--- a/add_ind_def.ML Tue Oct 24 14:59:17 1995 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,244 +0,0 @@
-(* Title: HOL/add_ind_def.ML
- ID: $Id$
- Author: Lawrence C Paulson, Cambridge University Computer Laboratory
- Copyright 1994 University of Cambridge
-
-Fixedpoint definition module -- for Inductive/Coinductive Definitions
-
-Features:
-* least or greatest fixedpoints
-* user-specified product and sum constructions
-* mutually recursive definitions
-* definitions involving arbitrary monotone operators
-* automatically proves introduction and elimination rules
-
-The recursive sets must *already* be declared as constants in parent theory!
-
- Introduction rules have the form
- [| ti:M(Sj), ..., P(x), ... |] ==> t: Sk |]
- where M is some monotone operator (usually the identity)
- P(x) is any (non-conjunctive) side condition on the free variables
- ti, t are any terms
- Sj, Sk are two of the sets being defined in mutual recursion
-
-Sums are used only for mutual recursion;
-Products are used only to derive "streamlined" induction rules for relations
-
-Nestings of disjoint sum types:
- (a+(b+c)) for 3, ((a+b)+(c+d)) for 4, ((a+b)+(c+(d+e))) for 5,
- ((a+(b+c))+(d+(e+f))) for 6
-*)
-
-signature FP = (** Description of a fixed point operator **)
- sig
- val oper : string * typ * term -> term (*fixed point operator*)
- val Tarski : thm (*Tarski's fixed point theorem*)
- val induct : thm (*induction/coinduction rule*)
- end;
-
-
-signature ADD_INDUCTIVE_DEF =
- sig
- val add_fp_def_i : term list * term list -> theory -> theory
- end;
-
-
-
-(*Declares functions to add fixedpoint/constructor defs to a theory*)
-functor Add_inductive_def_Fun (Fp: FP) : ADD_INDUCTIVE_DEF =
-struct
-open Logic Ind_Syntax;
-
-(*internal version*)
-fun add_fp_def_i (rec_tms, intr_tms) thy =
- let
- val sign = sign_of thy;
-
- (*recT and rec_params should agree for all mutually recursive components*)
- val rec_hds = map head_of rec_tms;
-
- val _ = assert_all is_Const rec_hds
- (fn t => "Recursive set not previously declared as constant: " ^
- Sign.string_of_term sign t);
-
- (*Now we know they are all Consts, so get their names, type and params*)
- val rec_names = map (#1 o dest_Const) rec_hds
- and (Const(_,recT),rec_params) = strip_comb (hd rec_tms);
-
- val _ = assert_all Syntax.is_identifier rec_names
- (fn a => "Name of recursive set not an identifier: " ^ a);
-
- local (*Checking the introduction rules*)
- val intr_sets = map (#2 o rule_concl_msg sign) intr_tms;
- fun intr_ok set =
- case head_of set of Const(a,_) => a mem rec_names | _ => false;
- in
- val _ = assert_all intr_ok intr_sets
- (fn t => "Conclusion of rule does not name a recursive set: " ^
- Sign.string_of_term sign t);
- end;
-
- val _ = assert_all is_Free rec_params
- (fn t => "Param in recursion term not a free variable: " ^
- Sign.string_of_term sign t);
-
- (*** Construct the lfp definition ***)
- val mk_variant = variant (foldr add_term_names (intr_tms,[]));
-
- val z = mk_variant"z" and X = mk_variant"X" and w = mk_variant"w";
-
- (*Probably INCORRECT for mutual recursion!*)
- val domTs = summands(dest_setT (body_type recT));
- val dom_sumT = fold_bal mk_sum domTs;
- val dom_set = mk_setT dom_sumT;
-
- val freez = Free(z, dom_sumT)
- and freeX = Free(X, dom_set);
- (*type of w may be any of the domTs*)
-
- fun dest_tprop (Const("Trueprop",_) $ P) = P
- | dest_tprop Q = error ("Ill-formed premise of introduction rule: " ^
- Sign.string_of_term sign Q);
-
- (*Makes a disjunct from an introduction rule*)
- fun lfp_part intr = (*quantify over rule's free vars except parameters*)
- let val prems = map dest_tprop (strip_imp_prems intr)
- val _ = seq (fn rec_hd => seq (chk_prem rec_hd) prems) rec_hds
- val exfrees = term_frees intr \\ rec_params
- val zeq = eq_const dom_sumT $ freez $ (#1 (rule_concl intr))
- in foldr mk_exists (exfrees, fold_bal (app conj) (zeq::prems)) end;
-
- (*The Part(A,h) terms -- compose injections to make h*)
- fun mk_Part (Bound 0, _) = freeX (*no mutual rec, no Part needed*)
- | mk_Part (h, domT) =
- let val goodh = mend_sum_types (h, dom_sumT)
- and Part_const =
- Const("Part", [dom_set, domT-->dom_sumT]---> dom_set)
- in Part_const $ freeX $ Abs(w,domT,goodh) end;
-
- (*Access to balanced disjoint sums via injections*)
- val parts = map mk_Part
- (accesses_bal (ap Inl, ap Inr, Bound 0) (length domTs) ~~
- domTs);
-
- (*replace each set by the corresponding Part(A,h)*)
- val part_intrs = map (subst_free (rec_tms ~~ parts) o lfp_part) intr_tms;
-
- val lfp_rhs = Fp.oper(X, dom_sumT,
- mk_Collect(z, dom_sumT,
- fold_bal (app disj) part_intrs))
-
- val _ = seq (fn rec_hd => deny (rec_hd occs lfp_rhs)
- "Illegal occurrence of recursion operator")
- rec_hds;
-
- (*** Make the new theory ***)
-
- (*A key definition:
- If no mutual recursion then it equals the one recursive set.
- If mutual recursion then it differs from all the recursive sets. *)
- val big_rec_name = space_implode "_" rec_names;
-
- (*Big_rec... is the union of the mutually recursive sets*)
- val big_rec_tm = list_comb(Const(big_rec_name,recT), rec_params);
-
- (*The individual sets must already be declared*)
- val axpairs = map mk_defpair
- ((big_rec_tm, lfp_rhs) ::
- (case parts of
- [_] => [] (*no mutual recursion*)
- | _ => rec_tms ~~ (*define the sets as Parts*)
- map (subst_atomic [(freeX, big_rec_tm)]) parts));
-
- val _ = seq (writeln o Sign.string_of_term sign o #2) axpairs
-
- in thy |> add_defs_i axpairs end
-
-
-(****************************************************************OMITTED
-
-(*Expects the recursive sets to have been defined already.
- con_ty_lists specifies the constructors in the form (name,prems,mixfix) *)
-fun add_constructs_def (rec_names, con_ty_lists) thy =
-* let
-* val _ = writeln" Defining the constructor functions...";
-* val case_name = "f"; (*name for case variables*)
-
-* (** Define the constructors **)
-
-* (*The empty tuple is 0*)
-* fun mk_tuple [] = Const("0",iT)
-* | mk_tuple args = foldr1 mk_Pair args;
-
-* fun mk_inject n k u = access_bal(ap Inl, ap Inr, u) n k;
-
-* val npart = length rec_names; (*total # of mutually recursive parts*)
-
-* (*Make constructor definition; kpart is # of this mutually recursive part*)
-* fun mk_con_defs (kpart, con_ty_list) =
-* let val ncon = length con_ty_list (*number of constructors*)
- fun mk_def (((id,T,syn), name, args, prems), kcon) =
- (*kcon is index of constructor*)
- mk_defpair (list_comb (Const(name,T), args),
- mk_inject npart kpart
- (mk_inject ncon kcon (mk_tuple args)))
-* in map mk_def (con_ty_list ~~ (1 upto ncon)) end;
-
-* (** Define the case operator **)
-
-* (*Combine split terms using case; yields the case operator for one part*)
-* fun call_case case_list =
-* let fun call_f (free,args) =
- ap_split T free (map (#2 o dest_Free) args)
-* in fold_bal (app sum_case) (map call_f case_list) end;
-
-* (** Generating function variables for the case definition
- Non-identifiers (e.g. infixes) get a name of the form f_op_nnn. **)
-
-* (*Treatment of a single constructor*)
-* fun add_case (((id,T,syn), name, args, prems), (opno,cases)) =
- if Syntax.is_identifier id
- then (opno,
- (Free(case_name ^ "_" ^ id, T), args) :: cases)
- else (opno+1,
- (Free(case_name ^ "_op_" ^ string_of_int opno, T), args) ::
- cases)
-
-* (*Treatment of a list of constructors, for one part*)
-* fun add_case_list (con_ty_list, (opno,case_lists)) =
- let val (opno',case_list) = foldr add_case (con_ty_list, (opno,[]))
- in (opno', case_list :: case_lists) end;
-
-* (*Treatment of all parts*)
-* val (_, case_lists) = foldr add_case_list (con_ty_lists, (1,[]));
-
-* val big_case_typ = flat (map (map (#2 o #1)) con_ty_lists) ---> (iT-->iT);
-
-* val big_rec_name = space_implode "_" rec_names;
-
-* val big_case_name = big_rec_name ^ "_case";
-
-* (*The list of all the function variables*)
-* val big_case_args = flat (map (map #1) case_lists);
-
-* val big_case_tm =
- list_comb (Const(big_case_name, big_case_typ), big_case_args);
-
-* val big_case_def = mk_defpair
- (big_case_tm, fold_bal (app sum_case) (map call_case case_lists));
-
-* (** Build the new theory **)
-
-* val const_decs =
- (big_case_name, big_case_typ, NoSyn) :: map #1 (flat con_ty_lists);
-
-* val axpairs =
- big_case_def :: flat (map mk_con_defs ((1 upto npart) ~~ con_ty_lists))
-
-* in thy |> add_consts_i const_decs |> add_defs_i axpairs end;
-****************************************************************)
-end;
-
-
-
-