author | wenzelm |
Thu, 23 Oct 2008 16:07:03 +0200 | |
changeset 28678 | d93980a6c3cb |
parent 28083 | 103d9282a946 |
child 28839 | 32d498cf7595 |
permissions | -rw-r--r-- |
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(* Title: ZF/Tools/inductive_package.ML |
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ID: $Id$ |
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Copyright 1994 University of Cambridge |
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Fixedpoint definition module -- for Inductive/Coinductive Definitions |
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The functor will be instantiated for normal sums/products (inductive defs) |
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and non-standard sums/products (coinductive defs) |
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Sums are used only for mutual recursion; |
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Products are used only to derive "streamlined" induction rules for relations |
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*) |
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type inductive_result = |
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{defs : thm list, (*definitions made in thy*) |
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bnd_mono : thm, (*monotonicity for the lfp definition*) |
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dom_subset : thm, (*inclusion of recursive set in dom*) |
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intrs : thm list, (*introduction rules*) |
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elim : thm, (*case analysis theorem*) |
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mk_cases : string -> thm, (*generates case theorems*) |
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induct : thm, (*main induction rule*) |
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mutual_induct : thm}; (*mutual induction rule*) |
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(*Functor's result signature*) |
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signature INDUCTIVE_PACKAGE = |
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sig |
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(*Insert definitions for the recursive sets, which |
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must *already* be declared as constants in parent theory!*) |
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val add_inductive_i: bool -> term list * term -> |
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((Name.binding * term) * attribute list) list -> |
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thm list * thm list * thm list * thm list -> theory -> theory * inductive_result |
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val add_inductive: string list * string -> |
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((Name.binding * string) * Attrib.src list) list -> |
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(Facts.ref * Attrib.src list) list * (Facts.ref * Attrib.src list) list * |
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(Facts.ref * Attrib.src list) list * (Facts.ref * Attrib.src list) list -> |
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theory -> theory * inductive_result |
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end; |
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(*Declares functions to add fixedpoint/constructor defs to a theory. |
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Recursive sets must *already* be declared as constants.*) |
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functor Add_inductive_def_Fun |
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(structure Fp: FP and Pr : PR and CP: CARTPROD and Su : SU val coind: bool) |
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: INDUCTIVE_PACKAGE = |
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struct |
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open Ind_Syntax; |
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val co_prefix = if coind then "co" else ""; |
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(* utils *) |
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(*make distinct individual variables a1, a2, a3, ..., an. *) |
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fun mk_frees a [] = [] |
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| mk_frees a (T::Ts) = Free(a,T) :: mk_frees (Symbol.bump_string a) Ts; |
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(* add_inductive(_i) *) |
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(*internal version, accepting terms*) |
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fun add_inductive_i verbose (rec_tms, dom_sum) |
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raw_intr_specs (monos, con_defs, type_intrs, type_elims) thy = |
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let |
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val _ = Theory.requires thy "Inductive_ZF" "(co)inductive definitions"; |
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val ctxt = ProofContext.init thy; |
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val intr_specs = map (apfst (apfst Name.name_of)) raw_intr_specs; |
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val (intr_names, intr_tms) = split_list (map fst intr_specs); |
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val case_names = RuleCases.case_names intr_names; |
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(*recT and rec_params should agree for all mutually recursive components*) |
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val rec_hds = map head_of rec_tms; |
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val dummy = assert_all is_Const rec_hds |
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(fn t => "Recursive set not previously declared as constant: " ^ |
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Syntax.string_of_term ctxt t); |
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(*Now we know they are all Consts, so get their names, type and params*) |
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val rec_names = map (#1 o dest_Const) rec_hds |
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and (Const(_,recT),rec_params) = strip_comb (hd rec_tms); |
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val rec_base_names = map Sign.base_name rec_names; |
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val dummy = assert_all Syntax.is_identifier rec_base_names |
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(fn a => "Base name of recursive set not an identifier: " ^ a); |
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local (*Checking the introduction rules*) |
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val intr_sets = map (#2 o rule_concl_msg thy) intr_tms; |
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fun intr_ok set = |
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case head_of set of Const(a,recT) => a mem rec_names | _ => false; |
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in |
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val dummy = assert_all intr_ok intr_sets |
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(fn t => "Conclusion of rule does not name a recursive set: " ^ |
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Syntax.string_of_term ctxt t); |
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end; |
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val dummy = assert_all is_Free rec_params |
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(fn t => "Param in recursion term not a free variable: " ^ |
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Syntax.string_of_term ctxt t); |
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(*** Construct the fixedpoint definition ***) |
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val mk_variant = Name.variant (foldr add_term_names [] intr_tms); |
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val z' = mk_variant"z" and X' = mk_variant"X" and w' = mk_variant"w"; |
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fun dest_tprop (Const("Trueprop",_) $ P) = P |
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| dest_tprop Q = error ("Ill-formed premise of introduction rule: " ^ |
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Syntax.string_of_term ctxt Q); |
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(*Makes a disjunct from an introduction rule*) |
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fun fp_part intr = (*quantify over rule's free vars except parameters*) |
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let val prems = map dest_tprop (Logic.strip_imp_prems intr) |
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val dummy = List.app (fn rec_hd => List.app (chk_prem rec_hd) prems) rec_hds |
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val exfrees = term_frees intr \\ rec_params |
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val zeq = FOLogic.mk_eq (Free(z',iT), #1 (rule_concl intr)) |
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in foldr FOLogic.mk_exists |
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(BalancedTree.make FOLogic.mk_conj (zeq::prems)) exfrees |
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end; |
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(*The Part(A,h) terms -- compose injections to make h*) |
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fun mk_Part (Bound 0) = Free(X',iT) (*no mutual rec, no Part needed*) |
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| mk_Part h = @{const Part} $ Free(X',iT) $ Abs(w',iT,h); |
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(*Access to balanced disjoint sums via injections*) |
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val parts = map mk_Part |
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(BalancedTree.accesses {left = fn t => Su.inl $ t, right = fn t => Su.inr $ t, init = Bound 0} |
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(length rec_tms)); |
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(*replace each set by the corresponding Part(A,h)*) |
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val part_intrs = map (subst_free (rec_tms ~~ parts) o fp_part) intr_tms; |
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val fp_abs = absfree(X', iT, |
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mk_Collect(z', dom_sum, |
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BalancedTree.make FOLogic.mk_disj part_intrs)); |
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val fp_rhs = Fp.oper $ dom_sum $ fp_abs |
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val dummy = List.app (fn rec_hd => (Logic.occs (rec_hd, fp_rhs) andalso |
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error "Illegal occurrence of recursion operator"; ())) |
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rec_hds; |
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(*** Make the new theory ***) |
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(*A key definition: |
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If no mutual recursion then it equals the one recursive set. |
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If mutual recursion then it differs from all the recursive sets. *) |
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val big_rec_base_name = space_implode "_" rec_base_names; |
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val big_rec_name = Sign.intern_const thy big_rec_base_name; |
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val _ = |
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if verbose then |
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writeln ((if coind then "Coind" else "Ind") ^ "uctive definition " ^ quote big_rec_name) |
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else (); |
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(*Big_rec... is the union of the mutually recursive sets*) |
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val big_rec_tm = list_comb(Const(big_rec_name,recT), rec_params); |
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(*The individual sets must already be declared*) |
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val axpairs = map PrimitiveDefs.mk_defpair |
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((big_rec_tm, fp_rhs) :: |
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(case parts of |
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[_] => [] (*no mutual recursion*) |
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| _ => rec_tms ~~ (*define the sets as Parts*) |
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map (subst_atomic [(Free(X',iT),big_rec_tm)]) parts)); |
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(*tracing: print the fixedpoint definition*) |
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val dummy = if !Ind_Syntax.trace then |
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writeln (cat_lines (map (Syntax.string_of_term ctxt o #2) axpairs)) |
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else () |
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(*add definitions of the inductive sets*) |
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val (_, thy1) = |
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thy |
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|> Sign.add_path big_rec_base_name |
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|> PureThy.add_defs false (map Thm.no_attributes axpairs); |
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val ctxt1 = ProofContext.init thy1; |
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(*fetch fp definitions from the theory*) |
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val big_rec_def::part_rec_defs = |
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map (Thm.get_def thy1) |
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(case rec_names of [_] => rec_names |
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| _ => big_rec_base_name::rec_names); |
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(********) |
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val dummy = writeln " Proving monotonicity..."; |
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val bnd_mono = |
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Goal.prove_global thy1 [] [] (FOLogic.mk_Trueprop (Fp.bnd_mono $ dom_sum $ fp_abs)) |
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(fn _ => EVERY |
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[rtac (@{thm Collect_subset} RS @{thm bnd_monoI}) 1, |
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REPEAT (ares_tac (@{thms basic_monos} @ monos) 1)]); |
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val dom_subset = standard (big_rec_def RS Fp.subs); |
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val unfold = standard ([big_rec_def, bnd_mono] MRS Fp.Tarski); |
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(********) |
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val dummy = writeln " Proving the introduction rules..."; |
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(*Mutual recursion? Helps to derive subset rules for the |
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individual sets.*) |
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val Part_trans = |
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case rec_names of |
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[_] => asm_rl |
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| _ => standard (@{thm Part_subset} RS @{thm subset_trans}); |
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(*To type-check recursive occurrences of the inductive sets, possibly |
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enclosed in some monotonic operator M.*) |
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val rec_typechecks = |
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[dom_subset] RL (asm_rl :: ([Part_trans] RL monos)) |
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RL [@{thm subsetD}]; |
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(*Type-checking is hardest aspect of proof; |
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disjIn selects the correct disjunct after unfolding*) |
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fun intro_tacsf disjIn = |
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[DETERM (stac unfold 1), |
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REPEAT (resolve_tac [@{thm Part_eqI}, @{thm CollectI}] 1), |
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(*Now 2-3 subgoals: typechecking, the disjunction, perhaps equality.*) |
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rtac disjIn 2, |
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(*Not ares_tac, since refl must be tried before equality assumptions; |
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backtracking may occur if the premises have extra variables!*) |
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DEPTH_SOLVE_1 (resolve_tac [refl,exI,conjI] 2 APPEND assume_tac 2), |
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(*Now solve the equations like Tcons(a,f) = Inl(?b4)*) |
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rewrite_goals_tac con_defs, |
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REPEAT (rtac @{thm refl} 2), |
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(*Typechecking; this can fail*) |
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if !Ind_Syntax.trace then print_tac "The type-checking subgoal:" |
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else all_tac, |
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REPEAT (FIRSTGOAL ( dresolve_tac rec_typechecks |
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ORELSE' eresolve_tac (asm_rl::@{thm PartE}::@{thm SigmaE2}:: |
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type_elims) |
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ORELSE' hyp_subst_tac)), |
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if !Ind_Syntax.trace then print_tac "The subgoal after monos, type_elims:" |
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else all_tac, |
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DEPTH_SOLVE (swap_res_tac (@{thm SigmaI}::@{thm subsetI}::type_intrs) 1)]; |
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(*combines disjI1 and disjI2 to get the corresponding nested disjunct...*) |
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val mk_disj_rls = BalancedTree.accesses |
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{left = fn rl => rl RS @{thm disjI1}, |
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right = fn rl => rl RS @{thm disjI2}, |
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init = @{thm asm_rl}}; |
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val intrs = |
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(intr_tms, map intro_tacsf (mk_disj_rls (length intr_tms))) |
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|> ListPair.map (fn (t, tacs) => |
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Goal.prove_global thy1 [] [] t |
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(fn _ => EVERY (rewrite_goals_tac part_rec_defs :: tacs))) |
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handle MetaSimplifier.SIMPLIFIER (msg, thm) => (Display.print_thm thm; error msg); |
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(********) |
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val dummy = writeln " Proving the elimination rule..."; |
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(*Breaks down logical connectives in the monotonic function*) |
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val basic_elim_tac = |
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REPEAT (SOMEGOAL (eresolve_tac (Ind_Syntax.elim_rls @ Su.free_SEs) |
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ORELSE' bound_hyp_subst_tac)) |
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THEN prune_params_tac |
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(*Mutual recursion: collapse references to Part(D,h)*) |
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THEN fold_tac part_rec_defs; |
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(*Elimination*) |
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val elim = rule_by_tactic basic_elim_tac |
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269 |
(unfold RS Ind_Syntax.equals_CollectD) |
6051 | 270 |
|
271 |
(*Applies freeness of the given constructors, which *must* be unfolded by |
|
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272 |
the given defs. Cannot simply use the local con_defs because |
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273 |
con_defs=[] for inference systems. |
12175 | 274 |
Proposition A should have the form t:Si where Si is an inductive set*) |
275 |
fun make_cases ss A = |
|
276 |
rule_by_tactic |
|
277 |
(basic_elim_tac THEN ALLGOALS (asm_full_simp_tac ss) THEN basic_elim_tac) |
|
278 |
(Thm.assume A RS elim) |
|
279 |
|> Drule.standard'; |
|
280 |
fun mk_cases a = make_cases (*delayed evaluation of body!*) |
|
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281 |
(simpset ()) |
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282 |
let val thy = Thm.theory_of_thm elim in cterm_of thy (Syntax.read_prop_global thy a) end; |
6051 | 283 |
|
284 |
fun induction_rules raw_induct thy = |
|
285 |
let |
|
286 |
val dummy = writeln " Proving the induction rule..."; |
|
287 |
||
288 |
(*** Prove the main induction rule ***) |
|
289 |
||
290 |
val pred_name = "P"; (*name for predicate variables*) |
|
291 |
||
292 |
(*Used to make induction rules; |
|
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293 |
ind_alist = [(rec_tm1,pred1),...] associates predicates with rec ops |
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294 |
prem is a premise of an intr rule*) |
26189 | 295 |
fun add_induct_prem ind_alist (prem as Const (@{const_name Trueprop}, _) $ |
296 |
(Const (@{const_name mem}, _) $ t $ X), iprems) = |
|
17314 | 297 |
(case AList.lookup (op aconv) ind_alist X of |
15531 | 298 |
SOME pred => prem :: FOLogic.mk_Trueprop (pred $ t) :: iprems |
299 |
| NONE => (*possibly membership in M(rec_tm), for M monotone*) |
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300 |
let fun mk_sb (rec_tm,pred) = |
26189 | 301 |
(rec_tm, @{const Collect} $ rec_tm $ pred) |
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302 |
in subst_free (map mk_sb ind_alist) prem :: iprems end) |
6051 | 303 |
| add_induct_prem ind_alist (prem,iprems) = prem :: iprems; |
304 |
||
305 |
(*Make a premise of the induction rule.*) |
|
306 |
fun induct_prem ind_alist intr = |
|
307 |
let val quantfrees = map dest_Free (term_frees intr \\ rec_params) |
|
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308 |
val iprems = foldr (add_induct_prem ind_alist) [] |
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|
309 |
(Logic.strip_imp_prems intr) |
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310 |
val (t,X) = Ind_Syntax.rule_concl intr |
17314 | 311 |
val (SOME pred) = AList.lookup (op aconv) ind_alist X |
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312 |
val concl = FOLogic.mk_Trueprop (pred $ t) |
6051 | 313 |
in list_all_free (quantfrees, Logic.list_implies (iprems,concl)) end |
314 |
handle Bind => error"Recursion term not found in conclusion"; |
|
315 |
||
316 |
(*Minimizes backtracking by delivering the correct premise to each goal. |
|
317 |
Intro rules with extra Vars in premises still cause some backtracking *) |
|
318 |
fun ind_tac [] 0 = all_tac |
|
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319 |
| ind_tac(prem::prems) i = |
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320 |
DEPTH_SOLVE_1 (ares_tac [prem, refl] i) THEN ind_tac prems (i-1); |
6051 | 321 |
|
322 |
val pred = Free(pred_name, Ind_Syntax.iT --> FOLogic.oT); |
|
323 |
||
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324 |
val ind_prems = map (induct_prem (map (rpair pred) rec_tms)) |
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325 |
intr_tms; |
6051 | 326 |
|
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|
327 |
val dummy = if !Ind_Syntax.trace then |
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|
328 |
(writeln "ind_prems = "; |
26189 | 329 |
List.app (writeln o Syntax.string_of_term ctxt1) ind_prems; |
26928 | 330 |
writeln "raw_induct = "; Display.print_thm raw_induct) |
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331 |
else (); |
6051 | 332 |
|
333 |
||
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334 |
(*We use a MINIMAL simpset. Even FOL_ss contains too many simpules. |
6051 | 335 |
If the premises get simplified, then the proofs could fail.*) |
17892 | 336 |
val min_ss = Simplifier.theory_context thy empty_ss |
12725 | 337 |
setmksimps (map mk_eq o ZF_atomize o gen_all) |
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|
338 |
setSolver (mk_solver "minimal" |
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|
339 |
(fn prems => resolve_tac (triv_rls@prems) |
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340 |
ORELSE' assume_tac |
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341 |
ORELSE' etac FalseE)); |
6051 | 342 |
|
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|
343 |
val quant_induct = |
20342 | 344 |
Goal.prove_global thy1 [] ind_prems |
17985 | 345 |
(FOLogic.mk_Trueprop (Ind_Syntax.mk_all_imp (big_rec_tm, pred))) |
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|
346 |
(fn {prems, ...} => EVERY |
17985 | 347 |
[rewrite_goals_tac part_rec_defs, |
26189 | 348 |
rtac (@{thm impI} RS @{thm allI}) 1, |
17985 | 349 |
DETERM (etac raw_induct 1), |
350 |
(*Push Part inside Collect*) |
|
24893 | 351 |
full_simp_tac (min_ss addsimps [@{thm Part_Collect}]) 1, |
17985 | 352 |
(*This CollectE and disjE separates out the introduction rules*) |
26189 | 353 |
REPEAT (FIRSTGOAL (eresolve_tac [@{thm CollectE}, @{thm disjE}])), |
17985 | 354 |
(*Now break down the individual cases. No disjE here in case |
355 |
some premise involves disjunction.*) |
|
26189 | 356 |
REPEAT (FIRSTGOAL (eresolve_tac [@{thm CollectE}, @{thm exE}, @{thm conjE}] |
17985 | 357 |
ORELSE' bound_hyp_subst_tac)), |
20046 | 358 |
ind_tac (rev (map (rewrite_rule part_rec_defs) prems)) (length prems)]); |
6051 | 359 |
|
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|
360 |
val dummy = if !Ind_Syntax.trace then |
26928 | 361 |
(writeln "quant_induct = "; Display.print_thm quant_induct) |
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|
362 |
else (); |
6051 | 363 |
|
364 |
||
365 |
(*** Prove the simultaneous induction rule ***) |
|
366 |
||
367 |
(*Make distinct predicates for each inductive set*) |
|
368 |
||
369 |
(*The components of the element type, several if it is a product*) |
|
370 |
val elem_type = CP.pseudo_type dom_sum; |
|
371 |
val elem_factors = CP.factors elem_type; |
|
372 |
val elem_frees = mk_frees "za" elem_factors; |
|
373 |
val elem_tuple = CP.mk_tuple Pr.pair elem_type elem_frees; |
|
374 |
||
375 |
(*Given a recursive set and its domain, return the "fsplit" predicate |
|
376 |
and a conclusion for the simultaneous induction rule. |
|
377 |
NOTE. This will not work for mutually recursive predicates. Previously |
|
378 |
a summand 'domt' was also an argument, but this required the domain of |
|
379 |
mutual recursion to invariably be a disjoint sum.*) |
|
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|
380 |
fun mk_predpair rec_tm = |
6051 | 381 |
let val rec_name = (#1 o dest_Const o head_of) rec_tm |
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|
382 |
val pfree = Free(pred_name ^ "_" ^ Sign.base_name rec_name, |
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|
383 |
elem_factors ---> FOLogic.oT) |
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|
384 |
val qconcl = |
15574
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|
385 |
foldr FOLogic.mk_all |
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|
386 |
(FOLogic.imp $ |
26189 | 387 |
(@{const mem} $ elem_tuple $ rec_tm) |
15574
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|
388 |
$ (list_comb (pfree, elem_frees))) elem_frees |
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|
389 |
in (CP.ap_split elem_type FOLogic.oT pfree, |
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|
390 |
qconcl) |
6051 | 391 |
end; |
392 |
||
393 |
val (preds,qconcls) = split_list (map mk_predpair rec_tms); |
|
394 |
||
395 |
(*Used to form simultaneous induction lemma*) |
|
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|
396 |
fun mk_rec_imp (rec_tm,pred) = |
26189 | 397 |
FOLogic.imp $ (@{const mem} $ Bound 0 $ rec_tm) $ |
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|
398 |
(pred $ Bound 0); |
6051 | 399 |
|
400 |
(*To instantiate the main induction rule*) |
|
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|
401 |
val induct_concl = |
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|
402 |
FOLogic.mk_Trueprop |
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|
403 |
(Ind_Syntax.mk_all_imp |
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|
404 |
(big_rec_tm, |
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|
405 |
Abs("z", Ind_Syntax.iT, |
23419 | 406 |
BalancedTree.make FOLogic.mk_conj |
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|
407 |
(ListPair.map mk_rec_imp (rec_tms, preds))))) |
6051 | 408 |
and mutual_induct_concl = |
23419 | 409 |
FOLogic.mk_Trueprop(BalancedTree.make FOLogic.mk_conj qconcls); |
6051 | 410 |
|
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|
411 |
val dummy = if !Ind_Syntax.trace then |
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|
412 |
(writeln ("induct_concl = " ^ |
26189 | 413 |
Syntax.string_of_term ctxt1 induct_concl); |
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|
414 |
writeln ("mutual_induct_concl = " ^ |
26189 | 415 |
Syntax.string_of_term ctxt1 mutual_induct_concl)) |
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|
416 |
else (); |
6051 | 417 |
|
418 |
||
26189 | 419 |
val lemma_tac = FIRST' [eresolve_tac [@{thm asm_rl}, @{thm conjE}, @{thm PartE}, @{thm mp}], |
420 |
resolve_tac [@{thm allI}, @{thm impI}, @{thm conjI}, @{thm Part_eqI}], |
|
421 |
dresolve_tac [@{thm spec}, @{thm mp}, Pr.fsplitD]]; |
|
6051 | 422 |
|
423 |
val need_mutual = length rec_names > 1; |
|
424 |
||
425 |
val lemma = (*makes the link between the two induction rules*) |
|
426 |
if need_mutual then |
|
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|
427 |
(writeln " Proving the mutual induction rule..."; |
20342 | 428 |
Goal.prove_global thy1 [] [] |
17985 | 429 |
(Logic.mk_implies (induct_concl, mutual_induct_concl)) |
430 |
(fn _ => EVERY |
|
431 |
[rewrite_goals_tac part_rec_defs, |
|
20046 | 432 |
REPEAT (rewrite_goals_tac [Pr.split_eq] THEN lemma_tac 1)])) |
26189 | 433 |
else (writeln " [ No mutual induction rule needed ]"; @{thm TrueI}); |
6051 | 434 |
|
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|
435 |
val dummy = if !Ind_Syntax.trace then |
26928 | 436 |
(writeln "lemma = "; Display.print_thm lemma) |
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|
437 |
else (); |
6051 | 438 |
|
439 |
||
440 |
(*Mutual induction follows by freeness of Inl/Inr.*) |
|
441 |
||
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|
442 |
(*Simplification largely reduces the mutual induction rule to the |
6051 | 443 |
standard rule*) |
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|
444 |
val mut_ss = |
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|
445 |
min_ss addsimps [Su.distinct, Su.distinct', Su.inl_iff, Su.inr_iff]; |
6051 | 446 |
|
447 |
val all_defs = con_defs @ part_rec_defs; |
|
448 |
||
449 |
(*Removes Collects caused by M-operators in the intro rules. It is very |
|
450 |
hard to simplify |
|
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|
451 |
list({v: tf. (v : t --> P_t(v)) & (v : f --> P_f(v))}) |
6051 | 452 |
where t==Part(tf,Inl) and f==Part(tf,Inr) to list({v: tf. P_t(v)}). |
453 |
Instead the following rules extract the relevant conjunct. |
|
454 |
*) |
|
24893 | 455 |
val cmonos = [@{thm subset_refl} RS @{thm Collect_mono}] RL monos |
456 |
RLN (2,[@{thm rev_subsetD}]); |
|
6051 | 457 |
|
458 |
(*Minimizes backtracking by delivering the correct premise to each goal*) |
|
459 |
fun mutual_ind_tac [] 0 = all_tac |
|
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|
460 |
| mutual_ind_tac(prem::prems) i = |
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|
461 |
DETERM |
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|
462 |
(SELECT_GOAL |
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|
463 |
( |
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|
464 |
(*Simplify the assumptions and goal by unfolding Part and |
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|
465 |
using freeness of the Sum constructors; proves all but one |
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|
466 |
conjunct by contradiction*) |
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|
467 |
rewrite_goals_tac all_defs THEN |
24893 | 468 |
simp_tac (mut_ss addsimps [@{thm Part_iff}]) 1 THEN |
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|
469 |
IF_UNSOLVED (*simp_tac may have finished it off!*) |
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|
470 |
((*simplify assumptions*) |
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|
471 |
(*some risk of excessive simplification here -- might have |
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|
472 |
to identify the bare minimum set of rewrites*) |
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|
473 |
full_simp_tac |
26287 | 474 |
(mut_ss addsimps @{thms conj_simps} @ @{thms imp_simps} @ @{thms quant_simps}) 1 |
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|
475 |
THEN |
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|
476 |
(*unpackage and use "prem" in the corresponding place*) |
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|
477 |
REPEAT (rtac impI 1) THEN |
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|
478 |
rtac (rewrite_rule all_defs prem) 1 THEN |
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|
479 |
(*prem must not be REPEATed below: could loop!*) |
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|
480 |
DEPTH_SOLVE (FIRSTGOAL (ares_tac [impI] ORELSE' |
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changeset
|
481 |
eresolve_tac (conjE::mp::cmonos)))) |
1ef58b332ca9
support co/inductive definitions in new-style theories;
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parents:
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changeset
|
482 |
) i) |
1ef58b332ca9
support co/inductive definitions in new-style theories;
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parents:
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changeset
|
483 |
THEN mutual_ind_tac prems (i-1); |
6051 | 484 |
|
12132
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support co/inductive definitions in new-style theories;
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changeset
|
485 |
val mutual_induct_fsplit = |
6051 | 486 |
if need_mutual then |
20342 | 487 |
Goal.prove_global thy1 [] (map (induct_prem (rec_tms~~preds)) intr_tms) |
17985 | 488 |
mutual_induct_concl |
26712
e2dcda7b0401
adapted to ProofContext.revert_skolem: extra Name.clean required;
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parents:
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changeset
|
489 |
(fn {prems, ...} => EVERY |
17985 | 490 |
[rtac (quant_induct RS lemma) 1, |
20046 | 491 |
mutual_ind_tac (rev prems) (length prems)]) |
6051 | 492 |
else TrueI; |
493 |
||
494 |
(** Uncurrying the predicate in the ordinary induction rule **) |
|
495 |
||
496 |
(*instantiate the variable to a tuple, if it is non-trivial, in order to |
|
497 |
allow the predicate to be "opened up". |
|
498 |
The name "x.1" comes from the "RS spec" !*) |
|
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support co/inductive definitions in new-style theories;
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|
499 |
val inst = |
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support co/inductive definitions in new-style theories;
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parents:
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changeset
|
500 |
case elem_frees of [_] => I |
20342 | 501 |
| _ => instantiate ([], [(cterm_of thy1 (Var(("x",1), Ind_Syntax.iT)), |
502 |
cterm_of thy1 elem_tuple)]); |
|
6051 | 503 |
|
504 |
(*strip quantifier and the implication*) |
|
26189 | 505 |
val induct0 = inst (quant_induct RS spec RSN (2, @{thm rev_mp})); |
6051 | 506 |
|
26189 | 507 |
val Const (@{const_name Trueprop}, _) $ (pred_var $ _) = concl_of induct0 |
6051 | 508 |
|
12132
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support co/inductive definitions in new-style theories;
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parents:
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changeset
|
509 |
val induct = CP.split_rule_var(pred_var, elem_type-->FOLogic.oT, induct0) |
1ef58b332ca9
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changeset
|
510 |
|> standard |
6051 | 511 |
and mutual_induct = CP.remove_split mutual_induct_fsplit |
8438 | 512 |
|
18377 | 513 |
val ([induct', mutual_induct'], thy') = |
514 |
thy |
|
18643 | 515 |
|> PureThy.add_thms [((co_prefix ^ "induct", induct), |
24861
cc669ca5f382
tuned Induct interface: prefer pred'' over set'';
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changeset
|
516 |
[case_names, Induct.induct_pred big_rec_name]), |
18643 | 517 |
(("mutual_induct", mutual_induct), [case_names])]; |
12227 | 518 |
in ((thy', induct'), mutual_induct') |
6051 | 519 |
end; (*of induction_rules*) |
520 |
||
521 |
val raw_induct = standard ([big_rec_def, bnd_mono] MRS Fp.induct) |
|
522 |
||
12227 | 523 |
val ((thy2, induct), mutual_induct) = |
524 |
if not coind then induction_rules raw_induct thy1 |
|
18377 | 525 |
else |
526 |
(thy1 |
|
527 |
|> PureThy.add_thms [((co_prefix ^ "induct", raw_induct), [])] |
|
528 |
|> apfst hd |> Library.swap, TrueI) |
|
6051 | 529 |
and defs = big_rec_def :: part_rec_defs |
530 |
||
531 |
||
18377 | 532 |
val (([bnd_mono', dom_subset', elim'], [defs', intrs']), thy3) = |
8438 | 533 |
thy2 |
12183 | 534 |
|> IndCases.declare big_rec_name make_cases |
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|
535 |
|> PureThy.add_thms |
1ef58b332ca9
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parents:
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diff
changeset
|
536 |
[(("bnd_mono", bnd_mono), []), |
1ef58b332ca9
support co/inductive definitions in new-style theories;
wenzelm
parents:
11680
diff
changeset
|
537 |
(("dom_subset", dom_subset), []), |
24861
cc669ca5f382
tuned Induct interface: prefer pred'' over set'';
wenzelm
parents:
24830
diff
changeset
|
538 |
(("cases", elim), [case_names, Induct.cases_pred big_rec_name])] |
18377 | 539 |
||>> (PureThy.add_thmss o map Thm.no_attributes) |
8438 | 540 |
[("defs", defs), |
12175 | 541 |
("intros", intrs)]; |
18377 | 542 |
val (intrs'', thy4) = |
543 |
thy3 |
|
544 |
|> PureThy.add_thms ((intr_names ~~ intrs') ~~ map #2 intr_specs) |
|
24712
64ed05609568
proper Sign operations instead of Theory aliases;
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parents:
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diff
changeset
|
545 |
||> Sign.parent_path; |
8438 | 546 |
in |
12132
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support co/inductive definitions in new-style theories;
wenzelm
parents:
11680
diff
changeset
|
547 |
(thy4, |
8438 | 548 |
{defs = defs', |
549 |
bnd_mono = bnd_mono', |
|
550 |
dom_subset = dom_subset', |
|
12132
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support co/inductive definitions in new-style theories;
wenzelm
parents:
11680
diff
changeset
|
551 |
intrs = intrs'', |
8438 | 552 |
elim = elim', |
553 |
mk_cases = mk_cases, |
|
554 |
induct = induct, |
|
555 |
mutual_induct = mutual_induct}) |
|
556 |
end; |
|
6051 | 557 |
|
12132
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support co/inductive definitions in new-style theories;
wenzelm
parents:
11680
diff
changeset
|
558 |
(*source version*) |
1ef58b332ca9
support co/inductive definitions in new-style theories;
wenzelm
parents:
11680
diff
changeset
|
559 |
fun add_inductive (srec_tms, sdom_sum) intr_srcs |
1ef58b332ca9
support co/inductive definitions in new-style theories;
wenzelm
parents:
11680
diff
changeset
|
560 |
(raw_monos, raw_con_defs, raw_type_intrs, raw_type_elims) thy = |
1ef58b332ca9
support co/inductive definitions in new-style theories;
wenzelm
parents:
11680
diff
changeset
|
561 |
let |
24726 | 562 |
val ctxt = ProofContext.init thy; |
563 |
val read_terms = map (Syntax.parse_term ctxt #> TypeInfer.constrain Ind_Syntax.iT) |
|
564 |
#> Syntax.check_terms ctxt; |
|
565 |
||
18728 | 566 |
val intr_atts = map (map (Attrib.attribute thy) o snd) intr_srcs; |
17937 | 567 |
val sintrs = map fst intr_srcs ~~ intr_atts; |
24726 | 568 |
val rec_tms = read_terms srec_tms; |
569 |
val dom_sum = singleton read_terms sdom_sum; |
|
570 |
val intr_tms = Syntax.read_props ctxt (map (snd o fst) sintrs); |
|
17937 | 571 |
val intr_specs = (map (fst o fst) sintrs ~~ intr_tms) ~~ map snd sintrs; |
24726 | 572 |
val monos = Attrib.eval_thms ctxt raw_monos; |
573 |
val con_defs = Attrib.eval_thms ctxt raw_con_defs; |
|
574 |
val type_intrs = Attrib.eval_thms ctxt raw_type_intrs; |
|
575 |
val type_elims = Attrib.eval_thms ctxt raw_type_elims; |
|
12132
1ef58b332ca9
support co/inductive definitions in new-style theories;
wenzelm
parents:
11680
diff
changeset
|
576 |
in |
18418
bf448d999b7e
re-arranged tuples (theory * 'a) to ('a * theory) in Pure
haftmann
parents:
18377
diff
changeset
|
577 |
thy |
24726 | 578 |
|> add_inductive_i true (rec_tms, dom_sum) intr_specs (monos, con_defs, type_intrs, type_elims) |
18418
bf448d999b7e
re-arranged tuples (theory * 'a) to ('a * theory) in Pure
haftmann
parents:
18377
diff
changeset
|
579 |
end; |
12132
1ef58b332ca9
support co/inductive definitions in new-style theories;
wenzelm
parents:
11680
diff
changeset
|
580 |
|
1ef58b332ca9
support co/inductive definitions in new-style theories;
wenzelm
parents:
11680
diff
changeset
|
581 |
|
1ef58b332ca9
support co/inductive definitions in new-style theories;
wenzelm
parents:
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diff
changeset
|
582 |
(* outer syntax *) |
1ef58b332ca9
support co/inductive definitions in new-style theories;
wenzelm
parents:
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diff
changeset
|
583 |
|
17057 | 584 |
local structure P = OuterParse and K = OuterKeyword in |
12132
1ef58b332ca9
support co/inductive definitions in new-style theories;
wenzelm
parents:
11680
diff
changeset
|
585 |
|
27354 | 586 |
val _ = List.app OuterKeyword.keyword |
24867 | 587 |
["domains", "intros", "monos", "con_defs", "type_intros", "type_elims"]; |
588 |
||
12132
1ef58b332ca9
support co/inductive definitions in new-style theories;
wenzelm
parents:
11680
diff
changeset
|
589 |
fun mk_ind (((((doms, intrs), monos), con_defs), type_intrs), type_elims) = |
1ef58b332ca9
support co/inductive definitions in new-style theories;
wenzelm
parents:
11680
diff
changeset
|
590 |
#1 o add_inductive doms (map P.triple_swap intrs) (monos, con_defs, type_intrs, type_elims); |
1ef58b332ca9
support co/inductive definitions in new-style theories;
wenzelm
parents:
11680
diff
changeset
|
591 |
|
1ef58b332ca9
support co/inductive definitions in new-style theories;
wenzelm
parents:
11680
diff
changeset
|
592 |
val ind_decl = |
1ef58b332ca9
support co/inductive definitions in new-style theories;
wenzelm
parents:
11680
diff
changeset
|
593 |
(P.$$$ "domains" |-- P.!!! (P.enum1 "+" P.term -- |
25985 | 594 |
((P.$$$ "\<subseteq>" || P.$$$ "<=") |-- P.term))) -- |
12132
1ef58b332ca9
support co/inductive definitions in new-style theories;
wenzelm
parents:
11680
diff
changeset
|
595 |
(P.$$$ "intros" |-- |
22101 | 596 |
P.!!! (Scan.repeat1 (SpecParse.opt_thm_name ":" -- P.prop))) -- |
597 |
Scan.optional (P.$$$ "monos" |-- P.!!! SpecParse.xthms1) [] -- |
|
598 |
Scan.optional (P.$$$ "con_defs" |-- P.!!! SpecParse.xthms1) [] -- |
|
599 |
Scan.optional (P.$$$ "type_intros" |-- P.!!! SpecParse.xthms1) [] -- |
|
600 |
Scan.optional (P.$$$ "type_elims" |-- P.!!! SpecParse.xthms1) [] |
|
12132
1ef58b332ca9
support co/inductive definitions in new-style theories;
wenzelm
parents:
11680
diff
changeset
|
601 |
>> (Toplevel.theory o mk_ind); |
1ef58b332ca9
support co/inductive definitions in new-style theories;
wenzelm
parents:
11680
diff
changeset
|
602 |
|
24867 | 603 |
val _ = OuterSyntax.command (co_prefix ^ "inductive") |
12227 | 604 |
("define " ^ co_prefix ^ "inductive sets") K.thy_decl ind_decl; |
12132
1ef58b332ca9
support co/inductive definitions in new-style theories;
wenzelm
parents:
11680
diff
changeset
|
605 |
|
6051 | 606 |
end; |
12132
1ef58b332ca9
support co/inductive definitions in new-style theories;
wenzelm
parents:
11680
diff
changeset
|
607 |
|
1ef58b332ca9
support co/inductive definitions in new-style theories;
wenzelm
parents:
11680
diff
changeset
|
608 |
end; |
15705 | 609 |