "A" + i)
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  else if i<52 then chr (ord "a" + i - 26)
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  else chr (ord "0" + i - 52);
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val char_vec = Vector.tabulate (62, gensym_char);
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fun newid n = implode (map (fn i => Vector.sub (char_vec, i)) (radixpand (62, n)));
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val gensym_seed = Synchronized.var "gensym_seed" (0: int);
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in
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  fun gensym pre =
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    Synchronized.change_result gensym_seed (fn i => (pre ^ newid i, i + 1));
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end;
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(*Convert all Vars in a theorem to Frees.  Also return a function for
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  reversing that operation.  DOES NOT WORK FOR TYPE VARIABLES.*)
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fun freeze_thaw_robust th =
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 let val fth = Thm.legacy_freezeT th
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     val thy = Thm.theory_of_thm fth
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 in
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   case Thm.fold_terms Term.add_vars fth [] of
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       [] => (fth, fn _ => fn x => x)   (*No vars: nothing to do!*)
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     | vars =>
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         let fun newName (ix,_) = (ix, gensym (string_of_indexname ix))
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             val alist = map newName vars
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             fun mk_inst (v,T) =
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                 (cterm_of thy (Var(v,T)),
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                  cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
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             val insts = map mk_inst vars
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             fun thaw i th' = (*i is non-negative increment for Var indexes*)
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                 th' |> forall_intr_list (map #2 insts)
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                     |> forall_elim_list (map (Thm.incr_indexes_cterm i o #1) insts)
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         in  (Thm.instantiate ([],insts) fth, thaw)  end
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 end;
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(*Basic version of the function above. No option to rename Vars apart in thaw.
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  The Frees created from Vars have nice names.*)
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fun freeze_thaw th =
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 let val fth = Thm.legacy_freezeT th
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     val thy = Thm.theory_of_thm fth
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 in
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   case Thm.fold_terms Term.add_vars fth [] of
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       [] => (fth, fn x => x)
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     | vars =>
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         let fun newName (ix, _) (pairs, used) =
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                   let val v = singleton (Name.variant_list used) (string_of_indexname ix)
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                   in  ((ix,v)::pairs, v::used)  end;
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             val (alist, _) =
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                 fold_rev newName vars ([], Thm.fold_terms Term.add_free_names fth [])
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             fun mk_inst (v, T) =
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                 (cterm_of thy (Var(v,T)),
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                  cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
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             val insts = map mk_inst vars
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             fun thaw th' =
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                 th' |> forall_intr_list (map #2 insts)
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                     |> forall_elim_list (map #1 insts)
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         in  (Thm.instantiate ([],insts) fth, thaw)  end
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 end;
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end;
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