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(* Title: Pure/Isar/local_defs.ML


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ID: $Id$


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Author: Makarius


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Basic operations on local definitions.


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*)


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signature LOCAL_DEFS =


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sig


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val mk_def: ProofContext.context > (string * term) list > term list


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val cert_def: ProofContext.context > term > string * term


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val abs_def: term > (string * typ) * term


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val derived_def: ProofContext.context > term >


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((string * typ) * term) * (ProofContext.context > term > thm > thm)


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val def_export: ProofContext.export


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val add_def: string * term > ProofContext.context >


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((string * typ) * thm) * ProofContext.context


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end;


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structure LocalDefs: LOCAL_DEFS =


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struct


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(* prepare defs *)


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fun mk_def ctxt args =


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let


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val (xs, rhss) = split_list args;


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val (bind, _) = ProofContext.bind_fixes xs ctxt;


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val lhss = map (fn (x, rhs) => bind (Free (x, Term.fastype_of rhs))) args;


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in map Logic.mk_equals (lhss ~~ rhss) end;


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fun cert_def ctxt eq =


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let


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fun err msg = cat_error msg


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("The error(s) above occurred in definition: " ^ ProofContext.string_of_term ctxt eq);


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val (lhs, rhs) = Logic.dest_equals (Term.strip_all_body eq)


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handle TERM _ => err "Not a metaequality (==)";


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val (f, xs) = Term.strip_comb (Pattern.beta_eta_contract lhs);


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val (c, _) = Term.dest_Free f handle TERM _ =>


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err "Head of lhs must be a free/fixed variable";


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fun check_arg (Bound _) = true


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 check_arg (Free (x, _)) = not (ProofContext.is_fixed ctxt x)


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 check_arg t = (case try Logic.dest_type t of SOME (TFree _) => true  _ => false);


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fun close_arg (Free (x, T)) t = Term.all T $ Term.absfree (x, T, t)


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 close_arg (Const ("TYPE", T)) t = Term.all T $ Term.absdummy (T, t)


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 close_arg _ t = t;


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val extra_frees = Term.fold_aterms (fn v as Free (x, _) =>


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if ProofContext.is_fixed ctxt x orelse member (op aconv) xs v then I


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else insert (op =) x  _ => I) rhs [];


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in


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if not (forall check_arg xs) orelse has_duplicates (op =) xs then


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err "Arguments of lhs must be distinct free/bound variables"


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else if not (null extra_frees) then


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err ("Extra free variables on rhs: " ^ commas_quote extra_frees)


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else if Term.exists_subterm (fn t => t = f) rhs then


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err "Element to be defined occurs on rhs"


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else (c, fold_rev close_arg xs eq)


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end;


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fun abs_def eq =


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let


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val body = Term.strip_all_body eq;


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val vars = map Free (Term.rename_wrt_term body (Term.strip_all_vars eq));


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val (lhs, rhs) = Logic.dest_equals (Term.subst_bounds (vars, body));


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val (f, xs) = Term.strip_comb (Pattern.beta_eta_contract lhs);


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val eq' = Term.list_abs_free (map Term.dest_Free xs, rhs);


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in (Term.dest_Free f, eq') end;


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(* derived defs  potentially within the objectlogic *)


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fun derived_def ctxt prop =


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let


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val thy = ProofContext.theory_of ctxt;


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val ((c, T), rhs) = prop


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> Thm.cterm_of thy


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> ObjectLogic.meta_rewrite_cterm


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> (snd o Logic.dest_equals o Thm.prop_of)


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> Logic.strip_imp_concl


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> (snd o cert_def ctxt)


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> abs_def;


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fun prove ctxt' t def =


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let


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val thy' = ProofContext.theory_of ctxt';


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val prop' = Term.subst_atomic [(Free (c, T), t)] prop;


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val frees = Term.fold_aterms (fn Free (x, _) =>


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if ProofContext.is_fixed ctxt' x then I else insert (op =) x  _ => I) prop' [];


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in


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Goal.prove thy' frees [] prop' (K (ALLGOALS


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(ObjectLogic.meta_rewrite_tac THEN'


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Tactic.rewrite_goal_tac [def] THEN'


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Tactic.resolve_tac [Drule.reflexive_thm])))


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handle ERROR msg => cat_error msg "Failed to prove definitional specification."


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end;


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in (((c, T), rhs), prove) end;


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(* export defs *)


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fun head_of_def cprop =


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#1 (Term.strip_comb (#1 (Logic.dest_equals (Term.strip_all_body (Thm.term_of cprop)))))


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> Thm.cterm_of (Thm.theory_of_cterm cprop);


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fun def_export _ cprops thm =


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thm


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> Drule.implies_intr_list cprops


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> Drule.forall_intr_list (map head_of_def cprops)


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> Drule.forall_elim_vars 0


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> RANGE (replicate (length cprops) (Tactic.rtac Drule.reflexive_thm)) 1;


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(* add defs *)


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fun add_def (x, t) ctxt =


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let


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val [eq] = mk_def ctxt [(x, t)];


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val x' = Term.dest_Free (fst (Logic.dest_equals eq));


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in


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ctxt


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> ProofContext.add_fixes_i [(x, NONE, NoSyn)] > snd


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> ProofContext.add_assms_i def_export [(("", []), [(eq, ([], []))])]


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>> (fn [(_, [th])] => (x', th))


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end;


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end;
