datatype.ML
author clasohm
Thu, 08 Dec 1994 12:50:38 +0100
changeset 199 ad45e477926c
parent 186 6be2f3e03786
child 211 9b403e123c1b
permissions -rw-r--r--
replaced store_thm by bind_thm
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(* Title:       HOL/datatype.ML
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   ID:          $Id$
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   Author:      Max Breitling, Carsten Clasohm, Tobias Nipkow, Norbert Voelker
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   Copyright 1994 TU Muenchen
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*)
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(*used for constructor parameters*)
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datatype dt_type = dtVar of string |
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  dtTyp of dt_type list * string |
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  dtRek of dt_type list * string;
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local 
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val mysort = sort;
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open ThyParse HOLogic;
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exception Impossible;
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exception RecError of string;
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val is_dtRek = (fn dtRek _ => true  |  _  => false);
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fun opt_parens s = if s = "" then "" else enclose "(" ")" s; 
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(* ----------------------------------------------------------------------- *)
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(* Derivation of the primrec combinator application from the equations     *)
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(* subst. applications fname(ls,xk,rs) by yk(ls,rs) for xk in rargs *)
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fun subst_apps (_,_) [] t = t
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  | subst_apps (fname,cpos) pairs t =
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    let 
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    fun subst (Abs(a,T,t)) = Abs(a,T,subst t)
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      | subst (funct $ body) = 
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	let val (f,b) = strip_comb (funct$body)
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	in 
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	  if is_Const f andalso fst(dest_Const f) = fname 
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	    then 
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	      let val (ls,rest) = (take(cpos,b), drop (cpos,b));
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		val (xk,rs) = (hd rest,tl rest)
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		  handle LIST _ => raise RecError "not enough arguments \
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		   \ in recursive application on rhs"
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              in 
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		(case assoc (pairs,xk) of 
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		   None => raise RecError 
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		     ("illegal occurence of " ^ fname ^ " on rhs")
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		 | Some(U) => list_comb(U,ls @ rs))
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	      end
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	  else list_comb(f, map subst b)
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	end
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      | subst(t) = t
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    in subst t end;
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(* abstract rhs *)
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fun abst_rec (fname,cpos,tc,ls,cargs,rs,rhs) =       
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  let val rargs = (map fst o 
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		   (filter (fn (a,T) => is_dtRek T))) (cargs ~~ tc);
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      val subs = map (fn (s,T) => (s,dummyT))
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	           (rev(rename_wrt_term rhs rargs));
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      val subst_rhs = subst_apps (fname,cpos)
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	                (map Free rargs ~~ map Free subs) rhs;
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      val res = list_abs_free (cargs @ subs @ ls @ rs, subst_rhs);
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  in
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    if fname mem add_term_names (res,[]) 
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      then raise RecError ("illegal occurence of " ^ fname ^ " on rhs")
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    else res
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  end;
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(* parsing the prim rec equations *)
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fun dest_eq ( Const("Trueprop",_) $ (Const ("op =",_) $ lhs $ rhs))
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                 = (lhs, rhs)
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   | dest_eq _ = raise RecError "not a proper equation"; 
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fun dest_rec eq = 
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  let val (lhs,rhs) = dest_eq eq; 
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    val (name,args) = strip_comb lhs; 
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    val (ls',rest)  = take_prefix is_Free args; 
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    val (middle,rs') = take_suffix is_Free rest;
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    val cpos = length ls';
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    val (c,cargs') = strip_comb (hd middle)
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      handle LIST "hd" => raise RecError "constructor missing";
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    val (ls,cargs,rs) = (map dest_Free ls', map dest_Free cargs'
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			 , map dest_Free rs')
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      handle TERM ("dest_Free",_) => 
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	  raise RecError "constructor has illegal argument in pattern";
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  in 
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    if length middle > 1 then 
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      raise RecError "more than one non-variable in pattern"
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    else if not(null(findrep (map fst (ls @ rs @ cargs)))) then 
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      raise RecError "repeated variable name in pattern" 
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	 else (fst(dest_Const name) handle TERM _ => 
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	       raise RecError "function is not declared as constant in theory"
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		 ,cpos,ls,fst( dest_Const c),cargs,rs,rhs)
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  end; 
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(* check function specified for all constructors and sort function terms *)
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fun check_and_sort (n,its) = 
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  if length its = n 
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    then map snd (mysort (fn ((i : int,_),(j,_)) => i<j) its)
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  else raise error "Primrec definition error:\n\
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   \Please give an equation for every constructor";
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(* translate rec equations into function arguments suitable for rec comb *)
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(* theory parameter needed for printing error messages                   *) 
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fun trans_recs _ _ [] = error("No primrec equations.")
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  | trans_recs thy cs' (eq1::eqs) = 
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    let val (name1,cpos1,ls1,_,_,_,_) = dest_rec eq1
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      handle RecError s =>
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	error("Primrec definition error: " ^ s ^ ":\n" 
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	      ^ "   " ^ Sign.string_of_term (sign_of thy) eq1);
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      val tcs = map (fn (_,c,T,_) => (c,T)) cs';  
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      val cs = map fst tcs;
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      fun trans_recs' _ [] = []
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        | trans_recs' cis (eq::eqs) = 
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	  let val (name,cpos,ls,c,cargs,rs,rhs) = dest_rec eq; 
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	    val tc = assoc(tcs,c);
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	    val i = (1 + find (c,cs))  handle LIST "find" => 0; 
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	  in
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	  if name <> name1 then 
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	    raise RecError "function names inconsistent"
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	  else if cpos <> cpos1 then 
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	    raise RecError "position of rec. argument inconsistent"
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	  else if i = 0 then 
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	    raise RecError "illegal argument in pattern" 
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	  else if i mem cis then
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	    raise RecError "constructor already occured as pattern "
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	       else (i,abst_rec (name,cpos,the tc,ls,cargs,rs,rhs))
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		     :: trans_recs' (i::cis) eqs 
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	  end
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	  handle RecError s =>
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	        error("Primrec definition error\n" ^ s ^ "\n" 
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		      ^ "   " ^ Sign.string_of_term (sign_of thy) eq);
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    in (  name1, ls1
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	, check_and_sort (length cs, trans_recs' [] (eq1::eqs)))
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    end ;
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in
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  fun add_datatype (typevars, tname, cons_list') thy = 
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    let (*search for free type variables and convert recursive *)
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      fun analyse_types (cons, typlist, syn) =
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	let fun analyse(t as dtVar v) =
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	  if t mem typevars then t
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	  else error ("Free type variable " ^ v ^ " on rhs.")
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	      | analyse(dtTyp(typl,s)) =
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		if tname <> s then dtTyp(analyses typl, s)
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		else if typevars = typl then dtRek(typl, s)
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                     else error (s ^ " used in different ways")
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	      | analyse(dtRek _) = raise Impossible
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	    and analyses ts = map analyse ts;
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	in (cons, Syntax.const_name cons syn, analyses typlist, syn) 
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	end;
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     (*test if all elements are recursive, i.e. if the type is empty*)
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      fun non_empty (cs : ('a * 'b * dt_type list * 'c) list) = 
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	not(forall (exists is_dtRek o #3) cs) orelse
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	error("Empty datatype not allowed!");
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      val cons_list = map analyse_types cons_list';
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      val dummy = non_empty cons_list;
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      val num_of_cons = length cons_list;
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     (* Auxiliary functions to construct argument and equation lists *)
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     (*generate 'var_n, ..., var_m'*)
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      fun Args(var, delim, n, m) = 
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	space_implode delim (map (fn n => var^string_of_int(n)) (n upto m));
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     (*generate 'name_1', ..., 'name_n'*)
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      fun C_exp(name, n, var) =
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        if n > 0 then name ^ parens(Args(var, ",", 1, n)) else name;
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     (*generate 'x_n = y_n, ..., x_m = y_m'*)
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      fun Arg_eql(n,m) = 
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        if n=m then "x" ^ string_of_int(n) ^ "=y" ^ string_of_int(n) 
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        else "x" ^ string_of_int(n) ^ "=y" ^ string_of_int(n) ^ " & " ^ 
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	  Arg_eql(n+1, m);
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     (*Pretty printers for type lists;
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       pp_typlist1: parentheses, pp_typlist2: brackets*)
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      fun pp_typ (dtVar s) = s
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        | pp_typ (dtTyp (typvars, id)) =
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	  if null typvars then id else (pp_typlist1 typvars) ^ id
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        | pp_typ (dtRek (typvars, id)) = (pp_typlist1 typvars) ^ id
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      and
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	pp_typlist' ts = commas (map pp_typ ts)
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      and
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	pp_typlist1 ts = if null ts then "" else parens (pp_typlist' ts);
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      fun pp_typlist2 ts = if null ts then "" else brackets (pp_typlist' ts);
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     (* Generate syntax translation for case rules *)
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      fun calc_xrules c_nr y_nr ((_, name, typlist, _) :: cs) = 
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	let val arity = length typlist;
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	  val body  = "z" ^ string_of_int(c_nr);
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	  val args1 = if arity=0 then ""
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		      else parens (Args ("y", ",", y_nr, y_nr+arity-1));
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	  val args2 = if arity=0 then ""
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		      else "% " ^ Args ("y", " ", y_nr, y_nr+arity-1) 
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			^ ". ";
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	  val (rest1,rest2) = 
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	    if null cs then ("","")
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	    else let val (h1, h2) = calc_xrules (c_nr+1) (y_nr+arity) cs
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	    in (" | " ^ h1, ", " ^ h2) end;
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	in (name ^ args1 ^ " => " ^ body ^ rest1, args2 ^ body ^ rest2) end
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        | calc_xrules _ _ [] = raise Impossible;
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      val xrules =
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	let val (first_part, scnd_part) = calc_xrules 1 1 cons_list
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	in  [("logic", "case x of " ^ first_part) <->
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	     ("logic", tname ^ "_case(" ^ scnd_part ^ ", x)" )]
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	end;
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     (*type declarations for constructors*)
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      fun const_type (id, _, typlist, syn) =
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	(id,  
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	 (if null typlist then "" else pp_typlist2 typlist ^ " => ") ^
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	    pp_typlist1 typevars ^ tname, syn);
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      fun assumpt (dtRek _ :: ts, v :: vs ,found) =
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	let val h = if found then ";P(" ^ v ^ ")" else "[| P(" ^ v ^ ")"
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	in h ^ (assumpt (ts, vs, true)) end
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        | assumpt (t :: ts, v :: vs, found) = assumpt (ts, vs, found)
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      | assumpt ([], [], found) = if found then "|] ==>" else ""
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        | assumpt _ = raise Impossible;
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     (*insert type with suggested name 'varname' into table*)
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      fun insert typ varname ((tri as (t, s, n)) :: xs) = 
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	if typ = t then (t, s, n+1) :: xs
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	else tri :: (if varname = s then insert typ (varname ^ "'") xs
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		     else insert typ varname xs)
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        | insert typ varname [] = [(typ, varname, 1)];
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      fun typid(dtRek(_,id)) = id
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        | typid(dtVar s) = implode (tl (explode s))
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        | typid(dtTyp(_,id)) = id;
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      val insert_types = foldl (fn (tab,typ) => insert typ (typid typ) tab);
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      fun update(dtRek _, s, v :: vs, (dtRek _) :: ts) = s :: vs
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        | update(t, s, v :: vs, t1 :: ts) = 
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	  if t=t1 then s :: vs else v :: (update (t, s, vs, ts))
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        | update _ = raise Impossible;
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      fun update_n (dtRek r1, s, v :: vs, (dtRek r2) :: ts, n) =
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	if r1 = r2 then (s ^ string_of_int n) :: 
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	  (update_n (dtRek r1, s, vs, ts, n+1))
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	else v :: (update_n (dtRek r1, s, vs, ts, n))
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        | update_n (t, s, v :: vs, t1 :: ts, n) = 
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	  if t = t1 then (s ^ string_of_int n) :: 
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	    (update_n (t, s, vs, ts, n+1))
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	  else v :: (update_n (t, s, vs, ts, n))
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        | update_n (_,_,[],[],_) = []
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        | update_n _ = raise Impossible;
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     (*insert type variables into table*)
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      fun convert typs =
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        let fun conv(vars, (t, s, n)) =
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	  if n=1 then update (t, s, vars, typs)
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	  else update_n (t, s, vars, typs, 1)
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        in foldl conv 
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	end;
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      fun empty_list n = replicate n "";
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      fun t_inducting ((_, name, typl, _) :: cs) =
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	let val tab = insert_types([],typl);
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	  val arity = length typl;
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	  val var_list = convert typl (empty_list arity,tab); 
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	  val h = if arity = 0 then " P(" ^ name ^ ")"
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		  else " !!" ^ (space_implode " " var_list) ^ "." ^
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		    (assumpt (typl, var_list, false)) ^ "P(" ^ 
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		    name ^ "(" ^ (commas var_list) ^ "))";
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	  val rest = t_inducting cs;
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	in if rest = "" then h else h ^ "; " ^ rest end
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        | t_inducting [] = "";
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      fun t_induct cl typ_name =
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        "[|" ^ t_inducting cl ^ "|] ==> P(" ^ typ_name ^ ")";
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      fun gen_typlist typevar f ((_, _, ts, _) :: cs) =
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	let val h = if (length ts) > 0
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		      then pp_typlist2(f ts) ^ "=>"
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		    else ""
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	in h ^ typevar ^  "," ^ (gen_typlist typevar f cs) end
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        | gen_typlist _ _ [] = "";
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(* -------------------------------------------------------------------- *)
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(* The case constant and rules 	        				*)
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      val t_case = tname ^ "_case";
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      fun case_rule n (id, name, ts, _) =
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	let val args = opt_parens(Args("x", ",", 1, length ts))
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	in (t_case ^ "_" ^ id,
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	    t_case ^ "(" ^ Args("f", ",", 1, num_of_cons)
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	    ^ "," ^ name ^ args 
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	    ^ ") = f"  ^ string_of_int(n) ^ args)
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	end
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      fun case_rules n (c :: cs) = case_rule n c :: case_rules(n+1) cs
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        | case_rules _ [] = [];
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      val datatype_arity = length typevars;
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      val types = [(tname, datatype_arity, NoSyn)];
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      val arities = 
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        let val term_list = replicate datatype_arity termS;
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        in [(tname, term_list, termS)] 
129
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	end;
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      val datatype_name = pp_typlist1 typevars ^ tname;
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      val new_tvar_name = variant (map (fn dtVar s => s) typevars) "'z";
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      val case_const =
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	(t_case,
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	 "[" ^ gen_typlist new_tvar_name I cons_list 
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	 ^  pp_typlist1 typevars ^ tname ^ "] =>" ^ new_tvar_name,
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	 NoSyn);
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      val rules_case = case_rules 1 cons_list;
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(* -------------------------------------------------------------------- *)
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(* The prim-rec combinator						*) 
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      val t_rec = tname ^ "_rec"
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(* adding type variables for dtRek types to end of list of dt_types      *)   
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      fun add_reks ts = 
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	ts @ map (fn _ => dtVar new_tvar_name) (filter is_dtRek ts); 
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(* positions of the dtRek types in a list of dt_types, starting from 1  *)
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      fun rek_pos ts = 
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	map snd (filter (is_dtRek o fst) (ts ~~ (1 upto length ts)))
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      fun rec_rule n (id,name,ts,_) = 
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	let val args = Args("x",",",1,length ts)
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	  val fargs = Args("f",",",1,num_of_cons)
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	  fun rarg i = "," ^ t_rec ^ parens(fargs ^ "," ^ "x" ^ 
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					    string_of_int(i)) 
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	  val rargs = implode (map rarg (rek_pos ts)) 
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	in     
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	  ( t_rec ^ "_" ^ id
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	   , t_rec ^ parens(fargs ^  "," ^ name ^ (opt_parens args)) ^ " = f"
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	   ^ string_of_int(n) ^ opt_parens (args ^ rargs)) 
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	end
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      fun rec_rules n (c::cs) = rec_rule n c :: rec_rules (n+1) cs 
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	| rec_rules _ [] = [];
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      val rec_const =
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	(t_rec,
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	 "[" ^ (gen_typlist new_tvar_name add_reks cons_list) 
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	 ^ (pp_typlist1 typevars) ^ tname ^ "] =>" ^ new_tvar_name,
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	 NoSyn);
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      val rules_rec = rec_rules 1 cons_list
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(* -------------------------------------------------------------------- *)
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      val consts = 
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	map const_type cons_list
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	@ (if num_of_cons < dtK then []
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	   else [(tname ^ "_ord", datatype_name ^ "=>nat", NoSyn)])
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	@ [case_const,rec_const];
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      fun Ci_ing ((id, name, typlist, _) :: cs) =
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	let val arity = length typlist;
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	in if arity = 0 then Ci_ing cs
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	   else ("inject_" ^ id,
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		 "(" ^ C_exp(name,arity,"x") ^ "=" ^ C_exp(name,arity,"y") 
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		 ^ ") = (" ^ Arg_eql (1, arity) ^ ")") :: (Ci_ing cs)
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	end
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	| Ci_ing [] = [];
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      fun Ci_negOne (id1, name1, tl1, _) (id2, name2, tl2, _) =
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	let val ax = C_exp(name1, length tl1, "x") ^ "~=" ^
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	  C_exp(name2, length tl2, "y")
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	in (id1 ^ "_not_" ^ id2, ax) 
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	end;
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      fun Ci_neg1 [] = []
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	| Ci_neg1 (c1::cs) = (map (Ci_negOne c1) cs) @ Ci_neg1 cs;
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      fun suc_expr n = 
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	if n=0 then "0" else "Suc(" ^ suc_expr(n-1) ^ ")";
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      fun Ci_neg2() =
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	let val ord_t = tname ^ "_ord";
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	  val cis = cons_list ~~ (0 upto (num_of_cons - 1))
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	  fun Ci_neg2equals ((id, name, typlist, _), n) =
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	    let val ax = ord_t ^ "(" ^ (C_exp(name, length typlist, "x")) 
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   401
	      ^ ") = " ^ (suc_expr n)
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   402
	    in (ord_t ^ "_" ^ id, ax) end
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   403
	in (ord_t ^ "_distinct", ord_t^"(x) ~= "^ord_t^"(y) ==> x ~= y") ::
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   404
	  (map Ci_neg2equals cis)
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   405
	end;
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   406
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   407
      val rules_distinct = if num_of_cons < dtK then Ci_neg1 cons_list
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   408
			   else Ci_neg2();
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   409
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   410
      val rules_inject = Ci_ing cons_list;
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   411
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   412
      val rule_induct = (tname ^ "_induct", t_induct cons_list tname);
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   413
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   414
      val rules = rule_induct ::
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   415
	(rules_inject @ rules_distinct @ rules_case @ rules_rec);
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   416
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   417
      fun add_primrec eqns thy =
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   418
	let val rec_comb = Const(t_rec,dummyT)
143
3226f25f88e7 improved error reporting for primrec
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   419
	  val teqns = map (fn neq => snd(read_axm (sign_of thy) neq)) eqns
129
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   420
	  val (fname,ls,fns) = trans_recs thy cons_list teqns
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   421
	  val rhs = 
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   422
	    list_abs_free
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   423
	    (ls @ [(tname,dummyT)]
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   424
	     ,list_comb(rec_comb
0bba840aa07c New version of datatype.ML with primrec (Norbert).
nipkow
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   425
			, fns @ map Bound (0 ::(length ls downto 1))));
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   426
          val sg = sign_of thy;
147
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diff changeset
   427
          val defpair =  mk_defpair (Const(fname,dummyT),rhs)
8ff6c8c95870 Small simplification in add_datatype.
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diff changeset
   428
	  val defpairT as (_, _ $ Const(_,T) $ _ ) = inferT_axm sg defpair;
129
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   429
	  val varT = Type.varifyT T;
186
6be2f3e03786 replaced ["term"] by termS;
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   430
          val ftyp = the (Sign.const_type sg fname);
129
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   431
	in
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   432
	  if Type.typ_instance (#tsig(Sign.rep_sg sg), ftyp, varT)
147
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   433
	  then add_defs_i [defpairT] thy
129
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   434
	  else error("Primrec definition error: \ntype of " ^ fname 
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   435
		     ^ " is not instance of type deduced from equations")
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   436
	end;
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   437
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   438
    in 
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   439
      (thy
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   440
      |> add_types types
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   441
      |> add_arities arities
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   442
      |> add_consts consts
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   443
      |> add_trrules xrules
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   444
      |> add_axioms rules,add_primrec)
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   445
    end
0bba840aa07c New version of datatype.ML with primrec (Norbert).
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   446
end