src/ZF/constructor.ML
author clasohm
Fri Jul 01 11:03:42 1994 +0200 (1994-07-01 ago)
changeset 444 3ca9d49fd662
parent 231 cb6a24451544
child 448 d7ff85d292c7
permissions -rw-r--r--
replaced extend_theory by new add_* functions;
changed syntax of datatype declaration
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(*  Title: 	ZF/constructor.ML
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    ID:         $Id$
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    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1993  University of Cambridge
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Constructor function module -- for Datatype Definitions
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Defines constructors and a case-style eliminator (no primitive recursion)
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Features:
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* least or greatest fixedpoints
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* user-specified product and sum constructions
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* mutually recursive datatypes
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* recursion over arbitrary monotone operators
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* flexible: can derive any reasonable set of introduction rules
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* automatically constructs a case analysis operator (but no recursion op)
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* efficient treatment of large declarations (e.g. 60 constructors)
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*)
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(** STILL NEEDS: some treatment of recursion **)
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signature CONSTRUCTOR =
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  sig
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  val thy        : theory		(*parent theory*)
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  val rec_specs  : (string * string * (string list * string * mixfix)list) list
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                      (*recursion ops, types, domains, constructors*)
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  val rec_styp	 : string		(*common type of all recursion ops*)
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  val sintrs     : string list		(*desired introduction rules*)
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  val monos      : thm list		(*monotonicity of each M operator*)
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  val type_intrs : thm list		(*type-checking intro rules*)
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  val type_elims : thm list		(*type-checking elim rules*)
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  end;
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signature CONSTRUCTOR_RESULT =
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  sig
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  val con_thy	 : theory		(*theory defining the constructors*)
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  val con_defs	 : thm list		(*definitions made in con_thy*)
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  val case_eqns  : thm list		(*equations for case operator*)
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  val free_iffs  : thm list		(*freeness rewrite rules*)
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  val free_SEs   : thm list		(*freeness destruct rules*)
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  val mk_free    : string -> thm	(*makes freeness theorems*)
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  end;
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functor Constructor_Fun (structure Const: CONSTRUCTOR and
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                      Pr : PR and Su : SU) : CONSTRUCTOR_RESULT =
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struct
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open Logic Const;
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val dummy = writeln"Defining the constructor functions...";
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val case_name = "f";		(*name for case variables*)
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(** Extract basic information from arguments **)
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val sign = sign_of thy;
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val rdty = typ_of o read_ctyp sign;
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val rec_names = map #1 rec_specs;
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val dummy = assert_all Syntax.is_identifier rec_names
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   (fn a => "Name of recursive set not an identifier: " ^ a);
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(*Expands multiple constant declarations*)
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fun flatten_consts ((names, typ, mfix) :: cs) =
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      let fun mk_const name = (name, typ, mfix)
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      in (map mk_const names) @ (flatten_consts cs) end
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  | flatten_consts [] = [];
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(*Constructors with types and arguments*)
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fun mk_con_ty_list cons_pairs = 
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  let fun mk_con_ty (a, st, syn) =
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	  let val T = rdty st;
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	      val args = mk_frees "xa" (binder_types T);
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              val name = const_name a syn; (* adds "op" to infix constructors*)
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	  in (name, T, args) end;
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      fun pairtypes c = flatten_consts [c];
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  in map mk_con_ty (flat (map pairtypes cons_pairs))  end;
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val con_ty_lists = map (mk_con_ty_list o #3) rec_specs;
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(** Define the constructors **)
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(*We identify 0 (the empty set) with the empty tuple*)
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fun mk_tuple [] = Const("0",iT)
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  | mk_tuple args = foldr1 (app Pr.pair) args;
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fun mk_inject n k u = access_bal(ap Su.inl, ap Su.inr, u) n k;
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val npart = length rec_names;		(*number of mutually recursive parts*)
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(*Make constructor definition*)
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fun mk_con_defs (kpart, con_ty_list) = 
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  let val ncon = length con_ty_list	   (*number of constructors*)
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      fun mk_def ((a,T,args), kcon) = (*kcon = index of this constructor*)
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	  mk_defpair sign 
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	     (list_comb (Const(a,T), args),
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	      mk_inject npart kpart (mk_inject ncon kcon (mk_tuple args)))
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  in  map mk_def (con_ty_list ~~ (1 upto ncon))  end;
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(** Define the case operator **)
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(*Combine split terms using case; yields the case operator for one part*)
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fun call_case case_list = 
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  let fun call_f (free,args) = 
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          ap_split Pr.split_const free (map (#2 o dest_Free) args)
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  in  fold_bal (app Su.elim) (map call_f case_list)  end;
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(** Generating function variables for the case definition
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    Non-identifiers (e.g. infixes) get a name of the form f_op_nnn. **)
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(*Treatment of a single constructor*)
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fun add_case ((a,T,args), (opno,cases)) =
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    if Syntax.is_identifier a
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    then (opno,   
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	  (Free(case_name ^ "_" ^ a, T), args) :: cases)
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    else (opno+1, 
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	  (Free(case_name ^ "_op_" ^ string_of_int opno, T), args) :: cases);
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(*Treatment of a list of constructors, for one part*)
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fun add_case_list (con_ty_list, (opno,case_lists)) =
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    let val (opno',case_list) = foldr add_case (con_ty_list, (opno,[]))
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    in (opno', case_list :: case_lists) end;
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(*Treatment of all parts*)
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val (_, case_lists) = foldr add_case_list (con_ty_lists, (1,[]));
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val big_case_typ = flat (map (map #2) con_ty_lists) ---> (iT-->iT);
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val big_rec_name = space_implode "_" rec_names;
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val big_case_name = big_rec_name ^ "_case";
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(*The list of all the function variables*)
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val big_case_args = flat (map (map #1) case_lists);
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val big_case_tm = 
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    list_comb (Const(big_case_name, big_case_typ), big_case_args); 
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val big_case_def = 
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  mk_defpair sign 
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    (big_case_tm, fold_bal (app Su.elim) (map call_case case_lists)); 
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(** Build the new theory **)
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val axpairs =
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    big_case_def :: flat (map mk_con_defs ((1 upto npart) ~~ con_ty_lists));
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val const_decs = flatten_consts
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		   (([big_case_name], flatten_typ sign big_case_typ, NoSyn) ::
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		    (big_rec_name ins rec_names, rec_styp, NoSyn) ::
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		    flat (map #3 rec_specs));
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val con_thy = thy
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              |> add_consts const_decs
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              |> add_axioms axpairs
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              |> add_thyname (big_rec_name ^ "_Constructors");
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(*1st element is the case definition; others are the constructors*)
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val con_defs = map (get_axiom con_thy o #1) axpairs;
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(** Prove the case theorem **)
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(*Each equation has the form 
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  rec_case(f_con1,...,f_conn)(coni(args)) = f_coni(args) *)
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fun mk_case_equation ((a,T,args), case_free) = 
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  mk_tprop 
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   (eq_const $ (big_case_tm $ (list_comb (Const(a,T), args)))
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	     $ (list_comb (case_free, args)));
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val case_trans = hd con_defs RS def_trans;
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(*proves a single case equation*)
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fun case_tacsf con_def _ = 
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  [rewtac con_def,
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   rtac case_trans 1,
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   REPEAT (resolve_tac [refl, Pr.split_eq RS trans, 
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			Su.case_inl RS trans, 
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			Su.case_inr RS trans] 1)];
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fun prove_case_equation (arg,con_def) =
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    prove_term (sign_of con_thy) [] 
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        (mk_case_equation arg, case_tacsf con_def);
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val free_iffs = 
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    map standard (con_defs RL [def_swap_iff]) @
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    [Su.distinct, Su.distinct', Su.inl_iff, Su.inr_iff, Pr.pair_iff];
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val free_SEs   = map (gen_make_elim [conjE,FalseE]) (free_iffs RL [iffD1]);
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val free_cs = ZF_cs addSEs free_SEs;
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(*Typical theorems have the form ~con1=con2, con1=con2==>False,
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  con1(x)=con1(y) ==> x=y, con1(x)=con1(y) <-> x=y, etc.  *)
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fun mk_free s =
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    prove_goalw con_thy con_defs s
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      (fn prems => [cut_facts_tac prems 1, fast_tac free_cs 1]);
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val case_eqns = map prove_case_equation 
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		    (flat con_ty_lists ~~ big_case_args ~~ tl con_defs);
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end;
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