(* Title: ZF/Tools/inductive_package.ML
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Fixedpoint definition module -- for Inductive/Coinductive Definitions
The functor will be instantiated for normal sums/products (inductive defs)
and non-standard sums/products (coinductive defs)
Sums are used only for mutual recursion;
Products are used only to derive "streamlined" induction rules for relations
*)
type inductive_result =
{defs : thm list, (*definitions made in thy*)
bnd_mono : thm, (*monotonicity for the lfp definition*)
dom_subset : thm, (*inclusion of recursive set in dom*)
intrs : thm list, (*introduction rules*)
elim : thm, (*case analysis theorem*)
induct : thm, (*main induction rule*)
mutual_induct : thm}; (*mutual induction rule*)
(*Functor's result signature*)
signature INDUCTIVE_PACKAGE =
sig
(*Insert definitions for the recursive sets, which
must *already* be declared as constants in parent theory!*)
val add_inductive_i: bool -> term list * term ->
((binding * term) * attribute list) list ->
thm list * thm list * thm list * thm list -> theory -> theory * inductive_result
val add_inductive: string list * string ->
((binding * string) * Token.src list) list ->
(Facts.ref * Token.src list) list * (Facts.ref * Token.src list) list *
(Facts.ref * Token.src list) list * (Facts.ref * Token.src list) list ->
theory -> theory * inductive_result
end;
(*Declares functions to add fixedpoint/constructor defs to a theory.
Recursive sets must *already* be declared as constants.*)
functor Add_inductive_def_Fun
(structure Fp: FP and Pr : PR and CP: CARTPROD and Su : SU val coind: bool)
: INDUCTIVE_PACKAGE =
struct
val co_prefix = if coind then "co" else "";
(* utils *)
(*make distinct individual variables a1, a2, a3, ..., an. *)
fun mk_frees a [] = []
| mk_frees a (T::Ts) = Free(a,T) :: mk_frees (Symbol.bump_string a) Ts;
(* add_inductive(_i) *)
(*internal version, accepting terms*)
fun add_inductive_i verbose (rec_tms, dom_sum)
raw_intr_specs (monos, con_defs, type_intrs, type_elims) thy0 =
let
val ctxt0 = Proof_Context.init_global thy0;
val intr_specs = map (apfst (apfst Binding.name_of)) raw_intr_specs;
val (intr_names, intr_tms) = split_list (map fst intr_specs);
val case_names = Rule_Cases.case_names intr_names;
(*recT and rec_params should agree for all mutually recursive components*)
val rec_hds = map head_of rec_tms;
val dummy = rec_hds |> forall (fn t => is_Const t orelse
error ("Recursive set not previously declared as constant: " ^
Syntax.string_of_term ctxt0 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 rec_base_names = map Long_Name.base_name rec_names;
val dummy = rec_base_names |> forall (fn a => Symbol_Pos.is_identifier a orelse
error ("Base name of recursive set not an identifier: " ^ a));
local (*Checking the introduction rules*)
val intr_sets = map (#2 o Ind_Syntax.rule_concl_msg thy0) intr_tms;
fun intr_ok set =
case head_of set of Const(a,recT) => member (op =) rec_names a | _ => false;
in
val dummy = intr_sets |> forall (fn t => intr_ok t orelse
error ("Conclusion of rule does not name a recursive set: " ^
Syntax.string_of_term ctxt0 t));
end;
val dummy = rec_params |> forall (fn t => is_Free t orelse
error ("Param in recursion term not a free variable: " ^
Syntax.string_of_term ctxt0 t));
(*** Construct the fixedpoint definition ***)
val mk_variant = singleton (Name.variant_list (List.foldr Misc_Legacy.add_term_names [] intr_tms));
val z' = mk_variant"z" and X' = mk_variant"X" and w' = mk_variant"w";
fun dest_tprop \<^Const_>\<open>Trueprop for P\<close> = P
| dest_tprop Q = error ("Ill-formed premise of introduction rule: " ^
Syntax.string_of_term ctxt0 Q);
(*Makes a disjunct from an introduction rule*)
fun fp_part intr = (*quantify over rule's free vars except parameters*)
let val prems = map dest_tprop (Logic.strip_imp_prems intr)
val dummy = List.app (fn rec_hd => List.app (Ind_Syntax.chk_prem rec_hd) prems) rec_hds
val exfrees = subtract (op =) rec_params (Misc_Legacy.term_frees intr)
val zeq = FOLogic.mk_eq (Free(z', \<^Type>\<open>i\<close>), #1 (Ind_Syntax.rule_concl intr))
in
fold_rev (FOLogic.mk_exists o Term.dest_Free) exfrees
(Balanced_Tree.make FOLogic.mk_conj (zeq::prems))
end;
(*The Part(A,h) terms -- compose injections to make h*)
fun mk_Part (Bound 0) = Free(X', \<^Type>\<open>i\<close>) (*no mutual rec, no Part needed*)
| mk_Part h = \<^Const>\<open>Part\<close> $ Free(X', \<^Type>\<open>i\<close>) $ Abs (w', \<^Type>\<open>i\<close>, h);
(*Access to balanced disjoint sums via injections*)
val parts = map mk_Part
(Balanced_Tree.accesses {left = fn t => Su.inl $ t, right = fn t => Su.inr $ t, init = Bound 0}
(length rec_tms));
(*replace each set by the corresponding Part(A,h)*)
val part_intrs = map (subst_free (rec_tms ~~ parts) o fp_part) intr_tms;
val fp_abs =
absfree (X', \<^Type>\<open>i\<close>)
(Ind_Syntax.mk_Collect (z', dom_sum,
Balanced_Tree.make FOLogic.mk_disj part_intrs));
val fp_rhs = Fp.oper $ dom_sum $ fp_abs
val dummy = List.app (fn rec_hd => (Logic.occs (rec_hd, fp_rhs) andalso
error "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_base_name = space_implode "_" rec_base_names;
val big_rec_name = Proof_Context.intern_const ctxt0 big_rec_base_name;
val _ =
if verbose then
writeln ((if coind then "Coind" else "Ind") ^ "uctive definition " ^ quote big_rec_name)
else ();
(*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 Misc_Legacy.mk_defpair
((big_rec_tm, fp_rhs) ::
(case parts of
[_] => [] (*no mutual recursion*)
| _ => rec_tms ~~ (*define the sets as Parts*)
map (subst_atomic [(Free (X', \<^Type>\<open>i\<close>), big_rec_tm)]) parts));
(*tracing: print the fixedpoint definition*)
val dummy = if !Ind_Syntax.trace then
writeln (cat_lines (map (Syntax.string_of_term ctxt0 o #2) axpairs))
else ()
(*add definitions of the inductive sets*)
val (_, thy1) =
thy0
|> Sign.add_path big_rec_base_name
|> Global_Theory.add_defs false (map (Thm.no_attributes o apfst Binding.name) axpairs);
(*fetch fp definitions from the theory*)
val big_rec_def::part_rec_defs =
map (Misc_Legacy.get_def thy1)
(case rec_names of [_] => rec_names
| _ => big_rec_base_name::rec_names);
(********)
val dummy = writeln " Proving monotonicity...";
val bnd_mono0 =
Goal.prove_global thy1 [] [] (\<^make_judgment> (Fp.bnd_mono $ dom_sum $ fp_abs))
(fn {context = ctxt, ...} => EVERY
[resolve_tac ctxt [@{thm Collect_subset} RS @{thm bnd_monoI}] 1,
REPEAT (ares_tac ctxt (@{thms basic_monos} @ monos) 1)]);
val dom_subset0 = Drule.export_without_context (big_rec_def RS Fp.subs);
val ([bnd_mono, dom_subset], thy2) = thy1
|> Global_Theory.add_thms
[((Binding.name "bnd_mono", bnd_mono0), []),
((Binding.name "dom_subset", dom_subset0), [])];
val unfold = Drule.export_without_context ([big_rec_def, bnd_mono] MRS Fp.Tarski);
(********)
val dummy = writeln " Proving the introduction rules...";
(*Mutual recursion? Helps to derive subset rules for the
individual sets.*)
val Part_trans =
case rec_names of
[_] => asm_rl
| _ => Drule.export_without_context (@{thm Part_subset} RS @{thm subset_trans});
(*To type-check recursive occurrences of the inductive sets, possibly
enclosed in some monotonic operator M.*)
val rec_typechecks =
[dom_subset] RL (asm_rl :: ([Part_trans] RL monos))
RL [@{thm subsetD}];
(*Type-checking is hardest aspect of proof;
disjIn selects the correct disjunct after unfolding*)
fun intro_tacsf disjIn ctxt =
[DETERM (stac ctxt unfold 1),
REPEAT (resolve_tac ctxt [@{thm Part_eqI}, @{thm CollectI}] 1),
(*Now 2-3 subgoals: typechecking, the disjunction, perhaps equality.*)
resolve_tac ctxt [disjIn] 2,
(*Not ares_tac, since refl must be tried before equality assumptions;
backtracking may occur if the premises have extra variables!*)
DEPTH_SOLVE_1 (resolve_tac ctxt [@{thm refl}, @{thm exI}, @{thm conjI}] 2 APPEND assume_tac ctxt 2),
(*Now solve the equations like Tcons(a,f) = Inl(?b4)*)
rewrite_goals_tac ctxt con_defs,
REPEAT (resolve_tac ctxt @{thms refl} 2),
(*Typechecking; this can fail*)
if !Ind_Syntax.trace then print_tac ctxt "The type-checking subgoal:"
else all_tac,
REPEAT (FIRSTGOAL (dresolve_tac ctxt rec_typechecks
ORELSE' eresolve_tac ctxt (asm_rl :: @{thm PartE} :: @{thm SigmaE2} ::
type_elims)
ORELSE' hyp_subst_tac ctxt)),
if !Ind_Syntax.trace then print_tac ctxt "The subgoal after monos, type_elims:"
else all_tac,
DEPTH_SOLVE (swap_res_tac ctxt (@{thm SigmaI} :: @{thm subsetI} :: type_intrs) 1)];
(*combines disjI1 and disjI2 to get the corresponding nested disjunct...*)
val mk_disj_rls = Balanced_Tree.accesses
{left = fn rl => rl RS @{thm disjI1},
right = fn rl => rl RS @{thm disjI2},
init = @{thm asm_rl}};
val intrs0 =
(intr_tms, map intro_tacsf (mk_disj_rls (length intr_tms)))
|> ListPair.map (fn (t, tacs) =>
Goal.prove_global thy2 [] [] t
(fn {context = ctxt, ...} => EVERY (rewrite_goals_tac ctxt part_rec_defs :: tacs ctxt)));
val ([intrs], thy3) = thy2
|> Global_Theory.add_thmss [((Binding.name "intros", intrs0), [])];
val ctxt3 = Proof_Context.init_global thy3;
(********)
val dummy = writeln " Proving the elimination rule...";
(*Breaks down logical connectives in the monotonic function*)
fun basic_elim_tac ctxt =
REPEAT (SOMEGOAL (eresolve_tac ctxt (Ind_Syntax.elim_rls @ Su.free_SEs)
ORELSE' bound_hyp_subst_tac ctxt))
THEN prune_params_tac ctxt
(*Mutual recursion: collapse references to Part(D,h)*)
THEN (PRIMITIVE (fold_rule ctxt part_rec_defs));
(*Elimination*)
val (elim, thy4) = thy3
|> Global_Theory.add_thm
((Binding.name "elim",
rule_by_tactic ctxt3 (basic_elim_tac ctxt3) (unfold RS Ind_Syntax.equals_CollectD)), []);
val ctxt4 = Proof_Context.init_global thy4;
(*Applies freeness of the given constructors, which *must* be unfolded by
the given defs. Cannot simply use the local con_defs because
con_defs=[] for inference systems.
Proposition A should have the form t:Si where Si is an inductive set*)
fun make_cases ctxt A =
rule_by_tactic ctxt
(basic_elim_tac ctxt THEN ALLGOALS (asm_full_simp_tac ctxt) THEN basic_elim_tac ctxt)
(Thm.assume A RS elim)
|> Drule.export_without_context_open;
fun induction_rules raw_induct =
let
val dummy = writeln " Proving the induction rule...";
(*** Prove the main induction rule ***)
val pred_name = "P"; (*name for predicate variables*)
(*Used to make induction rules;
ind_alist = [(rec_tm1,pred1),...] associates predicates with rec ops
prem is a premise of an intr rule*)
fun add_induct_prem ind_alist (prem as \<^Const_>\<open>Trueprop for \<^Const_>\<open>mem for t X\<close>\<close>, iprems) =
(case AList.lookup (op aconv) ind_alist X of
SOME pred => prem :: \<^make_judgment> (pred $ t) :: iprems
| NONE => (*possibly membership in M(rec_tm), for M monotone*)
let fun mk_sb (rec_tm,pred) =
(rec_tm, \<^Const>\<open>Collect\<close> $ rec_tm $ pred)
in subst_free (map mk_sb ind_alist) prem :: iprems end)
| add_induct_prem ind_alist (prem,iprems) = prem :: iprems;
(*Make a premise of the induction rule.*)
fun induct_prem ind_alist intr =
let val xs = subtract (op =) rec_params (Misc_Legacy.term_frees intr)
val iprems = List.foldr (add_induct_prem ind_alist) []
(Logic.strip_imp_prems intr)
val (t,X) = Ind_Syntax.rule_concl intr
val (SOME pred) = AList.lookup (op aconv) ind_alist X
val concl = \<^make_judgment> (pred $ t)
in fold_rev Logic.all xs (Logic.list_implies (iprems,concl)) end
handle Bind => error"Recursion term not found in conclusion";
(*Minimizes backtracking by delivering the correct premise to each goal.
Intro rules with extra Vars in premises still cause some backtracking *)
fun ind_tac _ [] 0 = all_tac
| ind_tac ctxt (prem::prems) i =
DEPTH_SOLVE_1 (ares_tac ctxt [prem, @{thm refl}] i) THEN ind_tac ctxt prems (i-1);
val pred = Free(pred_name, \<^Type>\<open>i\<close> --> \<^Type>\<open>o\<close>);
val ind_prems = map (induct_prem (map (rpair pred) rec_tms))
intr_tms;
val dummy =
if ! Ind_Syntax.trace then
writeln (cat_lines
(["ind_prems:"] @ map (Syntax.string_of_term ctxt4) ind_prems @
["raw_induct:", Thm.string_of_thm ctxt4 raw_induct]))
else ();
(*We use a MINIMAL simpset. Even FOL_ss contains too many simpules.
If the premises get simplified, then the proofs could fail.*)
val min_ss =
(empty_simpset ctxt4
|> Simplifier.set_mksimps (fn ctxt => map mk_eq o ZF_atomize o Variable.gen_all ctxt))
setSolver (mk_solver "minimal"
(fn ctxt => resolve_tac ctxt (triv_rls @ Simplifier.prems_of ctxt)
ORELSE' assume_tac ctxt
ORELSE' eresolve_tac ctxt @{thms FalseE}));
val quant_induct =
Goal.prove_global thy4 [] ind_prems
(\<^make_judgment> (Ind_Syntax.mk_all_imp (big_rec_tm, pred)))
(fn {context = ctxt, prems} => EVERY
[rewrite_goals_tac ctxt part_rec_defs,
resolve_tac ctxt [@{thm impI} RS @{thm allI}] 1,
DETERM (eresolve_tac ctxt [raw_induct] 1),
(*Push Part inside Collect*)
full_simp_tac (min_ss addsimps [@{thm Part_Collect}]) 1,
(*This CollectE and disjE separates out the introduction rules*)
REPEAT (FIRSTGOAL (eresolve_tac ctxt [@{thm CollectE}, @{thm disjE}])),
(*Now break down the individual cases. No disjE here in case
some premise involves disjunction.*)
REPEAT (FIRSTGOAL (eresolve_tac ctxt [@{thm CollectE}, @{thm exE}, @{thm conjE}]
ORELSE' (bound_hyp_subst_tac ctxt))),
ind_tac ctxt (rev (map (rewrite_rule ctxt part_rec_defs) prems)) (length prems)]);
val dummy =
if ! Ind_Syntax.trace then
writeln ("quant_induct:\n" ^ Thm.string_of_thm ctxt4 quant_induct)
else ();
(*** Prove the simultaneous induction rule ***)
(*Make distinct predicates for each inductive set*)
(*The components of the element type, several if it is a product*)
val elem_type = CP.pseudo_type dom_sum;
val elem_factors = CP.factors elem_type;
val elem_frees = mk_frees "za" elem_factors;
val elem_tuple = CP.mk_tuple Pr.pair elem_type elem_frees;
(*Given a recursive set and its domain, return the "fsplit" predicate
and a conclusion for the simultaneous induction rule.
NOTE. This will not work for mutually recursive predicates. Previously
a summand 'domt' was also an argument, but this required the domain of
mutual recursion to invariably be a disjoint sum.*)
fun mk_predpair rec_tm =
let val rec_name = (#1 o dest_Const o head_of) rec_tm
val pfree = Free(pred_name ^ "_" ^ Long_Name.base_name rec_name,
elem_factors ---> \<^Type>\<open>o\<close>)
val qconcl =
fold_rev (FOLogic.mk_all o Term.dest_Free) elem_frees
\<^Const>\<open>imp for \<^Const>\<open>mem for elem_tuple rec_tm\<close> \<open>list_comb (pfree, elem_frees)\<close>\<close>
in (CP.ap_split elem_type \<^Type>\<open>o\<close> pfree,
qconcl)
end;
val (preds,qconcls) = split_list (map mk_predpair rec_tms);
(*Used to form simultaneous induction lemma*)
fun mk_rec_imp (rec_tm,pred) =
\<^Const>\<open>imp for \<^Const>\<open>mem for \<open>Bound 0\<close> rec_tm\<close> \<open>pred $ Bound 0\<close>\<close>;
(*To instantiate the main induction rule*)
val induct_concl =
\<^make_judgment>
(Ind_Syntax.mk_all_imp
(big_rec_tm,
Abs("z", \<^Type>\<open>i\<close>,
Balanced_Tree.make FOLogic.mk_conj
(ListPair.map mk_rec_imp (rec_tms, preds)))))
and mutual_induct_concl =
\<^make_judgment> (Balanced_Tree.make FOLogic.mk_conj qconcls);
val dummy = if !Ind_Syntax.trace then
(writeln ("induct_concl = " ^
Syntax.string_of_term ctxt4 induct_concl);
writeln ("mutual_induct_concl = " ^
Syntax.string_of_term ctxt4 mutual_induct_concl))
else ();
fun lemma_tac ctxt =
FIRST' [eresolve_tac ctxt [@{thm asm_rl}, @{thm conjE}, @{thm PartE}, @{thm mp}],
resolve_tac ctxt [@{thm allI}, @{thm impI}, @{thm conjI}, @{thm Part_eqI}],
dresolve_tac ctxt [@{thm spec}, @{thm mp}, Pr.fsplitD]];
val need_mutual = length rec_names > 1;
val lemma = (*makes the link between the two induction rules*)
if need_mutual then
(writeln " Proving the mutual induction rule...";
Goal.prove_global thy4 [] []
(Logic.mk_implies (induct_concl, mutual_induct_concl))
(fn {context = ctxt, ...} => EVERY
[rewrite_goals_tac ctxt part_rec_defs,
REPEAT (rewrite_goals_tac ctxt [Pr.split_eq] THEN lemma_tac ctxt 1)]))
else (writeln " [ No mutual induction rule needed ]"; @{thm TrueI});
val dummy =
if ! Ind_Syntax.trace then
writeln ("lemma: " ^ Thm.string_of_thm ctxt4 lemma)
else ();
(*Mutual induction follows by freeness of Inl/Inr.*)
(*Simplification largely reduces the mutual induction rule to the
standard rule*)
val mut_ss =
min_ss addsimps [Su.distinct, Su.distinct', Su.inl_iff, Su.inr_iff];
val all_defs = con_defs @ part_rec_defs;
(*Removes Collects caused by M-operators in the intro rules. It is very
hard to simplify
list({v: tf. (v : t --> P_t(v)) & (v : f --> P_f(v))})
where t==Part(tf,Inl) and f==Part(tf,Inr) to list({v: tf. P_t(v)}).
Instead the following rules extract the relevant conjunct.
*)
val cmonos = [@{thm subset_refl} RS @{thm Collect_mono}] RL monos
RLN (2,[@{thm rev_subsetD}]);
(*Minimizes backtracking by delivering the correct premise to each goal*)
fun mutual_ind_tac _ [] 0 = all_tac
| mutual_ind_tac ctxt (prem::prems) i =
DETERM
(SELECT_GOAL
(
(*Simplify the assumptions and goal by unfolding Part and
using freeness of the Sum constructors; proves all but one
conjunct by contradiction*)
rewrite_goals_tac ctxt all_defs THEN
simp_tac (mut_ss addsimps [@{thm Part_iff}]) 1 THEN
IF_UNSOLVED (*simp_tac may have finished it off!*)
((*simplify assumptions*)
(*some risk of excessive simplification here -- might have
to identify the bare minimum set of rewrites*)
full_simp_tac
(mut_ss addsimps @{thms conj_simps} @ @{thms imp_simps} @ @{thms quant_simps}) 1
THEN
(*unpackage and use "prem" in the corresponding place*)
REPEAT (resolve_tac ctxt @{thms impI} 1) THEN
resolve_tac ctxt [rewrite_rule ctxt all_defs prem] 1 THEN
(*prem must not be REPEATed below: could loop!*)
DEPTH_SOLVE (FIRSTGOAL (ares_tac ctxt [@{thm impI}] ORELSE'
eresolve_tac ctxt (@{thm conjE} :: @{thm mp} :: cmonos))))
) i)
THEN mutual_ind_tac ctxt prems (i-1);
val mutual_induct_fsplit =
if need_mutual then
Goal.prove_global thy4 [] (map (induct_prem (rec_tms~~preds)) intr_tms)
mutual_induct_concl
(fn {context = ctxt, prems} => EVERY
[resolve_tac ctxt [quant_induct RS lemma] 1,
mutual_ind_tac ctxt (rev prems) (length prems)])
else @{thm TrueI};
(** Uncurrying the predicate in the ordinary induction rule **)
(*instantiate the variable to a tuple, if it is non-trivial, in order to
allow the predicate to be "opened up".
The name "x.1" comes from the "RS spec" !*)
val inst =
case elem_frees of [_] => I
| _ => Drule.instantiate_normalize (TVars.empty,
Vars.make [(\<^var>\<open>?x1::i\<close>, Thm.global_cterm_of thy4 elem_tuple)]);
(*strip quantifier and the implication*)
val induct0 = inst (quant_induct RS @{thm spec} RSN (2, @{thm rev_mp}));
val \<^Const_>\<open>Trueprop for \<open>pred_var $ _\<close>\<close> = Thm.concl_of induct0
val induct0 =
CP.split_rule_var ctxt4
(pred_var, elem_type --> \<^Type>\<open>o\<close>, induct0)
|> Drule.export_without_context
and mutual_induct = CP.remove_split ctxt4 mutual_induct_fsplit
val ([induct, mutual_induct], thy5) =
thy4
|> Global_Theory.add_thms [((Binding.name (co_prefix ^ "induct"), induct0),
[case_names, Induct.induct_pred big_rec_name]),
((Binding.name "mutual_induct", mutual_induct), [case_names])];
in ((induct, mutual_induct), thy5)
end; (*of induction_rules*)
val raw_induct = Drule.export_without_context ([big_rec_def, bnd_mono] MRS Fp.induct)
val ((induct, mutual_induct), thy5) =
if not coind then induction_rules raw_induct
else
thy4
|> Global_Theory.add_thms [((Binding.name (co_prefix ^ "induct"), raw_induct), [])]
|> apfst (hd #> pair @{thm TrueI});
val (([cases], [defs]), thy6) =
thy5
|> IndCases.declare big_rec_name make_cases
|> Global_Theory.add_thms
[((Binding.name "cases", elim), [case_names, Induct.cases_pred big_rec_name])]
||>> (Global_Theory.add_thmss o map Thm.no_attributes)
[(Binding.name "defs", big_rec_def :: part_rec_defs)];
val (named_intrs, thy7) =
thy6
|> Global_Theory.add_thms ((map Binding.name intr_names ~~ intrs) ~~ map #2 intr_specs)
||> Sign.parent_path;
in
(thy7,
{defs = defs,
bnd_mono = bnd_mono,
dom_subset = dom_subset,
intrs = named_intrs,
elim = cases,
induct = induct,
mutual_induct = mutual_induct})
end;
(*source version*)
fun add_inductive (srec_tms, sdom_sum) intr_srcs
(raw_monos, raw_con_defs, raw_type_intrs, raw_type_elims) thy =
let
val ctxt = Proof_Context.init_global thy;
val read_terms = map (Syntax.parse_term ctxt #> Type.constraint \<^Type>\<open>i\<close>)
#> Syntax.check_terms ctxt;
val intr_atts = map (map (Attrib.attribute_cmd ctxt) o snd) intr_srcs;
val sintrs = map fst intr_srcs ~~ intr_atts;
val rec_tms = read_terms srec_tms;
val dom_sum = singleton read_terms sdom_sum;
val intr_tms = Syntax.read_props ctxt (map (snd o fst) sintrs);
val intr_specs = (map (fst o fst) sintrs ~~ intr_tms) ~~ map snd sintrs;
val monos = Attrib.eval_thms ctxt raw_monos;
val con_defs = Attrib.eval_thms ctxt raw_con_defs;
val type_intrs = Attrib.eval_thms ctxt raw_type_intrs;
val type_elims = Attrib.eval_thms ctxt raw_type_elims;
in
thy
|> add_inductive_i true (rec_tms, dom_sum) intr_specs (monos, con_defs, type_intrs, type_elims)
end;
(* outer syntax *)
fun mk_ind (((((doms, intrs), monos), con_defs), type_intrs), type_elims) =
#1 o add_inductive doms (map (fn ((x, y), z) => ((x, z), y)) intrs)
(monos, con_defs, type_intrs, type_elims);
val ind_decl =
(\<^keyword>\<open>domains\<close> |-- Parse.!!! (Parse.enum1 "+" Parse.term --
((\<^keyword>\<open>\<subseteq>\<close> || \<^keyword>\<open><=\<close>) |-- Parse.term))) --
(\<^keyword>\<open>intros\<close> |--
Parse.!!! (Scan.repeat1 (Parse_Spec.opt_thm_name ":" -- Parse.prop))) --
Scan.optional (\<^keyword>\<open>monos\<close> |-- Parse.!!! Parse.thms1) [] --
Scan.optional (\<^keyword>\<open>con_defs\<close> |-- Parse.!!! Parse.thms1) [] --
Scan.optional (\<^keyword>\<open>type_intros\<close> |-- Parse.!!! Parse.thms1) [] --
Scan.optional (\<^keyword>\<open>type_elims\<close> |-- Parse.!!! Parse.thms1) []
>> (Toplevel.theory o mk_ind);
val _ =
Outer_Syntax.command
(if coind then \<^command_keyword>\<open>coinductive\<close> else \<^command_keyword>\<open>inductive\<close>)
("define " ^ co_prefix ^ "inductive sets") ind_decl;
end;