923
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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 1995 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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structure Datatype =
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struct
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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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(* substitute fname(ls,xk,rs) by yk(ls,rs) in t for (xk,yk) in pairs *)
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fun subst_apps (_,_) [] t = t
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| subst_apps (fname,rpos) 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(rpos,b), drop(rpos,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,map subst (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,rpos,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,rpos)
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(map Free rargs ~~ map Free subs) rhs;
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in
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list_abs_free (cargs @ subs @ ls @ rs, subst_rhs)
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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 rpos = 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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,rpos,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,rpos1,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,rpos,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 rpos <> rpos1 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,rpos,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
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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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fun index_vnames(vn::vns,tab) =
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(case assoc(tab,vn) of
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None => if vn mem vns
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then (vn^"1") :: index_vnames(vns,(vn,2)::tab)
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else vn :: index_vnames(vns,tab)
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| Some(i) => (vn^(string_of_int i)) ::
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index_vnames(vns,(vn,i+1)::tab))
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| index_vnames([],tab) = [];
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fun mk_var_names types = index_vnames(map typid types,[]);
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(*search for free type variables and convert recursive *)
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fun analyse_types (cons, types, 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 types,
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mk_var_names types, 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 *'d) 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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fun C_exp name vns = name ^ opt_parens(space_implode ") (" vns);
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(*Arg_eqs([x1,...,xn],[y1,...,yn]) = "x1 = y1 & ... & xn = yn" *)
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fun arg_eqs vns vns' =
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let fun mkeq(x,x') = x ^ "=" ^ x'
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in space_implode " & " (map mkeq (vns~~vns')) end;
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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, _, vns, _) :: cs) =
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let val arity = length vns;
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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,
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"(" ^ args2 ^ body ^ rest2 ^ ")")
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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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fun t_inducting ((_, name, types, vns, _) :: cs) =
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let
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val h = if null types then " P(" ^ name ^ ")"
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else " !!" ^ (space_implode " " vns) ^ "." ^
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(assumpt (types, vns, false)) ^
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"P(" ^ C_exp name vns ^ ")";
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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, _, vns, _) =
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let val args = opt_parens(space_implode ") (" vns)
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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 ^ ") = 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)]
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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_vars ts vns = map snd (filter (is_dtRek o fst) (ts ~~ vns))
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fun rec_rule n (id,name,ts,vns,_) =
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let val args = space_implode ") (" vns
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val fargs = Args("f",") (",1,num_of_cons)
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fun rarg vn = ") (" ^ t_rec ^ parens(fargs ^ ") (" ^ vn)
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val rargs = implode (map rarg (rek_vars ts vns))
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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, _, vns, _) :: cs) =
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if null vns then Ci_ing cs
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else let val vns' = variantlist(vns,vns)
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in ("inject_" ^ id,
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"(" ^ (C_exp name vns) ^ "=" ^ (C_exp name vns')
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^ ") = (" ^ (arg_eqs vns vns') ^ ")") :: (Ci_ing cs)
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end
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| Ci_ing [] = [];
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fun Ci_negOne (id1,name1,_,vns1,_) (id2,name2,_,vns2,_) =
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let val vns2' = variantlist(vns2,vns1)
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val ax = C_exp name1 vns1 ^ "~=" ^ C_exp name2 vns2'
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in (id1 ^ "_not_" ^ id2, ax) 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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367 |
val cis = cons_list ~~ (0 upto (num_of_cons - 1))
|
|
368 |
fun Ci_neg2equals ((id, name, _, vns, _), n) =
|
|
369 |
let val ax = ord_t ^ "(" ^ (C_exp name vns) ^ ") = " ^ (suc_expr n)
|
|
370 |
in (ord_t ^ "_" ^ id, ax) end
|
|
371 |
in (ord_t ^ "_distinct", ord_t^"(x) ~= "^ord_t^"(y) ==> x ~= y") ::
|
|
372 |
(map Ci_neg2equals cis)
|
|
373 |
end;
|
|
374 |
|
|
375 |
val rules_distinct = if num_of_cons < dtK then Ci_neg1 cons_list
|
|
376 |
else Ci_neg2();
|
|
377 |
|
|
378 |
val rules_inject = Ci_ing cons_list;
|
|
379 |
|
|
380 |
val rule_induct = (tname ^ "_induct", t_induct cons_list tname);
|
|
381 |
|
|
382 |
val rules = rule_induct ::
|
|
383 |
(rules_inject @ rules_distinct @ rules_case @ rules_rec);
|
|
384 |
|
|
385 |
fun add_primrec eqns thy =
|
|
386 |
let val rec_comb = Const(t_rec,dummyT)
|
|
387 |
val teqns = map (fn neq => snd(read_axm (sign_of thy) neq)) eqns
|
|
388 |
val (fname,ls,fns) = trans_recs thy cons_list teqns
|
|
389 |
val rhs =
|
|
390 |
list_abs_free
|
|
391 |
(ls @ [(tname,dummyT)]
|
|
392 |
,list_comb(rec_comb
|
|
393 |
, fns @ map Bound (0 ::(length ls downto 1))));
|
|
394 |
val sg = sign_of thy;
|
|
395 |
val defpair = mk_defpair (Const(fname,dummyT),rhs)
|
|
396 |
val defpairT as (_, _ $ Const(_,T) $ _ ) = inferT_axm sg defpair;
|
|
397 |
val varT = Type.varifyT T;
|
|
398 |
val ftyp = the (Sign.const_type sg fname);
|
|
399 |
in
|
|
400 |
if Type.typ_instance (#tsig(Sign.rep_sg sg), ftyp, varT)
|
|
401 |
then add_defs_i [defpairT] thy
|
|
402 |
else error("Primrec definition error: \ntype of " ^ fname
|
|
403 |
^ " is not instance of type deduced from equations")
|
|
404 |
end;
|
|
405 |
|
|
406 |
in
|
|
407 |
(thy
|
|
408 |
|> add_types types
|
|
409 |
|> add_arities arities
|
|
410 |
|> add_consts consts
|
|
411 |
|> add_trrules xrules
|
|
412 |
|> add_axioms rules,add_primrec)
|
|
413 |
end
|
|
414 |
end
|
|
415 |
end
|
|
416 |
|
|
417 |
(*
|
|
418 |
Informal description of functions used in datatype.ML for the Isabelle/HOL
|
|
419 |
implementation of prim. rec. function definitions. (N. Voelker, Feb. 1995)
|
|
420 |
|
|
421 |
* subst_apps (fname,rpos) pairs t:
|
|
422 |
substitute the term
|
|
423 |
fname(ls,xk,rs)
|
|
424 |
by
|
|
425 |
yk(ls,rs)
|
|
426 |
in t for (xk,yk) in pairs, where rpos = length ls.
|
|
427 |
Applied with :
|
|
428 |
fname = function name
|
|
429 |
rpos = position of recursive argument
|
|
430 |
pairs = list of pairs (xk,yk), where
|
|
431 |
xk are the rec. arguments of the constructor in the pattern,
|
|
432 |
yk is a variable with name derived from xk
|
|
433 |
t = rhs of equation
|
|
434 |
|
|
435 |
* abst_rec (fname,rpos,tc,ls,cargs,rs,rhs)
|
|
436 |
- filter recursive arguments from constructor arguments cargs,
|
|
437 |
- perform substitutions on rhs,
|
|
438 |
- derive list subs of new variable names yk for use in subst_apps,
|
|
439 |
- abstract rhs with respect to cargs, subs, ls and rs.
|
|
440 |
|
|
441 |
* dest_eq t
|
|
442 |
destruct a term denoting an equation into lhs and rhs.
|
|
443 |
|
|
444 |
* dest_req eq
|
|
445 |
destruct an equation of the form
|
|
446 |
name (vl1..vlrpos, Ci(vi1..vin), vr1..vrn) = rhs
|
|
447 |
into
|
|
448 |
- function name (name)
|
|
449 |
- position of the first non-variable parameter (rpos)
|
|
450 |
- the list of first rpos parameters (ls = [vl1..vlrpos])
|
|
451 |
- the constructor (fst( dest_Const c) = Ci)
|
|
452 |
- the arguments of the constructor (cargs = [vi1..vin])
|
|
453 |
- the rest of the variables in the pattern (rs = [vr1..vrn])
|
|
454 |
- the right hand side of the equation (rhs).
|
|
455 |
|
|
456 |
* check_and_sort (n,its)
|
|
457 |
check that n = length its holds, and sort elements of its by
|
|
458 |
first component.
|
|
459 |
|
|
460 |
* trans_recs thy cs' (eq1::eqs)
|
|
461 |
destruct eq1 into name1, rpos1, ls1, etc..
|
|
462 |
get constructor list with and without type (tcs resp. cs) from cs',
|
|
463 |
for every equation:
|
|
464 |
destruct it into (name,rpos,ls,c,cargs,rs,rhs)
|
|
465 |
get typed constructor tc from c and tcs
|
|
466 |
determine the index i of the constructor
|
|
467 |
check function name and position of rec. argument by comparison
|
|
468 |
with first equation
|
|
469 |
check for repeated variable names in pattern
|
|
470 |
derive function term f_i which is used as argument of the rec. combinator
|
|
471 |
sort the terms f_i according to i and return them together
|
|
472 |
with the function name and the parameter of the definition (ls).
|
|
473 |
|
|
474 |
* Application:
|
|
475 |
|
|
476 |
The rec. combinator is applied to the function terms resulting from
|
|
477 |
trans_rec. This results in a function which takes the recursive arg.
|
|
478 |
as first parameter and then the arguments corresponding to ls. The
|
|
479 |
order of parameters is corrected by setting the rhs equal to
|
|
480 |
|
|
481 |
list_abs_free
|
|
482 |
(ls @ [(tname,dummyT)]
|
|
483 |
,list_comb(rec_comb
|
|
484 |
, fns @ map Bound (0 ::(length ls downto 1))));
|
|
485 |
|
|
486 |
Note the de-Bruijn indices counting the number of lambdas between the
|
|
487 |
variable and its binding.
|
|
488 |
*)
|