(*  Title:      ZF/ind_syntax.ML

    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory

    Copyright   1993  University of Cambridge

Abstract Syntax functions for Inductive Definitions.

*)

structure Ind_Syntax =

struct

(*Print tracing messages during processing of "inductive" theory sections*)

val trace = Unsynchronized.ref false;

fun traceIt msg thy t =

  if !trace then (tracing (msg ^ Syntax.string_of_term_global thy t); t)

  else t;

(** Abstract syntax definitions for ZF **)

val iT = Type(@{type_name i}, []);

(*Creates All(%v.v:A --> P(v)) rather than Ball(A,P) *)

fun mk_all_imp (A,P) =

    FOLogic.all_const iT $

      Abs("v", iT, FOLogic.imp $ (@{const mem} $ Bound 0 $ A) $

                   Term.betapply(P, Bound 0));

fun mk_Collect (a, D, t) = @{const Collect} $ D $ absfree (a, iT) t;

(*simple error-checking in the premises of an inductive definition*)

fun chk_prem rec_hd (Const (@{const_name conj}, _) $ _ $ _) =

        error"Premises may not be conjuctive"

  | chk_prem rec_hd (Const (@{const_name mem}, _) $ t $ X) =

        (Logic.occs(rec_hd,t) andalso error "Recursion term on left of member symbol"; ())

  | chk_prem rec_hd t =

        (Logic.occs(rec_hd,t) andalso error "Recursion term in side formula"; ());

(*Return the conclusion of a rule, of the form t:X*)

fun rule_concl rl =

    let val Const (@{const_name Trueprop}, _) $ (Const (@{const_name mem}, _) $ t $ X) =

                Logic.strip_imp_concl rl

    in  (t,X)  end;

(*As above, but return error message if bad*)

fun rule_concl_msg sign rl = rule_concl rl

    handle Bind => error ("Ill-formed conclusion of introduction rule: " ^

                          Syntax.string_of_term_global sign rl);

(*For deriving cases rules.  CollectD2 discards the domain, which is redundant;

  read_instantiate replaces a propositional variable by a formula variable*)

val equals_CollectD =

    read_instantiate @{context} [(("W", 0), "Q")] ["Q"]

        (make_elim (@{thm equalityD1} RS @{thm subsetD} RS @{thm CollectD2}));

(** For datatype definitions **)

(*Constructor name, type, mixfix info;

  internal name from mixfix, datatype sets, full premises*)

type constructor_spec =

    (string * typ * mixfix) * string * term list * term list;

fun dest_mem (Const (@{const_name mem}, _) $ x $ A) = (x, A)

  | dest_mem _ = error "Constructor specifications must have the form x:A";

(*read a constructor specification*)

fun read_construct ctxt (id: string, sprems, syn: mixfix) =

    let val prems = map (Syntax.parse_term ctxt #> Type.constraint FOLogic.oT) sprems

          |> Syntax.check_terms ctxt

        val args = map (#1 o dest_mem) prems

        val T = (map (#2 o dest_Free) args) ---> iT

                handle TERM _ => error

                    "Bad variable in constructor specification"

    in ((id,T,syn), id, args, prems) end;

val read_constructs = map o map o read_construct;

(*convert constructor specifications into introduction rules*)

fun mk_intr_tms sg (rec_tm, constructs) =

  let

    fun mk_intr ((id,T,syn), name, args, prems) =

      Logic.list_implies

        (map FOLogic.mk_Trueprop prems,

         FOLogic.mk_Trueprop

            (@{const mem} $ list_comb (Const (Sign.full_bname sg name, T), args)

                       $ rec_tm))

  in  map mk_intr constructs  end;

fun mk_all_intr_tms sg arg = flat (ListPair.map (mk_intr_tms sg) arg);

fun mk_Un (t1, t2) = @{const Un} $ t1 $ t2;

(*Make a datatype's domain: form the union of its set parameters*)

fun union_params (rec_tm, cs) =

  let val (_,args) = strip_comb rec_tm

      fun is_ind arg = (type_of arg = iT)

  in  case filter is_ind (args @ cs) of

         [] => @{const zero}

       | u_args => Balanced_Tree.make mk_Un u_args

  end;

(*Includes rules for succ and Pair since they are common constructions*)

val elim_rls =

  [@{thm asm_rl}, @{thm FalseE}, @{thm succ_neq_0}, @{thm sym} RS @{thm succ_neq_0},

   @{thm Pair_neq_0}, @{thm sym} RS @{thm Pair_neq_0}, @{thm Pair_inject},

   make_elim @{thm succ_inject}, @{thm refl_thin}, @{thm conjE}, @{thm exE}, @{thm disjE}];

(*From HOL/ex/meson.ML: raises exception if no rules apply -- unlike RL*)

fun tryres (th, rl::rls) = (th RS rl handle THM _ => tryres(th,rls))

  | tryres (th, []) = raise THM("tryres", 0, [th]);

fun gen_make_elim elim_rls rl =

  Drule.export_without_context (tryres (rl, elim_rls @ [revcut_rl]));

(*Turns iff rules into safe elimination rules*)

fun mk_free_SEs iffs = map (gen_make_elim [@{thm conjE}, @{thm FalseE}]) (iffs RL [@{thm iffD1}]);

end;