author  wenzelm 
Sat, 01 Mar 2008 14:10:15 +0100  
changeset 26189  9808cca5c54d 
parent 26056  6a0801279f4c 
child 26287  df8e5362cff9 
permissions  rwrr 
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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 nonstandard 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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((bstring * 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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((bstring * string) * Attrib.src list) list > 
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(thmref * Attrib.src list) list * (thmref * Attrib.src list) list * 

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(thmref * Attrib.src list) list * (thmref * 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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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_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 ("Illformed 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_i 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 (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 typecheck 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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(*Typechecking 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 23 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 typechecking 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) => (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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(unfold RS Ind_Syntax.equals_CollectD) 
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(*Applies freeness of the given constructors, which *must* be unfolded by 

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the given defs. Cannot simply use the local con_defs because 
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con_defs=[] for inference systems. 
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Proposition A should have the form t:Si where Si is an inductive set*) 
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fun make_cases ss A = 

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rule_by_tactic 

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(basic_elim_tac THEN ALLGOALS (asm_full_simp_tac ss) THEN basic_elim_tac) 

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(Thm.assume A RS elim) 

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> Drule.standard'; 

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fun mk_cases a = make_cases (*delayed evaluation of body!*) 

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(simpset ()) (Thm.read_cterm (Thm.theory_of_thm elim) (a, propT)); 
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fun induction_rules raw_induct thy = 

283 
let 

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val dummy = writeln " Proving the induction rule..."; 

285 

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(*** Prove the main induction rule ***) 

287 

288 
val pred_name = "P"; (*name for predicate variables*) 

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(*Used to make induction rules; 

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ind_alist = [(rec_tm1,pred1),...] associates predicates with rec ops 
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prem is a premise of an intr rule*) 
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fun add_induct_prem ind_alist (prem as Const (@{const_name Trueprop}, _) $ 
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(Const (@{const_name mem}, _) $ t $ X), iprems) = 

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(case AList.lookup (op aconv) ind_alist X of 
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SOME pred => prem :: FOLogic.mk_Trueprop (pred $ t) :: iprems 
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 NONE => (*possibly membership in M(rec_tm), for M monotone*) 

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let fun mk_sb (rec_tm,pred) = 
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(rec_tm, @{const Collect} $ rec_tm $ pred) 
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in subst_free (map mk_sb ind_alist) prem :: iprems end) 
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 add_induct_prem ind_alist (prem,iprems) = prem :: iprems; 
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(*Make a premise of the induction rule.*) 

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fun induct_prem ind_alist intr = 

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let val quantfrees = map dest_Free (term_frees intr \\ rec_params) 

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val iprems = foldr (add_induct_prem ind_alist) [] 
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(Logic.strip_imp_prems intr) 
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val (t,X) = Ind_Syntax.rule_concl intr 
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val (SOME pred) = AList.lookup (op aconv) ind_alist X 
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val concl = FOLogic.mk_Trueprop (pred $ t) 
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in list_all_free (quantfrees, Logic.list_implies (iprems,concl)) end 
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handle Bind => error"Recursion term not found in conclusion"; 

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(*Minimizes backtracking by delivering the correct premise to each goal. 

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Intro rules with extra Vars in premises still cause some backtracking *) 

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fun ind_tac [] 0 = all_tac 

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 ind_tac(prem::prems) i = 
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DEPTH_SOLVE_1 (ares_tac [prem, refl] i) THEN ind_tac prems (i1); 
6051  319 

320 
val pred = Free(pred_name, Ind_Syntax.iT > FOLogic.oT); 

321 

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val ind_prems = map (induct_prem (map (rpair pred) rec_tms)) 
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323 
intr_tms; 
6051  324 

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325 
val dummy = if !Ind_Syntax.trace then 
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(writeln "ind_prems = "; 
26189  327 
List.app (writeln o Syntax.string_of_term ctxt1) ind_prems; 
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328 
writeln "raw_induct = "; print_thm raw_induct) 
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else (); 
6051  330 

331 

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332 
(*We use a MINIMAL simpset. Even FOL_ss contains too many simpules. 
6051  333 
If the premises get simplified, then the proofs could fail.*) 
17892  334 
val min_ss = Simplifier.theory_context thy empty_ss 
12725  335 
setmksimps (map mk_eq o ZF_atomize o gen_all) 
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336 
setSolver (mk_solver "minimal" 
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337 
(fn prems => resolve_tac (triv_rls@prems) 
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338 
ORELSE' assume_tac 
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339 
ORELSE' etac FalseE)); 
6051  340 

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341 
val quant_induct = 
20342  342 
Goal.prove_global thy1 [] ind_prems 
17985  343 
(FOLogic.mk_Trueprop (Ind_Syntax.mk_all_imp (big_rec_tm, pred))) 
344 
(fn prems => EVERY 

345 
[rewrite_goals_tac part_rec_defs, 

26189  346 
rtac (@{thm impI} RS @{thm allI}) 1, 
17985  347 
DETERM (etac raw_induct 1), 
348 
(*Push Part inside Collect*) 

24893  349 
full_simp_tac (min_ss addsimps [@{thm Part_Collect}]) 1, 
17985  350 
(*This CollectE and disjE separates out the introduction rules*) 
26189  351 
REPEAT (FIRSTGOAL (eresolve_tac [@{thm CollectE}, @{thm disjE}])), 
17985  352 
(*Now break down the individual cases. No disjE here in case 
353 
some premise involves disjunction.*) 

26189  354 
REPEAT (FIRSTGOAL (eresolve_tac [@{thm CollectE}, @{thm exE}, @{thm conjE}] 
17985  355 
ORELSE' bound_hyp_subst_tac)), 
20046  356 
ind_tac (rev (map (rewrite_rule part_rec_defs) prems)) (length prems)]); 
6051  357 

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358 
val dummy = if !Ind_Syntax.trace then 
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359 
(writeln "quant_induct = "; print_thm quant_induct) 
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360 
else (); 
6051  361 

362 

363 
(*** Prove the simultaneous induction rule ***) 

364 

365 
(*Make distinct predicates for each inductive set*) 

366 

367 
(*The components of the element type, several if it is a product*) 

368 
val elem_type = CP.pseudo_type dom_sum; 

369 
val elem_factors = CP.factors elem_type; 

370 
val elem_frees = mk_frees "za" elem_factors; 

371 
val elem_tuple = CP.mk_tuple Pr.pair elem_type elem_frees; 

372 

373 
(*Given a recursive set and its domain, return the "fsplit" predicate 

374 
and a conclusion for the simultaneous induction rule. 

375 
NOTE. This will not work for mutually recursive predicates. Previously 

376 
a summand 'domt' was also an argument, but this required the domain of 

377 
mutual recursion to invariably be a disjoint sum.*) 

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378 
fun mk_predpair rec_tm = 
6051  379 
let val rec_name = (#1 o dest_Const o head_of) rec_tm 
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380 
val pfree = Free(pred_name ^ "_" ^ Sign.base_name rec_name, 
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381 
elem_factors > FOLogic.oT) 
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382 
val qconcl = 
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383 
foldr FOLogic.mk_all 
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384 
(FOLogic.imp $ 
26189  385 
(@{const mem} $ elem_tuple $ rec_tm) 
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386 
$ (list_comb (pfree, elem_frees))) elem_frees 
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387 
in (CP.ap_split elem_type FOLogic.oT pfree, 
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388 
qconcl) 
6051  389 
end; 
390 

391 
val (preds,qconcls) = split_list (map mk_predpair rec_tms); 

392 

393 
(*Used to form simultaneous induction lemma*) 

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394 
fun mk_rec_imp (rec_tm,pred) = 
26189  395 
FOLogic.imp $ (@{const mem} $ Bound 0 $ rec_tm) $ 
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396 
(pred $ Bound 0); 
6051  397 

398 
(*To instantiate the main induction rule*) 

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399 
val induct_concl = 
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400 
FOLogic.mk_Trueprop 
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401 
(Ind_Syntax.mk_all_imp 
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402 
(big_rec_tm, 
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403 
Abs("z", Ind_Syntax.iT, 
23419  404 
BalancedTree.make FOLogic.mk_conj 
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405 
(ListPair.map mk_rec_imp (rec_tms, preds))))) 
6051  406 
and mutual_induct_concl = 
23419  407 
FOLogic.mk_Trueprop(BalancedTree.make FOLogic.mk_conj qconcls); 
6051  408 

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409 
val dummy = if !Ind_Syntax.trace then 
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410 
(writeln ("induct_concl = " ^ 
26189  411 
Syntax.string_of_term ctxt1 induct_concl); 
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412 
writeln ("mutual_induct_concl = " ^ 
26189  413 
Syntax.string_of_term ctxt1 mutual_induct_concl)) 
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414 
else (); 
6051  415 

416 

26189  417 
val lemma_tac = FIRST' [eresolve_tac [@{thm asm_rl}, @{thm conjE}, @{thm PartE}, @{thm mp}], 
418 
resolve_tac [@{thm allI}, @{thm impI}, @{thm conjI}, @{thm Part_eqI}], 

419 
dresolve_tac [@{thm spec}, @{thm mp}, Pr.fsplitD]]; 

6051  420 

421 
val need_mutual = length rec_names > 1; 

422 

423 
val lemma = (*makes the link between the two induction rules*) 

424 
if need_mutual then 

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425 
(writeln " Proving the mutual induction rule..."; 
20342  426 
Goal.prove_global thy1 [] [] 
17985  427 
(Logic.mk_implies (induct_concl, mutual_induct_concl)) 
428 
(fn _ => EVERY 

429 
[rewrite_goals_tac part_rec_defs, 

20046  430 
REPEAT (rewrite_goals_tac [Pr.split_eq] THEN lemma_tac 1)])) 
26189  431 
else (writeln " [ No mutual induction rule needed ]"; @{thm TrueI}); 
6051  432 

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433 
val dummy = if !Ind_Syntax.trace then 
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434 
(writeln "lemma = "; print_thm lemma) 
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435 
else (); 
6051  436 

437 

438 
(*Mutual induction follows by freeness of Inl/Inr.*) 

439 

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440 
(*Simplification largely reduces the mutual induction rule to the 
6051  441 
standard rule*) 
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442 
val mut_ss = 
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443 
min_ss addsimps [Su.distinct, Su.distinct', Su.inl_iff, Su.inr_iff]; 
6051  444 

445 
val all_defs = con_defs @ part_rec_defs; 

446 

447 
(*Removes Collects caused by Moperators in the intro rules. It is very 

448 
hard to simplify 

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449 
list({v: tf. (v : t > P_t(v)) & (v : f > P_f(v))}) 
6051  450 
where t==Part(tf,Inl) and f==Part(tf,Inr) to list({v: tf. P_t(v)}). 
451 
Instead the following rules extract the relevant conjunct. 

452 
*) 

24893  453 
val cmonos = [@{thm subset_refl} RS @{thm Collect_mono}] RL monos 
454 
RLN (2,[@{thm rev_subsetD}]); 

6051  455 

456 
(*Minimizes backtracking by delivering the correct premise to each goal*) 

457 
fun mutual_ind_tac [] 0 = all_tac 

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458 
 mutual_ind_tac(prem::prems) i = 
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459 
DETERM 
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460 
(SELECT_GOAL 
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461 
( 
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462 
(*Simplify the assumptions and goal by unfolding Part and 
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463 
using freeness of the Sum constructors; proves all but one 
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464 
conjunct by contradiction*) 
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465 
rewrite_goals_tac all_defs THEN 
24893  466 
simp_tac (mut_ss addsimps [@{thm Part_iff}]) 1 THEN 
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467 
IF_UNSOLVED (*simp_tac may have finished it off!*) 
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468 
((*simplify assumptions*) 
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469 
(*some risk of excessive simplification here  might have 
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470 
to identify the bare minimum set of rewrites*) 
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471 
full_simp_tac 
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472 
(mut_ss addsimps conj_simps @ imp_simps @ quant_simps) 1 
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473 
THEN 
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474 
(*unpackage and use "prem" in the corresponding place*) 
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475 
REPEAT (rtac impI 1) THEN 
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476 
rtac (rewrite_rule all_defs prem) 1 THEN 
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477 
(*prem must not be REPEATed below: could loop!*) 
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478 
DEPTH_SOLVE (FIRSTGOAL (ares_tac [impI] ORELSE' 
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479 
eresolve_tac (conjE::mp::cmonos)))) 
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480 
) i) 
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481 
THEN mutual_ind_tac prems (i1); 
6051  482 

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483 
val mutual_induct_fsplit = 
6051  484 
if need_mutual then 
20342  485 
Goal.prove_global thy1 [] (map (induct_prem (rec_tms~~preds)) intr_tms) 
17985  486 
mutual_induct_concl 
487 
(fn prems => EVERY 

488 
[rtac (quant_induct RS lemma) 1, 

20046  489 
mutual_ind_tac (rev prems) (length prems)]) 
6051  490 
else TrueI; 
491 

492 
(** Uncurrying the predicate in the ordinary induction rule **) 

493 

494 
(*instantiate the variable to a tuple, if it is nontrivial, in order to 

495 
allow the predicate to be "opened up". 

496 
The name "x.1" comes from the "RS spec" !*) 

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497 
val inst = 
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498 
case elem_frees of [_] => I 
20342  499 
 _ => instantiate ([], [(cterm_of thy1 (Var(("x",1), Ind_Syntax.iT)), 
500 
cterm_of thy1 elem_tuple)]); 

6051  501 

502 
(*strip quantifier and the implication*) 

26189  503 
val induct0 = inst (quant_induct RS spec RSN (2, @{thm rev_mp})); 
6051  504 

26189  505 
val Const (@{const_name Trueprop}, _) $ (pred_var $ _) = concl_of induct0 
6051  506 

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507 
val induct = CP.split_rule_var(pred_var, elem_type>FOLogic.oT, induct0) 
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508 
> standard 
6051  509 
and mutual_induct = CP.remove_split mutual_induct_fsplit 
8438  510 

18377  511 
val ([induct', mutual_induct'], thy') = 
512 
thy 

18643  513 
> PureThy.add_thms [((co_prefix ^ "induct", induct), 
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514 
[case_names, Induct.induct_pred big_rec_name]), 
18643  515 
(("mutual_induct", mutual_induct), [case_names])]; 
12227  516 
in ((thy', induct'), mutual_induct') 
6051  517 
end; (*of induction_rules*) 
518 

519 
val raw_induct = standard ([big_rec_def, bnd_mono] MRS Fp.induct) 

520 

12227  521 
val ((thy2, induct), mutual_induct) = 
522 
if not coind then induction_rules raw_induct thy1 

18377  523 
else 
524 
(thy1 

525 
> PureThy.add_thms [((co_prefix ^ "induct", raw_induct), [])] 

526 
> apfst hd > Library.swap, TrueI) 

6051  527 
and defs = big_rec_def :: part_rec_defs 
528 

529 

18377  530 
val (([bnd_mono', dom_subset', elim'], [defs', intrs']), thy3) = 
8438  531 
thy2 
12183  532 
> IndCases.declare big_rec_name make_cases 
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533 
> PureThy.add_thms 
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534 
[(("bnd_mono", bnd_mono), []), 
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535 
(("dom_subset", dom_subset), []), 
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536 
(("cases", elim), [case_names, Induct.cases_pred big_rec_name])] 
18377  537 
>> (PureThy.add_thmss o map Thm.no_attributes) 
8438  538 
[("defs", defs), 
12175  539 
("intros", intrs)]; 
18377  540 
val (intrs'', thy4) = 
541 
thy3 

542 
> PureThy.add_thms ((intr_names ~~ intrs') ~~ map #2 intr_specs) 

24712
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543 
> Sign.parent_path; 
8438  544 
in 
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545 
(thy4, 
8438  546 
{defs = defs', 
547 
bnd_mono = bnd_mono', 

548 
dom_subset = dom_subset', 

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549 
intrs = intrs'', 
8438  550 
elim = elim', 
551 
mk_cases = mk_cases, 

552 
induct = induct, 

553 
mutual_induct = mutual_induct}) 

554 
end; 

6051  555 

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556 
(*source version*) 
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557 
fun add_inductive (srec_tms, sdom_sum) intr_srcs 
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558 
(raw_monos, raw_con_defs, raw_type_intrs, raw_type_elims) thy = 
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559 
let 
24726  560 
val ctxt = ProofContext.init thy; 
561 
val read_terms = map (Syntax.parse_term ctxt #> TypeInfer.constrain Ind_Syntax.iT) 

562 
#> Syntax.check_terms ctxt; 

563 

18728  564 
val intr_atts = map (map (Attrib.attribute thy) o snd) intr_srcs; 
17937  565 
val sintrs = map fst intr_srcs ~~ intr_atts; 
24726  566 
val rec_tms = read_terms srec_tms; 
567 
val dom_sum = singleton read_terms sdom_sum; 

568 
val intr_tms = Syntax.read_props ctxt (map (snd o fst) sintrs); 

17937  569 
val intr_specs = (map (fst o fst) sintrs ~~ intr_tms) ~~ map snd sintrs; 
24726  570 
val monos = Attrib.eval_thms ctxt raw_monos; 
571 
val con_defs = Attrib.eval_thms ctxt raw_con_defs; 

572 
val type_intrs = Attrib.eval_thms ctxt raw_type_intrs; 

573 
val type_elims = Attrib.eval_thms ctxt raw_type_elims; 

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574 
in 
18418
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575 
thy 
24726  576 
> add_inductive_i true (rec_tms, dom_sum) intr_specs (monos, con_defs, type_intrs, type_elims) 
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577 
end; 
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support co/inductive definitions in newstyle theories;
wenzelm
parents:
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578 

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support co/inductive definitions in newstyle theories;
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parents:
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579 

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580 
(* outer syntax *) 
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581 

17057  582 
local structure P = OuterParse and K = OuterKeyword in 
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583 

24867  584 
val _ = OuterSyntax.keywords 
585 
["domains", "intros", "monos", "con_defs", "type_intros", "type_elims"]; 

586 

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587 
fun mk_ind (((((doms, intrs), monos), con_defs), type_intrs), type_elims) = 
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588 
#1 o add_inductive doms (map P.triple_swap intrs) (monos, con_defs, type_intrs, type_elims); 
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589 

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590 
val ind_decl = 
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591 
(P.$$$ "domains"  P.!!! (P.enum1 "+" P.term  
25985  592 
((P.$$$ "\<subseteq>"  P.$$$ "<=")  P.term)))  
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593 
(P.$$$ "intros"  
22101  594 
P.!!! (Scan.repeat1 (SpecParse.opt_thm_name ":"  P.prop)))  
595 
Scan.optional (P.$$$ "monos"  P.!!! SpecParse.xthms1) []  

596 
Scan.optional (P.$$$ "con_defs"  P.!!! SpecParse.xthms1) []  

597 
Scan.optional (P.$$$ "type_intros"  P.!!! SpecParse.xthms1) []  

598 
Scan.optional (P.$$$ "type_elims"  P.!!! SpecParse.xthms1) [] 

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599 
>> (Toplevel.theory o mk_ind); 
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600 

24867  601 
val _ = OuterSyntax.command (co_prefix ^ "inductive") 
12227  602 
("define " ^ co_prefix ^ "inductive sets") K.thy_decl ind_decl; 
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603 

6051  604 
end; 
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605 

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606 
end; 
15705  607 