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(* Title: HOL/Tools/SMT/smt_util.ML
Author: Sascha Boehme, TU Muenchen
General utility functions.
*)
signature SMT_UTIL =
sig
(*basic combinators*)
val repeat: ('a -> 'a option) -> 'a -> 'a
val repeat_yield: ('a -> 'b -> ('a * 'b) option) -> 'a -> 'b -> 'a * 'b
datatype order = First_Order | Higher_Order
(*class dictionaries*)
type class = string list
val basicC: class
val string_of_class: class -> string
type 'a dict = (class * 'a) Ord_List.T
val dict_map_default: class * 'a -> ('a -> 'a) -> 'a dict -> 'a dict
val dict_update: class * 'a -> 'a dict -> 'a dict
val dict_merge: ('a * 'a -> 'a) -> 'a dict * 'a dict -> 'a dict
val dict_lookup: 'a dict -> class -> 'a list
val dict_get: 'a dict -> class -> 'a option
(*types*)
val dest_funT: int -> typ -> typ list * typ
(*terms*)
val dest_conj: term -> term * term
val dest_disj: term -> term * term
val under_quant: (term -> 'a) -> term -> 'a
val is_number: term -> bool
(*symbolic lists*)
val symb_nil_const: typ -> term
val symb_cons_const: typ -> term
val mk_symb_list: typ -> term list -> term
val dest_symb_list: term -> term list
(*patterns and instantiations*)
val mk_const_pat: theory -> string -> (ctyp -> 'a) -> 'a * cterm
val instTs: ctyp list -> ctyp list * cterm -> cterm
val instT: ctyp -> ctyp * cterm -> cterm
val instT': cterm -> ctyp * cterm -> cterm
(*certified terms*)
val dest_cabs: cterm -> Proof.context -> cterm * Proof.context
val dest_all_cabs: cterm -> Proof.context -> cterm * Proof.context
val dest_cbinder: cterm -> Proof.context -> cterm * Proof.context
val dest_all_cbinders: cterm -> Proof.context -> cterm * Proof.context
val mk_cprop: cterm -> cterm
val dest_cprop: cterm -> cterm
val mk_cequals: cterm -> cterm -> cterm
val term_of: cterm -> term
val prop_of: thm -> term
(*conversions*)
val if_conv: (term -> bool) -> conv -> conv -> conv
val if_true_conv: (term -> bool) -> conv -> conv
val if_exists_conv: (term -> bool) -> conv -> conv
val binders_conv: (Proof.context -> conv) -> Proof.context -> conv
val under_quant_conv: (Proof.context * cterm list -> conv) ->
Proof.context -> conv
val prop_conv: conv -> conv
end;
structure SMT_Util: SMT_UTIL =
struct
(* basic combinators *)
fun repeat f =
let fun rep x = (case f x of SOME y => rep y | NONE => x)
in rep end
fun repeat_yield f =
let fun rep x y = (case f x y of SOME (x', y') => rep x' y' | NONE => (x, y))
in rep end
(* order *)
datatype order = First_Order | Higher_Order
(* class dictionaries *)
type class = string list
val basicC = []
fun string_of_class [] = "basic"
| string_of_class cs = "basic." ^ space_implode "." cs
type 'a dict = (class * 'a) Ord_List.T
fun class_ord ((cs1, _), (cs2, _)) =
rev_order (list_ord fast_string_ord (cs1, cs2))
fun dict_insert (cs, x) d =
if AList.defined (op =) d cs then d
else Ord_List.insert class_ord (cs, x) d
fun dict_map_default (cs, x) f =
dict_insert (cs, x) #> AList.map_entry (op =) cs f
fun dict_update (e as (_, x)) = dict_map_default e (K x)
fun dict_merge val_merge = sort class_ord o AList.join (op =) (K val_merge)
fun dict_lookup d cs =
let fun match (cs', x) = if is_prefix (op =) cs' cs then SOME x else NONE
in map_filter match d end
fun dict_get d cs =
(case AList.lookup (op =) d cs of
NONE => (case cs of [] => NONE | _ => dict_get d (take (length cs - 1) cs))
| SOME x => SOME x)
(* types *)
val dest_funT =
let
fun dest Ts 0 T = (rev Ts, T)
| dest Ts i (Type ("fun", [T, U])) = dest (T::Ts) (i-1) U
| dest _ _ T = raise TYPE ("not a function type", [T], [])
in dest [] end
(* terms *)
fun dest_conj (\<^const>\<open>HOL.conj\<close> $ t $ u) = (t, u)
| dest_conj t = raise TERM ("not a conjunction", [t])
fun dest_disj (\<^const>\<open>HOL.disj\<close> $ t $ u) = (t, u)
| dest_disj t = raise TERM ("not a disjunction", [t])
fun under_quant f t =
(case t of
Const (\<^const_name>\<open>All\<close>, _) $ Abs (_, _, u) => under_quant f u
| Const (\<^const_name>\<open>Ex\<close>, _) $ Abs (_, _, u) => under_quant f u
| _ => f t)
val is_number =
let
fun is_num env (Const (\<^const_name>\<open>Let\<close>, _) $ t $ Abs (_, _, u)) = is_num (t :: env) u
| is_num env (Bound i) = i < length env andalso is_num env (nth env i)
| is_num _ t = can HOLogic.dest_number t
in is_num [] end
(* symbolic lists *)
fun symb_listT T = Type (\<^type_name>\<open>symb_list\<close>, [T])
fun symb_nil_const T = Const (\<^const_name>\<open>Symb_Nil\<close>, symb_listT T)
fun symb_cons_const T =
let val listT = symb_listT T in Const (\<^const_name>\<open>Symb_Cons\<close>, T --> listT --> listT) end
fun mk_symb_list T ts =
fold_rev (fn t => fn u => symb_cons_const T $ t $ u) ts (symb_nil_const T)
fun dest_symb_list (Const (\<^const_name>\<open>Symb_Nil\<close>, _)) = []
| dest_symb_list (Const (\<^const_name>\<open>Symb_Cons\<close>, _) $ t $ u) = t :: dest_symb_list u
(* patterns and instantiations *)
fun mk_const_pat thy name destT =
let val cpat = Thm.global_cterm_of thy (Const (name, Sign.the_const_type thy name))
in (destT (Thm.ctyp_of_cterm cpat), cpat) end
fun instTs cUs (cTs, ct) = Thm.instantiate_cterm (map (dest_TVar o Thm.typ_of) cTs ~~ cUs, []) ct
fun instT cU (cT, ct) = instTs [cU] ([cT], ct)
fun instT' ct = instT (Thm.ctyp_of_cterm ct)
(* certified terms *)
fun dest_cabs ct ctxt =
(case Thm.term_of ct of
Abs _ =>
let val (n, ctxt') = yield_singleton Variable.variant_fixes Name.uu ctxt
in (snd (Thm.dest_abs (SOME n) ct), ctxt') end
| _ => raise CTERM ("no abstraction", [ct]))
val dest_all_cabs = repeat_yield (try o dest_cabs)
fun dest_cbinder ct ctxt =
(case Thm.term_of ct of
Const _ $ Abs _ => dest_cabs (Thm.dest_arg ct) ctxt
| _ => raise CTERM ("not a binder", [ct]))
val dest_all_cbinders = repeat_yield (try o dest_cbinder)
val mk_cprop = Thm.apply (Thm.cterm_of \<^context> \<^const>\<open>Trueprop\<close>)
fun dest_cprop ct =
(case Thm.term_of ct of
\<^const>\<open>Trueprop\<close> $ _ => Thm.dest_arg ct
| _ => raise CTERM ("not a property", [ct]))
val equals = mk_const_pat \<^theory> \<^const_name>\<open>Pure.eq\<close> Thm.dest_ctyp0
fun mk_cequals ct cu = Thm.mk_binop (instT' ct equals) ct cu
val dest_prop = (fn \<^const>\<open>Trueprop\<close> $ t => t | t => t)
fun term_of ct = dest_prop (Thm.term_of ct)
fun prop_of thm = dest_prop (Thm.prop_of thm)
(* conversions *)
fun if_conv pred cv1 cv2 ct = if pred (Thm.term_of ct) then cv1 ct else cv2 ct
fun if_true_conv pred cv = if_conv pred cv Conv.all_conv
fun if_exists_conv pred = if_true_conv (Term.exists_subterm pred)
fun binders_conv cv ctxt =
Conv.binder_conv (binders_conv cv o snd) ctxt else_conv cv ctxt
fun under_quant_conv cv ctxt =
let
fun quant_conv inside ctxt cvs ct =
(case Thm.term_of ct of
Const (\<^const_name>\<open>All\<close>, _) $ Abs _ =>
Conv.binder_conv (under_conv cvs) ctxt
| Const (\<^const_name>\<open>Ex\<close>, _) $ Abs _ =>
Conv.binder_conv (under_conv cvs) ctxt
| _ => if inside then cv (ctxt, cvs) else Conv.all_conv) ct
and under_conv cvs (cv, ctxt) = quant_conv true ctxt (cv :: cvs)
in quant_conv false ctxt [] end
fun prop_conv cv ct =
(case Thm.term_of ct of
\<^const>\<open>Trueprop\<close> $ _ => Conv.arg_conv cv ct
| _ => raise CTERM ("not a property", [ct]))
end;
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