author | wenzelm |
Fri, 04 Jan 2019 23:22:53 +0100 | |
changeset 69593 | 3dda49e08b9d |
parent 66551 | 4df6b0ae900d |
child 69597 | ff784d5a5bfb |
permissions | -rw-r--r-- |
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(* Title: HOL/Tools/SMT/smt_util.ML |
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Author: Sascha Boehme, TU Muenchen |
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General utility functions. |
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*) |
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signature SMT_UTIL = |
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sig |
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(*basic combinators*) |
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val repeat: ('a -> 'a option) -> 'a -> 'a |
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val repeat_yield: ('a -> 'b -> ('a * 'b) option) -> 'a -> 'b -> 'a * 'b |
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datatype order = First_Order | Higher_Order |
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(*class dictionaries*) |
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type class = string list |
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val basicC: class |
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val string_of_class: class -> string |
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type 'a dict = (class * 'a) Ord_List.T |
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val dict_map_default: class * 'a -> ('a -> 'a) -> 'a dict -> 'a dict |
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val dict_update: class * 'a -> 'a dict -> 'a dict |
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val dict_merge: ('a * 'a -> 'a) -> 'a dict * 'a dict -> 'a dict |
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val dict_lookup: 'a dict -> class -> 'a list |
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val dict_get: 'a dict -> class -> 'a option |
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(*types*) |
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val dest_funT: int -> typ -> typ list * typ |
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(*terms*) |
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val dest_conj: term -> term * term |
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val dest_disj: term -> term * term |
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val under_quant: (term -> 'a) -> term -> 'a |
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val is_number: term -> bool |
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(*symbolic lists*) |
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val symb_nil_const: typ -> term |
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val symb_cons_const: typ -> term |
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val mk_symb_list: typ -> term list -> term |
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val dest_symb_list: term -> term list |
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(*patterns and instantiations*) |
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val mk_const_pat: theory -> string -> (ctyp -> 'a) -> 'a * cterm |
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val destT1: ctyp -> ctyp |
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val destT2: ctyp -> ctyp |
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val instTs: ctyp list -> ctyp list * cterm -> cterm |
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val instT: ctyp -> ctyp * cterm -> cterm |
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val instT': cterm -> ctyp * cterm -> cterm |
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(*certified terms*) |
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val dest_cabs: cterm -> Proof.context -> cterm * Proof.context |
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val dest_all_cabs: cterm -> Proof.context -> cterm * Proof.context |
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val dest_cbinder: cterm -> Proof.context -> cterm * Proof.context |
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val dest_all_cbinders: cterm -> Proof.context -> cterm * Proof.context |
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val mk_cprop: cterm -> cterm |
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val dest_cprop: cterm -> cterm |
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val mk_cequals: cterm -> cterm -> cterm |
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val term_of: cterm -> term |
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val prop_of: thm -> term |
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(*conversions*) |
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val if_conv: (term -> bool) -> conv -> conv -> conv |
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val if_true_conv: (term -> bool) -> conv -> conv |
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val if_exists_conv: (term -> bool) -> conv -> conv |
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val binders_conv: (Proof.context -> conv) -> Proof.context -> conv |
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val under_quant_conv: (Proof.context * cterm list -> conv) -> |
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Proof.context -> conv |
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val prop_conv: conv -> conv |
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end; |
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structure SMT_Util: SMT_UTIL = |
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struct |
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(* basic combinators *) |
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fun repeat f = |
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let fun rep x = (case f x of SOME y => rep y | NONE => x) |
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in rep end |
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fun repeat_yield f = |
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let fun rep x y = (case f x y of SOME (x', y') => rep x' y' | NONE => (x, y)) |
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in rep end |
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(* order *) |
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datatype order = First_Order | Higher_Order |
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(* class dictionaries *) |
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type class = string list |
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val basicC = [] |
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fun string_of_class [] = "basic" |
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| string_of_class cs = "basic." ^ space_implode "." cs |
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type 'a dict = (class * 'a) Ord_List.T |
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fun class_ord ((cs1, _), (cs2, _)) = |
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rev_order (list_ord fast_string_ord (cs1, cs2)) |
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fun dict_insert (cs, x) d = |
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if AList.defined (op =) d cs then d |
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else Ord_List.insert class_ord (cs, x) d |
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fun dict_map_default (cs, x) f = |
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dict_insert (cs, x) #> AList.map_entry (op =) cs f |
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fun dict_update (e as (_, x)) = dict_map_default e (K x) |
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fun dict_merge val_merge = sort class_ord o AList.join (op =) (K val_merge) |
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fun dict_lookup d cs = |
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let fun match (cs', x) = if is_prefix (op =) cs' cs then SOME x else NONE |
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in map_filter match d end |
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fun dict_get d cs = |
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(case AList.lookup (op =) d cs of |
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NONE => (case cs of [] => NONE | _ => dict_get d (take (length cs - 1) cs)) |
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| SOME x => SOME x) |
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(* types *) |
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val dest_funT = |
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let |
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fun dest Ts 0 T = (rev Ts, T) |
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| dest Ts i (Type ("fun", [T, U])) = dest (T::Ts) (i-1) U |
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| dest _ _ T = raise TYPE ("not a function type", [T], []) |
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in dest [] end |
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(* terms *) |
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fun dest_conj (@{const HOL.conj} $ t $ u) = (t, u) |
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| dest_conj t = raise TERM ("not a conjunction", [t]) |
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fun dest_disj (@{const HOL.disj} $ t $ u) = (t, u) |
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| dest_disj t = raise TERM ("not a disjunction", [t]) |
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fun under_quant f t = |
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(case t of |
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Const (\<^const_name>\<open>All\<close>, _) $ Abs (_, _, u) => under_quant f u |
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| Const (\<^const_name>\<open>Ex\<close>, _) $ Abs (_, _, u) => under_quant f u |
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| _ => f t) |
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val is_number = |
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let |
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fun is_num env (Const (\<^const_name>\<open>Let\<close>, _) $ t $ Abs (_, _, u)) = is_num (t :: env) u |
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| is_num env (Bound i) = i < length env andalso is_num env (nth env i) |
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| is_num _ t = can HOLogic.dest_number t |
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in is_num [] end |
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(* symbolic lists *) |
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fun symb_listT T = Type (\<^type_name>\<open>symb_list\<close>, [T]) |
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fun symb_nil_const T = Const (\<^const_name>\<open>Symb_Nil\<close>, symb_listT T) |
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fun symb_cons_const T = |
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let val listT = symb_listT T in Const (\<^const_name>\<open>Symb_Cons\<close>, T --> listT --> listT) end |
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fun mk_symb_list T ts = |
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fold_rev (fn t => fn u => symb_cons_const T $ t $ u) ts (symb_nil_const T) |
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||
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fun dest_symb_list (Const (\<^const_name>\<open>Symb_Nil\<close>, _)) = [] |
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| dest_symb_list (Const (\<^const_name>\<open>Symb_Cons\<close>, _) $ t $ u) = t :: dest_symb_list u |
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||
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(* patterns and instantiations *) |
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fun mk_const_pat thy name destT = |
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let val cpat = Thm.global_cterm_of thy (Const (name, Sign.the_const_type thy name)) |
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in (destT (Thm.ctyp_of_cterm cpat), cpat) end |
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val destT1 = hd o Thm.dest_ctyp |
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val destT2 = hd o tl o Thm.dest_ctyp |
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|
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fun instTs cUs (cTs, ct) = Thm.instantiate_cterm (map (dest_TVar o Thm.typ_of) cTs ~~ cUs, []) ct |
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fun instT cU (cT, ct) = instTs [cU] ([cT], ct) |
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fun instT' ct = instT (Thm.ctyp_of_cterm ct) |
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(* certified terms *) |
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fun dest_cabs ct ctxt = |
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(case Thm.term_of ct of |
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Abs _ => |
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let val (n, ctxt') = yield_singleton Variable.variant_fixes Name.uu ctxt |
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in (snd (Thm.dest_abs (SOME n) ct), ctxt') end |
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| _ => raise CTERM ("no abstraction", [ct])) |
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val dest_all_cabs = repeat_yield (try o dest_cabs) |
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fun dest_cbinder ct ctxt = |
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(case Thm.term_of ct of |
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Const _ $ Abs _ => dest_cabs (Thm.dest_arg ct) ctxt |
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| _ => raise CTERM ("not a binder", [ct])) |
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|
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val dest_all_cbinders = repeat_yield (try o dest_cbinder) |
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|
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val mk_cprop = Thm.apply (Thm.cterm_of \<^context> @{const Trueprop}) |
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fun dest_cprop ct = |
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(case Thm.term_of ct of |
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@{const Trueprop} $ _ => Thm.dest_arg ct |
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| _ => raise CTERM ("not a property", [ct])) |
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|
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val equals = mk_const_pat \<^theory> \<^const_name>\<open>Pure.eq\<close> destT1 |
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fun mk_cequals ct cu = Thm.mk_binop (instT' ct equals) ct cu |
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|
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val dest_prop = (fn @{const Trueprop} $ t => t | t => t) |
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fun term_of ct = dest_prop (Thm.term_of ct) |
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fun prop_of thm = dest_prop (Thm.prop_of thm) |
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|
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(* conversions *) |
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fun if_conv pred cv1 cv2 ct = if pred (Thm.term_of ct) then cv1 ct else cv2 ct |
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fun if_true_conv pred cv = if_conv pred cv Conv.all_conv |
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fun if_exists_conv pred = if_true_conv (Term.exists_subterm pred) |
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fun binders_conv cv ctxt = |
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Conv.binder_conv (binders_conv cv o snd) ctxt else_conv cv ctxt |
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|
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fun under_quant_conv cv ctxt = |
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let |
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fun quant_conv inside ctxt cvs ct = |
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(case Thm.term_of ct of |
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Const (\<^const_name>\<open>All\<close>, _) $ Abs _ => |
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Conv.binder_conv (under_conv cvs) ctxt |
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| Const (\<^const_name>\<open>Ex\<close>, _) $ Abs _ => |
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Conv.binder_conv (under_conv cvs) ctxt |
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| _ => if inside then cv (ctxt, cvs) else Conv.all_conv) ct |
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and under_conv cvs (cv, ctxt) = quant_conv true ctxt (cv :: cvs) |
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in quant_conv false ctxt [] end |
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|
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fun prop_conv cv ct = |
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(case Thm.term_of ct of |
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@{const Trueprop} $ _ => Conv.arg_conv cv ct |
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| _ => raise CTERM ("not a property", [ct])) |
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|
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end; |