author  nipkow 
Fri, 01 Dec 2006 16:08:45 +0100  
changeset 21618  1cbb1134cb6c 
parent 21541  ea881fbe0489 
child 21767  78ed5e22766a 
permissions  rwrr 
21541
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(* Title: HOL/Nominal/nominal_primrec.ML 
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ID: $Id$ 
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Author: Stefan Berghofer, TU Muenchen and Norbert Voelker, FernUni Hagen 
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Package for defining functions on nominal datatypes by primitive recursion. 
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Taken from HOL/Tools/primrec_package.ML 
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*) 
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signature NOMINAL_PRIMREC = 
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sig 
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val quiet_mode: bool ref 
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val add_primrec: string > string list option > string option > 
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((bstring * string) * Attrib.src list) list > theory > Proof.state 
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val add_primrec_unchecked: string > string list option > string option > 
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((bstring * string) * Attrib.src list) list > theory > Proof.state 
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val add_primrec_i: string > term list option > term option > 
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((bstring * term) * attribute list) list > theory > Proof.state 
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val add_primrec_unchecked_i: string > term list option > term option > 
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((bstring * term) * attribute list) list > theory > Proof.state 
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end; 
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structure NominalPrimrec : NOMINAL_PRIMREC = 
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struct 
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open DatatypeAux; 
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exception RecError of string; 
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fun primrec_err s = error ("Nominal primrec definition error:\n" ^ s); 
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fun primrec_eq_err thy s eq = 
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primrec_err (s ^ "\nin\n" ^ quote (Sign.string_of_term thy eq)); 
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(* messages *) 
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val quiet_mode = ref false; 
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fun message s = if ! quiet_mode then () else writeln s; 
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(* preprocessing of equations *) 
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fun process_eqn thy eq rec_fns = 
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let 
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val (lhs, rhs) = 
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if null (term_vars eq) then 
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HOLogic.dest_eq (HOLogic.dest_Trueprop (Logic.strip_imp_concl eq)) 
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handle TERM _ => raise RecError "not a proper equation" 
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else raise RecError "illegal schematic variable(s)"; 
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val (recfun, args) = strip_comb lhs; 
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val fnameT = dest_Const recfun handle TERM _ => 
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raise RecError "function is not declared as constant in theory"; 
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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 (constr, cargs') = if null middle then raise RecError "constructor missing" 
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else strip_comb (hd middle); 
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val (cname, T) = dest_Const constr 
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handle TERM _ => raise RecError "illformed constructor"; 
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val (tname, _) = dest_Type (body_type T) handle TYPE _ => 
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raise RecError "cannot determine datatype associated with function" 
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val (ls, cargs, rs) = 
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(map dest_Free ls', map dest_Free cargs', map dest_Free rs') 
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handle TERM _ => raise RecError "illegal argument in pattern"; 
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val lfrees = ls @ rs @ cargs; 
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fun check_vars _ [] = () 
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 check_vars s vars = raise RecError (s ^ commas_quote (map fst vars)) 
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in 
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if length middle > 1 then 
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raise RecError "more than one nonvariable in pattern" 
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else 
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(check_vars "repeated variable names in pattern: " (duplicates (op =) lfrees); 
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check_vars "extra variables on rhs: " 
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(map dest_Free (term_frees rhs) \\ lfrees); 
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case AList.lookup (op =) rec_fns fnameT of 
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NONE => 
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(fnameT, (tname, rpos, [(cname, (ls, cargs, rs, rhs, eq))]))::rec_fns 
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 SOME (_, rpos', eqns) => 
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if AList.defined (op =) eqns cname then 
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raise RecError "constructor already occurred as pattern" 
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else if rpos <> rpos' then 
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raise RecError "position of recursive argument inconsistent" 
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else 
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AList.update (op =) (fnameT, (tname, rpos, (cname, (ls, cargs, rs, rhs, eq))::eqns)) 
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rec_fns) 
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end 
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handle RecError s => primrec_eq_err thy s eq; 
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val param_err = "Parameters must be the same for all recursive functions"; 
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fun process_fun thy descr rec_eqns (i, fnameT as (fname, _)) (fnameTs, fnss) = 
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let 
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val (_, (tname, _, constrs)) = List.nth (descr, i); 
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(* substitute "fname ls x rs" by "y" for (x, (_, y)) in subs *) 
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fun subst [] t fs = (t, fs) 
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 subst subs (Abs (a, T, t)) fs = 
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fs 
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> subst subs t 
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> (fn t' => pair (Abs (a, T, t'))) 
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 subst subs (t as (_ $ _)) fs = 
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let 
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val (f, ts) = strip_comb t; 
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in 
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if is_Const f andalso dest_Const f mem map fst rec_eqns then 
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let 
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val fnameT' as (fname', _) = dest_Const f; 
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val (_, rpos, eqns) = the (AList.lookup (op =) rec_eqns fnameT'); 
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val ls = Library.take (rpos, ts); 
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val rest = Library.drop (rpos, ts); 
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val (x', rs) = (hd rest, tl rest) 
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handle Empty => raise RecError ("not enough arguments\ 
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\ in recursive application\nof function " ^ quote fname' ^ " on rhs"); 
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val _ = (case eqns of 
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(_, (ls', _, rs', _, _)) :: _ => 
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if ls = map Free ls' andalso rs = map Free rs' then () 
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else raise RecError param_err 
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 _ => ()); 
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val (x, xs) = strip_comb x' 
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in case AList.lookup (op =) subs x 
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of NONE => 
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fs 
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> fold_map (subst subs) ts 
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> (fn ts' => pair (list_comb (f, ts'))) 
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 SOME (i', y) => 
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fs 
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> fold_map (subst subs) xs 
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> process_fun thy descr rec_eqns (i', fnameT') 
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> (fn ts' => pair (list_comb (y, ts'))) 
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end 
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else 
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fs 
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> fold_map (subst subs) (f :: ts) 
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> (fn (f'::ts') => pair (list_comb (f', ts'))) 
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end 
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 subst _ t fs = (t, fs); 
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(* translate rec equations into function arguments suitable for rec comb *) 
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fun trans eqns (cname, cargs) (fnameTs', fnss', fns) = 
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(case AList.lookup (op =) eqns cname of 
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NONE => (warning ("No equation for constructor " ^ quote cname ^ 
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"\nin definition of function " ^ quote fname); 
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(fnameTs', fnss', (Const ("arbitrary", dummyT))::fns)) 
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 SOME (ls, cargs', rs, rhs, eq) => 
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let 
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val recs = filter (is_rec_type o snd) (cargs' ~~ cargs); 
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val rargs = map fst recs; 
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val subs = map (rpair dummyT o fst) 
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(rev (rename_wrt_term rhs rargs)); 
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val (rhs', (fnameTs'', fnss'')) = 
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(subst (map (fn ((x, y), z) => 
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(Free x, (body_index y, Free z))) 
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(recs ~~ subs)) rhs (fnameTs', fnss')) 
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handle RecError s => primrec_eq_err thy s eq 
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in (fnameTs'', fnss'', 
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(list_abs_free (cargs' @ subs, rhs'))::fns) 
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end) 
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in (case AList.lookup (op =) fnameTs i of 
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NONE => 
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if exists (equal fnameT o snd) fnameTs then 
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raise RecError ("inconsistent functions for datatype " ^ quote tname) 
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else 
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let 
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val SOME (_, _, eqns as (_, (ls, _, rs, _, _)) :: _) = 
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AList.lookup (op =) rec_eqns fnameT; 
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val (fnameTs', fnss', fns) = fold_rev (trans eqns) constrs 
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((i, fnameT)::fnameTs, fnss, []) 
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in 
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(fnameTs', (i, (fname, ls, rs, fns))::fnss') 
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end 
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 SOME fnameT' => 
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if fnameT = fnameT' then (fnameTs, fnss) 
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else raise RecError ("inconsistent functions for datatype " ^ quote tname)) 
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end; 
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(* prepare functions needed for definitions *) 
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fun get_fns fns ((i : int, (tname, _, constrs)), rec_name) (fs, defs) = 
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case AList.lookup (op =) fns i of 
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NONE => 
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let 
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val dummy_fns = map (fn (_, cargs) => Const ("arbitrary", 
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replicate ((length cargs) + (length (List.filter is_rec_type cargs))) 
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dummyT > HOLogic.unitT)) constrs; 
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val _ = warning ("No function definition for datatype " ^ quote tname) 
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in 
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(dummy_fns @ fs, defs) 
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end 
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 SOME (fname, ls, rs, fs') => (fs' @ fs, (fname, ls, rs, rec_name, tname) :: defs); 
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(* make definition *) 
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fun make_def thy fs (fname, ls, rs, rec_name, tname) = 
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let 
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val used = map fst (fold Term.add_frees fs []); 
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val x = (Name.variant used "x", dummyT); 
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val frees = ls @ x :: rs; 
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val rhs = list_abs_free (frees, 
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list_comb (Const (rec_name, dummyT), fs @ [Free x])) 
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val defpair = (Sign.base_name fname ^ "_" ^ Sign.base_name tname ^ "_def", 
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Logic.mk_equals (Const (fname, dummyT), rhs)); 
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val defpair' as (_, _ $ _ $ t) = Theory.inferT_axm thy defpair 
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in (defpair', subst_bounds (rev (map Free frees), strip_abs_body t)) end; 
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(* find datatypes which contain all datatypes in tnames' *) 
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216 

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fun find_dts (dt_info : NominalPackage.nominal_datatype_info Symtab.table) _ [] = [] 
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 find_dts dt_info tnames' (tname::tnames) = 
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(case Symtab.lookup dt_info tname of 
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NONE => primrec_err (quote tname ^ " is not a nominal datatype") 
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 SOME dt => 
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if tnames' subset (map (#1 o snd) (#descr dt)) then 
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(tname, dt)::(find_dts dt_info tnames' tnames) 
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else find_dts dt_info tnames' tnames); 
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225 

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fun common_prefix eq ([], _) = [] 
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 common_prefix eq (_, []) = [] 
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 common_prefix eq (x :: xs, y :: ys) = 
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if eq (x, y) then x :: common_prefix eq (xs, ys) else []; 
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local 
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232 

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fun gen_primrec_i note def alt_name invs fctxt eqns_atts thy = 
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let 
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val (eqns, atts) = split_list eqns_atts; 
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val dt_info = NominalPackage.get_nominal_datatypes thy; 
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val rec_eqns = fold_rev (process_eqn thy o snd) eqns []; 
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val lsrs :: lsrss = maps (fn (_, (_, _, eqns)) => 
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map (fn (_, (ls, _, rs, _, _)) => ls @ rs) eqns) rec_eqns 
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240 
val _ = 
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(if forall (curry eq_set lsrs) lsrss andalso forall 
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(fn (_, (_, _, (_, (ls, _, rs, _, _)) :: eqns)) => 
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forall (fn (_, (ls', _, rs', _, _)) => 
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ls = ls' andalso rs = rs') eqns 
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 _ => true) rec_eqns 
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then () else raise RecError param_err); 
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val tnames = distinct (op =) (map (#1 o snd) rec_eqns); 
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val dts = find_dts dt_info tnames tnames; 
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249 
val main_fns = 
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map (fn (tname, {index, ...}) => 
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(index, 
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(fst o the o find_first (fn f => (#1 o snd) f = tname)) rec_eqns)) 
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253 
dts; 
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254 
val {descr, rec_names, rec_rewrites, ...} = 
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255 
if null dts then 
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primrec_err ("datatypes " ^ commas_quote tnames ^ "\nare not mutually recursive") 
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else snd (hd dts); 
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258 
val (fnameTs, fnss) = 
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fold_rev (process_fun thy descr rec_eqns) main_fns ([], []); 
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val (fs, defs) = fold_rev (get_fns fnss) (descr ~~ rec_names) ([], []); 
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val defs' = map (make_def thy fs) defs; 
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val nameTs1 = map snd fnameTs; 
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263 
val nameTs2 = map fst rec_eqns; 
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val _ = if gen_eq_set (op =) (nameTs1, nameTs2) then () 
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else primrec_err ("functions " ^ commas_quote (map fst nameTs2) ^ 
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266 
"\nare not mutually recursive"); 
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val primrec_name = 
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if alt_name = "" then (space_implode "_" (map (Sign.base_name o #1) defs)) else alt_name; 
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val (defs_thms', thy') = 
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270 
thy 
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> Theory.add_path primrec_name 
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> fold_map def (map (fn ((name, t), _) => ((name, []), t)) defs'); 
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val cert = cterm_of thy'; 
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274 

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275 
fun mk_idx eq = 
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276 
let 
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val Const c = head_of (fst (HOLogic.dest_eq (HOLogic.dest_Trueprop 
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(Logic.strip_imp_concl eq)))); 
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val SOME i = AList.lookup op = (map swap fnameTs) c; 
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val SOME (_, _, constrs) = AList.lookup op = descr i; 
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val SOME (_, _, eqns) = AList.lookup op = rec_eqns c; 
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val SOME (cname, (_, cargs, _, _, _)) = find_first 
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(fn (_, (_, _, _, _, eq')) => eq = eq') eqns 
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in (i, find_index (fn (cname', _) => cname = cname') constrs, cargs) end; 
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285 

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286 
val rec_rewritess = 
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unflat (map (fn (_, (_, _, constrs)) => constrs) descr) rec_rewrites; 
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val fvars = rec_rewrites > hd > concl_of > HOLogic.dest_Trueprop > 
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HOLogic.dest_eq > fst > strip_comb > snd > take_prefix is_Var > fst; 
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290 
val (pvars, ctxtvars) = List.partition 
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291 
(equal HOLogic.boolT o body_type o snd) 
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292 
(fold Term.add_vars (map Logic.strip_assums_concl 
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293 
(prems_of (hd rec_rewrites))) [] \\ map dest_Var fvars); 
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val cfs = defs' > hd > snd > strip_comb > snd > 
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295 
curry (List.take o swap) (length fvars) > map cert; 
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val invs' = (case invs of 
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NONE => map (fn (i, _) => 
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298 
let 
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val SOME (_, T) = AList.lookup op = fnameTs i 
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val (Ts, U) = strip_type T 
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301 
in 
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Abs ("x", List.drop (Ts, length lsrs + 1) > U, HOLogic.true_const) 
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end) descr 
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304 
 SOME invs' => invs'); 
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val inst = (map cert fvars ~~ cfs) @ 
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306 
(map (cert o Var) pvars ~~ map cert invs') @ 
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307 
(case ctxtvars of 
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[ctxtvar] => [(cert (Var ctxtvar), cert (the_default HOLogic.unit fctxt))] 
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309 
 _ => []); 
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310 
val rec_rewrites' = map (fn (_, eq) => 
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311 
let 
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val (i, j, cargs) = mk_idx eq 
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val th = nth (nth rec_rewritess i) j; 
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val cargs' = th > concl_of > HOLogic.dest_Trueprop > 
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HOLogic.dest_eq > fst > strip_comb > snd > split_last > snd > 
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316 
strip_comb > snd 
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in (cargs, Logic.strip_imp_prems eq, 
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318 
Drule.cterm_instantiate (inst @ 
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319 
(map (cterm_of thy') cargs' ~~ map (cterm_of thy' o Free) cargs)) th) 
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320 
end) eqns; 
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321 

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val prems = foldr1 (common_prefix op aconv) (map (prems_of o #3) rec_rewrites'); 
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val cprems = map cert prems; 
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324 
val asms = map Thm.assume cprems; 
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325 
val premss = map (fn (cargs, eprems, eqn) => 
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326 
map (fn t => list_all_free (cargs, Logic.list_implies (eprems, t))) 
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327 
(List.drop (prems_of eqn, length prems))) rec_rewrites'; 
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328 
val cpremss = map (map cert) premss; 
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329 
val asmss = map (map Thm.assume) cpremss; 
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330 

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331 
fun mk_eqn ((cargs, eprems, eqn), asms') = 
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332 
let 
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333 
val ceprems = map cert eprems; 
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334 
val asms'' = map Thm.assume ceprems; 
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335 
val ccargs = map (cert o Free) cargs; 
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336 
val asms''' = map (fn th => implies_elim_list 
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337 
(forall_elim_list ccargs th) asms'') asms' 
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338 
in 
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339 
implies_elim_list eqn (asms @ asms''') > 
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340 
implies_intr_list ceprems > 
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341 
forall_intr_list ccargs 
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342 
end; 
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343 

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344 
val rule_prems = cprems @ flat cpremss; 
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345 
val rule = implies_intr_list rule_prems 
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346 
(foldr1 (uncurry Conjunction.intr) (map mk_eqn (rec_rewrites' ~~ asmss))); 
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347 

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348 
val goals = map (fn ((cargs, _, _), (_, eqn)) => 
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349 
(list_all_free (cargs, eqn), [])) (rec_rewrites' ~~ eqns); 
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350 

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351 
in 
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352 
thy' > 
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353 
ProofContext.init > 
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354 
Proof.theorem_i NONE 
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355 
(fn thss => ProofContext.theory (fn thy => 
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356 
let 
21618  357 
val simps = map standard (flat thss); 
21541
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358 
val (simps', thy') = 
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359 
fold_map note ((map fst eqns ~~ atts) ~~ map single simps) thy; 
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360 
val simps'' = maps snd simps' 
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361 
in 
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362 
thy' 
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363 
> note (("simps", [Simplifier.simp_add]), simps'') 
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364 
> snd 
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365 
> Theory.parent_path 
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366 
end)) 
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367 
[goals] > 
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368 
Proof.apply (Method.Basic (fn ctxt => Method.RAW_METHOD (fn ths => 
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369 
rewrite_goals_tac (map snd defs_thms') THEN 
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370 
compose_tac (false, rule, length rule_prems) 1))) > 
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371 
Seq.hd 
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372 
end; 
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373 

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374 
fun gen_primrec note def alt_name invs fctxt eqns thy = 
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375 
let 
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376 
fun readt T s = term_of (Thm.read_cterm thy (s, T)); 
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377 
val ((names, strings), srcss) = apfst split_list (split_list eqns); 
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378 
val atts = map (map (Attrib.attribute thy)) srcss; 
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379 
val eqn_ts = map (fn s => readt propT s 
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380 
handle ERROR msg => cat_error msg ("The error(s) above occurred for " ^ s)) strings; 
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381 
val rec_ts = map (fn eq => head_of (fst (HOLogic.dest_eq 
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382 
(HOLogic.dest_Trueprop (Logic.strip_imp_concl eq)))) 
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383 
handle TERM _ => primrec_eq_err thy "not a proper equation" eq) eqn_ts; 
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384 
val (_, eqn_ts') = OldInductivePackage.unify_consts thy rec_ts eqn_ts 
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385 
in 
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386 
gen_primrec_i note def alt_name 
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387 
(Option.map (map (readt TypeInfer.logicT)) invs) 
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388 
(Option.map (readt TypeInfer.logicT) fctxt) 
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389 
(names ~~ eqn_ts' ~~ atts) thy 
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390 
end; 
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391 

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392 
fun thy_note ((name, atts), thms) = 
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393 
PureThy.add_thmss [((name, thms), atts)] #> (fn [thms] => pair (name, thms)); 
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394 
fun thy_def false ((name, atts), t) = 
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395 
PureThy.add_defs_i false [((name, t), atts)] #> (fn [thm] => pair (name, thm)) 
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396 
 thy_def true ((name, atts), t) = 
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397 
PureThy.add_defs_unchecked_i false [((name, t), atts)] #> (fn [thm] => pair (name, thm)); 
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398 

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399 
in 
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400 

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401 
val add_primrec = gen_primrec thy_note (thy_def false); 
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402 
val add_primrec_unchecked = gen_primrec thy_note (thy_def true); 
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403 
val add_primrec_i = gen_primrec_i thy_note (thy_def false); 
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404 
val add_primrec_unchecked_i = gen_primrec_i thy_note (thy_def true); 
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405 

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406 
end; (*local*) 
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407 

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408 

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409 
(* outer syntax *) 
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410 

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411 
local structure P = OuterParse and K = OuterKeyword in 
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412 

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413 
val parser1 = P.$$$ "freshness_context"  P.$$$ ":"  (P.term >> SOME); 
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414 
val parser2 = 
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415 
P.$$$ "invariant"  P.$$$ ":"  
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416 
(Scan.repeat1 P.term >> SOME)  Scan.optional parser1 NONE  
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417 
(parser1 >> pair NONE); 
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418 
val parser3 = 
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419 
P.name  Scan.optional parser2 (NONE, NONE)  
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420 
(parser2 >> pair ""); 
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421 
val parser4 = 
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422 
(P.$$$ "unchecked" >> K true)  Scan.optional parser3 ("", (NONE, NONE))  
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423 
(parser3 >> pair false); 
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424 
val options = 
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425 
Scan.optional (P.$$$ "("  P.!!! 
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426 
(parser4  P.$$$ ")")) (false, ("", (NONE, NONE))); 
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Implemented new "nominal_primrec" command for defining
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diff
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427 

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428 
val primrec_decl = 
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429 
options  Scan.repeat1 (P.opt_thm_name ":"  P.prop); 
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430 

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431 
val primrecP = 
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432 
OuterSyntax.command "nominal_primrec" "define primitive recursive functions on nominal datatypes" K.thy_goal 
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Implemented new "nominal_primrec" command for defining
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433 
(primrec_decl >> (fn ((unchecked, (alt_name, (invs, fctxt))), eqns) => 
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434 
Toplevel.theory_to_proof 
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435 
((if unchecked then add_primrec_unchecked else add_primrec) alt_name invs fctxt 
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Implemented new "nominal_primrec" command for defining
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diff
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436 
(map P.triple_swap eqns)))); 
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berghofe
parents:
diff
changeset

437 

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438 
val _ = OuterSyntax.add_parsers [primrecP]; 
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Implemented new "nominal_primrec" command for defining
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diff
changeset

439 
val _ = OuterSyntax.add_keywords ["invariant", "freshness_context"]; 
ea881fbe0489
Implemented new "nominal_primrec" command for defining
berghofe
parents:
diff
changeset

440 

ea881fbe0489
Implemented new "nominal_primrec" command for defining
berghofe
parents:
diff
changeset

441 
end; 
ea881fbe0489
Implemented new "nominal_primrec" command for defining
berghofe
parents:
diff
changeset

442 

ea881fbe0489
Implemented new "nominal_primrec" command for defining
berghofe
parents:
diff
changeset

443 

ea881fbe0489
Implemented new "nominal_primrec" command for defining
berghofe
parents:
diff
changeset

444 
end; 
ea881fbe0489
Implemented new "nominal_primrec" command for defining
berghofe
parents:
diff
changeset

445 