src/HOL/Library/Old_SMT/old_smt_word.ML
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(*  Title:      HOL/Library/Old_SMT/old_smt_word.ML
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    Author:     Sascha Boehme, TU Muenchen
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SMT setup for words.
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*)
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structure Old_SMT_Word: sig end =
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struct
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open Word_Lib
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(* SMT-LIB logic *)
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fun smtlib_logic ts =
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  if exists (Term.exists_type (Term.exists_subtype is_wordT)) ts
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  then SOME "QF_AUFBV"
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  else NONE
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(* SMT-LIB builtins *)
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local
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  val smtlibC = Old_SMTLIB_Interface.smtlibC
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  val wordT = @{typ "'a::len word"}
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  fun index1 n i = n ^ "[" ^ string_of_int i ^ "]"
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  fun index2 n i j = n ^ "[" ^ string_of_int i ^ ":" ^ string_of_int j ^ "]"
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  fun word_typ (Type (@{type_name word}, [T])) =
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        Option.map (index1 "BitVec") (try dest_binT T)
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    | word_typ _ = NONE
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  fun word_num (Type (@{type_name word}, [T])) i =
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        Option.map (index1 ("bv" ^ string_of_int i)) (try dest_binT T)
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    | word_num _ _ = NONE
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  fun if_fixed pred m n T ts =
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    let val (Us, U) = Term.strip_type T
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    in
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      if pred (U, Us) then
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        SOME (n, length Us, ts, Term.list_comb o pair (Const (m, T)))
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      else NONE
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    end
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  fun if_fixed_all m = if_fixed (forall (can dest_wordT) o (op ::)) m
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  fun if_fixed_args m = if_fixed (forall (can dest_wordT) o snd) m
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  fun add_word_fun f (t, n) =
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    let val (m, _) = Term.dest_Const t
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    in Old_SMT_Builtin.add_builtin_fun smtlibC (Term.dest_Const t, K (f m n)) end
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  fun hd2 xs = hd (tl xs)
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  fun mk_nat i = @{const nat} $ HOLogic.mk_number @{typ nat} i
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  fun dest_nat (@{const nat} $ n) = snd (HOLogic.dest_number n)
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    | dest_nat t = raise TERM ("not a natural number", [t])
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  fun mk_shift c [t, u] = Const c $ t $ mk_nat (snd (HOLogic.dest_number u))
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    | mk_shift c ts = raise TERM ("bad arguments", Const c :: ts)
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  fun shift m n T ts =
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    let val U = Term.domain_type T
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    in
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      (case (can dest_wordT U, try (dest_nat o hd2) ts) of
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        (true, SOME i) =>
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          SOME (n, 2, [hd ts, HOLogic.mk_number U i], mk_shift (m, T))
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      | _ => NONE)   (* FIXME: also support non-numerical shifts *)
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    end
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  fun mk_extract c i ts = Term.list_comb (Const c, mk_nat i :: ts)
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  fun extract m n T ts =
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    let val U = Term.range_type (Term.range_type T)
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    in
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      (case (try (dest_nat o hd) ts, try dest_wordT U) of
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        (SOME lb, SOME i) =>
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          SOME (index2 n (i + lb - 1) lb, 1, tl ts, mk_extract (m, T) lb)
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      | _ => NONE)
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    end
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  fun mk_extend c ts = Term.list_comb (Const c, ts)
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  fun extend m n T ts =
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    let val (U1, U2) = Term.dest_funT T
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    in
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      (case (try dest_wordT U1, try dest_wordT U2) of
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        (SOME i, SOME j) =>
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          if j-i >= 0 then SOME (index1 n (j-i), 1, ts, mk_extend (m, T))
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          else NONE
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      | _ => NONE)
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    end
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  fun mk_rotate c i ts = Term.list_comb (Const c, mk_nat i :: ts)
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  fun rotate m n T ts =
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    let val U = Term.domain_type (Term.range_type T)
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    in
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      (case (can dest_wordT U, try (dest_nat o hd) ts) of
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        (true, SOME i) => SOME (index1 n i, 1, tl ts, mk_rotate (m, T) i)
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      | _ => NONE)
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    end
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in
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val setup_builtins =
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  Old_SMT_Builtin.add_builtin_typ smtlibC (wordT, word_typ, word_num) #>
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  fold (add_word_fun if_fixed_all) [
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    (@{term "uminus :: 'a::len word => _"}, "bvneg"),
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    (@{term "plus :: 'a::len word => _"}, "bvadd"),
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    (@{term "minus :: 'a::len word => _"}, "bvsub"),
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    (@{term "times :: 'a::len word => _"}, "bvmul"),
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    (@{term "bitNOT :: 'a::len word => _"}, "bvnot"),
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    (@{term "bitAND :: 'a::len word => _"}, "bvand"),
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    (@{term "bitOR :: 'a::len word => _"}, "bvor"),
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    (@{term "bitXOR :: 'a::len word => _"}, "bvxor"),
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    (@{term "word_cat :: 'a::len word => _"}, "concat") ] #>
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  fold (add_word_fun shift) [
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    (@{term "shiftl :: 'a::len word => _ "}, "bvshl"),
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    (@{term "shiftr :: 'a::len word => _"}, "bvlshr"),
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    (@{term "sshiftr :: 'a::len word => _"}, "bvashr") ] #>
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  add_word_fun extract
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    (@{term "slice :: _ => 'a::len word => _"}, "extract") #>
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  fold (add_word_fun extend) [
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    (@{term "ucast :: 'a::len word => _"}, "zero_extend"),
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    (@{term "scast :: 'a::len word => _"}, "sign_extend") ] #>
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  fold (add_word_fun rotate) [
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    (@{term word_rotl}, "rotate_left"),
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    (@{term word_rotr}, "rotate_right") ] #>
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  fold (add_word_fun if_fixed_args) [
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    (@{term "less :: 'a::len word => _"}, "bvult"),
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    (@{term "less_eq :: 'a::len word => _"}, "bvule"),
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    (@{term word_sless}, "bvslt"),
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    (@{term word_sle}, "bvsle") ]
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end
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(* setup *)
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val _ = 
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  Theory.setup
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    (Context.theory_map
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      (Old_SMTLIB_Interface.add_logic (20, smtlib_logic) #> setup_builtins))
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end