(* Title: ZF/Tools/primrec_package.ML Author: Norbert Voelker, FernUni Hagen Author: Stefan Berghofer, TU Muenchen Author: Lawrence C Paulson, Cambridge University Computer Laboratory Package for defining functions on datatypes by primitive recursion. *) signature PRIMREC_PACKAGE = sig val add_primrec: ((binding * string) * Attrib.src list) list -> theory -> theory * thm list val add_primrec_i: ((binding * term) * attribute list) list -> theory -> theory * thm list end; structure PrimrecPackage : PRIMREC_PACKAGE = struct exception RecError of string; (*Remove outer Trueprop and equality sign*) val dest_eqn = FOLogic.dest_eq o FOLogic.dest_Trueprop; fun primrec_err s = error ("Primrec definition error:\n" ^ s); fun primrec_eq_err sign s eq = primrec_err (s ^ "\nin equation\n" ^ Syntax.string_of_term_global sign eq); (* preprocessing of equations *) (*rec_fn_opt records equations already noted for this function*) fun process_eqn thy (eq, rec_fn_opt) = let val (lhs, rhs) = if null (Term.add_vars eq []) then dest_eqn eq handle TERM _ => raise RecError "not a proper equation" else raise RecError "illegal schematic variable(s)"; val (recfun, args) = strip_comb lhs; val (fname, ftype) = dest_Const recfun handle TERM _ => raise RecError "function is not declared as constant in theory"; val (ls_frees, rest) = take_prefix is_Free args; val (middle, rs_frees) = take_suffix is_Free rest; val (constr, cargs_frees) = if null middle then raise RecError "constructor missing" else strip_comb (hd middle); val (cname, _) = dest_Const constr handle TERM _ => raise RecError "ill-formed constructor"; val con_info = the (Symtab.lookup (ConstructorsData.get thy) cname) handle Option => raise RecError "cannot determine datatype associated with function" val (ls, cargs, rs) = (map dest_Free ls_frees, map dest_Free cargs_frees, map dest_Free rs_frees) handle TERM _ => raise RecError "illegal argument in pattern"; val lfrees = ls @ rs @ cargs; (*Constructor, frees to left of pattern, pattern variables, frees to right of pattern, rhs of equation, full original equation. *) val new_eqn = (cname, (rhs, cargs, eq)) in if has_duplicates (op =) lfrees then raise RecError "repeated variable name in pattern" else if not ((map dest_Free (OldTerm.term_frees rhs)) subset lfrees) then raise RecError "extra variables on rhs" else if length middle > 1 then raise RecError "more than one non-variable in pattern" else case rec_fn_opt of NONE => SOME (fname, ftype, ls, rs, con_info, [new_eqn]) | SOME (fname', _, ls', rs', con_info': constructor_info, eqns) => if AList.defined (op =) eqns cname then raise RecError "constructor already occurred as pattern" else if (ls <> ls') orelse (rs <> rs') then raise RecError "non-recursive arguments are inconsistent" else if #big_rec_name con_info <> #big_rec_name con_info' then raise RecError ("Mixed datatypes for function " ^ fname) else if fname <> fname' then raise RecError ("inconsistent functions for datatype " ^ #big_rec_name con_info) else SOME (fname, ftype, ls, rs, con_info, new_eqn::eqns) end handle RecError s => primrec_eq_err thy s eq; (*Instantiates a recursor equation with constructor arguments*) fun inst_recursor ((_ $ constr, rhs), cargs') = subst_atomic (#2 (strip_comb constr) ~~ map Free cargs') rhs; (*Convert a list of recursion equations into a recursor call*) fun process_fun thy (fname, ftype, ls, rs, con_info: constructor_info, eqns) = let val fconst = Const(fname, ftype) val fabs = list_comb (fconst, map Free ls @ [Bound 0] @ map Free rs) and {big_rec_name, constructors, rec_rewrites, ...} = con_info (*Replace X_rec(args,t) by fname(ls,t,rs) *) fun use_fabs (_ $ t) = subst_bound (t, fabs) | use_fabs t = t val cnames = map (#1 o dest_Const) constructors and recursor_pairs = map (dest_eqn o concl_of) rec_rewrites fun absterm (Free(a,T), body) = absfree (a,T,body) | absterm (t,body) = Abs("rec", Ind_Syntax.iT, abstract_over (t, body)) (*Translate rec equations into function arguments suitable for recursor. Missing cases are replaced by 0 and all cases are put into order.*) fun add_case ((cname, recursor_pair), cases) = let val (rhs, recursor_rhs, eq) = case AList.lookup (op =) eqns cname of NONE => (warning ("no equation for constructor " ^ cname ^ "\nin definition of function " ^ fname); (Const ("0", Ind_Syntax.iT), #2 recursor_pair, Const ("0", Ind_Syntax.iT))) | SOME (rhs, cargs', eq) => (rhs, inst_recursor (recursor_pair, cargs'), eq) val allowed_terms = map use_fabs (#2 (strip_comb recursor_rhs)) val abs = List.foldr absterm rhs allowed_terms in if !Ind_Syntax.trace then writeln ("recursor_rhs = " ^ Syntax.string_of_term_global thy recursor_rhs ^ "\nabs = " ^ Syntax.string_of_term_global thy abs) else(); if Logic.occs (fconst, abs) then primrec_eq_err thy ("illegal recursive occurrences of " ^ fname) eq else abs :: cases end val recursor = head_of (#1 (hd recursor_pairs)) (** make definition **) (*the recursive argument*) val rec_arg = Free (Name.variant (map #1 (ls@rs)) (Long_Name.base_name big_rec_name), Ind_Syntax.iT) val def_tm = Logic.mk_equals (subst_bound (rec_arg, fabs), list_comb (recursor, List.foldr add_case [] (cnames ~~ recursor_pairs)) $ rec_arg) in if !Ind_Syntax.trace then writeln ("primrec def:\n" ^ Syntax.string_of_term_global thy def_tm) else(); (Long_Name.base_name fname ^ "_" ^ Long_Name.base_name big_rec_name ^ "_def", def_tm) end; (* prepare functions needed for definitions *) fun add_primrec_i args thy = let val ((eqn_names, eqn_terms), eqn_atts) = apfst split_list (split_list args); val SOME (fname, ftype, ls, rs, con_info, eqns) = List.foldr (process_eqn thy) NONE eqn_terms; val def = process_fun thy (fname, ftype, ls, rs, con_info, eqns); val ([def_thm], thy1) = thy |> Sign.add_path (Long_Name.base_name fname) |> PureThy.add_defs false [Thm.no_attributes (apfst Binding.name def)]; val rewrites = def_thm :: map mk_meta_eq (#rec_rewrites con_info) val eqn_thms = eqn_terms |> map (fn t => Goal.prove_global thy1 [] [] (Ind_Syntax.traceIt "next primrec equation = " thy1 t) (fn _ => EVERY [rewrite_goals_tac rewrites, rtac refl 1])); val (eqn_thms', thy2) = thy1 |> PureThy.add_thms ((eqn_names ~~ eqn_thms) ~~ eqn_atts); val (_, thy3) = thy2 |> PureThy.add_thmss [((Binding.name "simps", eqn_thms'), [Simplifier.simp_add])] ||> Sign.parent_path; in (thy3, eqn_thms') end; fun add_primrec args thy = add_primrec_i (map (fn ((name, s), srcs) => ((name, Syntax.read_prop_global thy s), map (Attrib.attribute thy) srcs)) args) thy; (* outer syntax *) structure P = OuterParse and K = OuterKeyword; val _ = OuterSyntax.command "primrec" "define primitive recursive functions on datatypes" K.thy_decl (Scan.repeat1 (SpecParse.opt_thm_name ":" -- P.prop) >> (Toplevel.theory o (#1 oo (add_primrec o map P.triple_swap)))); end;