blanchet@58058: (*  Title:      HOL/Library/Old_SMT/old_smt_word.ML
boehmes@41060:     Author:     Sascha Boehme, TU Muenchen
boehmes@41060: 
boehmes@41060: SMT setup for words.
boehmes@41060: *)
boehmes@41060: 
blanchet@58058: signature OLD_SMT_WORD =
boehmes@41060: sig
boehmes@41060:   val setup: theory -> theory
boehmes@41060: end
boehmes@41060: 
blanchet@58058: structure Old_SMT_Word: OLD_SMT_WORD =
boehmes@41060: struct
boehmes@41060: 
thomas@47567: open Word_Lib
boehmes@41060: 
boehmes@41060: (* SMT-LIB logic *)
boehmes@41060: 
boehmes@41060: fun smtlib_logic ts =
boehmes@41060:   if exists (Term.exists_type (Term.exists_subtype is_wordT)) ts
boehmes@41060:   then SOME "QF_AUFBV"
boehmes@41060:   else NONE
boehmes@41060: 
boehmes@41060: 
boehmes@41060: (* SMT-LIB builtins *)
boehmes@41060: 
boehmes@41060: local
blanchet@58058:   val smtlibC = Old_SMTLIB_Interface.smtlibC
boehmes@41061: 
boehmes@41061:   val wordT = @{typ "'a::len word"}
boehmes@41061: 
boehmes@41060:   fun index1 n i = n ^ "[" ^ string_of_int i ^ "]"
boehmes@41060:   fun index2 n i j = n ^ "[" ^ string_of_int i ^ ":" ^ string_of_int j ^ "]"
boehmes@41060: 
boehmes@41061:   fun word_typ (Type (@{type_name word}, [T])) =
boehmes@41060:         Option.map (index1 "BitVec") (try dest_binT T)
boehmes@41061:     | word_typ _ = NONE
boehmes@41060: 
boehmes@41061:   fun word_num (Type (@{type_name word}, [T])) i =
boehmes@41060:         Option.map (index1 ("bv" ^ string_of_int i)) (try dest_binT T)
boehmes@41061:     | word_num _ _ = NONE
boehmes@41060: 
boehmes@41281:   fun if_fixed pred m n T ts =
boehmes@41127:     let val (Us, U) = Term.strip_type T
boehmes@41127:     in
boehmes@41281:       if pred (U, Us) then
boehmes@41281:         SOME (n, length Us, ts, Term.list_comb o pair (Const (m, T)))
boehmes@41127:       else NONE
boehmes@41127:     end
boehmes@41061: 
boehmes@41281:   fun if_fixed_all m = if_fixed (forall (can dest_wordT) o (op ::)) m
boehmes@41281:   fun if_fixed_args m = if_fixed (forall (can dest_wordT) o snd) m
boehmes@41281: 
boehmes@41061:   fun add_word_fun f (t, n) =
wenzelm@46124:     let val (m, _) = Term.dest_Const t
blanchet@58058:     in Old_SMT_Builtin.add_builtin_fun smtlibC (Term.dest_Const t, K (f m n)) end
boehmes@41281: 
boehmes@41281:   fun hd2 xs = hd (tl xs)
boehmes@41061: 
boehmes@41281:   fun mk_nat i = @{const nat} $ HOLogic.mk_number @{typ nat} i
boehmes@41281: 
boehmes@41281:   fun dest_nat (@{const nat} $ n) = snd (HOLogic.dest_number n)
boehmes@41281:     | dest_nat t = raise TERM ("not a natural number", [t])
boehmes@41281: 
boehmes@41281:   fun mk_shift c [t, u] = Const c $ t $ mk_nat (snd (HOLogic.dest_number u))
boehmes@41281:     | mk_shift c ts = raise TERM ("bad arguments", Const c :: ts)
boehmes@41061: 
boehmes@41281:   fun shift m n T ts =
boehmes@41281:     let val U = Term.domain_type T
boehmes@41281:     in
boehmes@41281:       (case (can dest_wordT U, try (dest_nat o hd2) ts) of
boehmes@41281:         (true, SOME i) =>
boehmes@41281:           SOME (n, 2, [hd ts, HOLogic.mk_number U i], mk_shift (m, T))
boehmes@41281:       | _ => NONE)   (* FIXME: also support non-numerical shifts *)
boehmes@41281:     end
boehmes@41060: 
boehmes@41281:   fun mk_extract c i ts = Term.list_comb (Const c, mk_nat i :: ts)
boehmes@41281: 
boehmes@41281:   fun extract m n T ts =
boehmes@41281:     let val U = Term.range_type (Term.range_type T)
boehmes@41060:     in
boehmes@41281:       (case (try (dest_nat o hd) ts, try dest_wordT U) of
boehmes@41281:         (SOME lb, SOME i) =>
boehmes@41281:           SOME (index2 n (i + lb - 1) lb, 1, tl ts, mk_extract (m, T) lb)
boehmes@41060:       | _ => NONE)
boehmes@41060:     end
boehmes@41060: 
boehmes@41281:   fun mk_extend c ts = Term.list_comb (Const c, ts)
boehmes@41061: 
boehmes@41281:   fun extend m n T ts =
boehmes@41281:     let val (U1, U2) = Term.dest_funT T
boehmes@41281:     in
boehmes@41281:       (case (try dest_wordT U1, try dest_wordT U2) of
boehmes@41281:         (SOME i, SOME j) =>
boehmes@41281:           if j-i >= 0 then SOME (index1 n (j-i), 1, ts, mk_extend (m, T))
boehmes@41281:           else NONE
boehmes@41281:       | _ => NONE)
boehmes@41281:     end
boehmes@41060: 
boehmes@41281:   fun mk_rotate c i ts = Term.list_comb (Const c, mk_nat i :: ts)
boehmes@41281: 
boehmes@41281:   fun rotate m n T ts =
boehmes@41281:     let val U = Term.domain_type (Term.range_type T)
boehmes@41127:     in
boehmes@41281:       (case (can dest_wordT U, try (dest_nat o hd) ts) of
boehmes@41281:         (true, SOME i) => SOME (index1 n i, 1, tl ts, mk_rotate (m, T) i)
boehmes@41281:       | _ => NONE)
boehmes@41127:     end
boehmes@41060: in
boehmes@41060: 
boehmes@41061: val setup_builtins =
blanchet@58058:   Old_SMT_Builtin.add_builtin_typ smtlibC (wordT, word_typ, word_num) #>
boehmes@41281:   fold (add_word_fun if_fixed_all) [
boehmes@41061:     (@{term "uminus :: 'a::len word => _"}, "bvneg"),
boehmes@41061:     (@{term "plus :: 'a::len word => _"}, "bvadd"),
boehmes@41061:     (@{term "minus :: 'a::len word => _"}, "bvsub"),
boehmes@41061:     (@{term "times :: 'a::len word => _"}, "bvmul"),
boehmes@41061:     (@{term "bitNOT :: 'a::len word => _"}, "bvnot"),
boehmes@41061:     (@{term "bitAND :: 'a::len word => _"}, "bvand"),
boehmes@41061:     (@{term "bitOR :: 'a::len word => _"}, "bvor"),
boehmes@41061:     (@{term "bitXOR :: 'a::len word => _"}, "bvxor"),
boehmes@41061:     (@{term "word_cat :: 'a::len word => _"}, "concat") ] #>
boehmes@41061:   fold (add_word_fun shift) [
boehmes@41061:     (@{term "shiftl :: 'a::len word => _ "}, "bvshl"),
boehmes@41061:     (@{term "shiftr :: 'a::len word => _"}, "bvlshr"),
boehmes@41061:     (@{term "sshiftr :: 'a::len word => _"}, "bvashr") ] #>
boehmes@41061:   add_word_fun extract
boehmes@41061:     (@{term "slice :: _ => 'a::len word => _"}, "extract") #>
boehmes@41061:   fold (add_word_fun extend) [
boehmes@41061:     (@{term "ucast :: 'a::len word => _"}, "zero_extend"),
boehmes@41061:     (@{term "scast :: 'a::len word => _"}, "sign_extend") ] #>
boehmes@41061:   fold (add_word_fun rotate) [
boehmes@41061:     (@{term word_rotl}, "rotate_left"),
boehmes@41061:     (@{term word_rotr}, "rotate_right") ] #>
boehmes@41281:   fold (add_word_fun if_fixed_args) [
boehmes@41061:     (@{term "less :: 'a::len word => _"}, "bvult"),
boehmes@41061:     (@{term "less_eq :: 'a::len word => _"}, "bvule"),
boehmes@41061:     (@{term word_sless}, "bvslt"),
boehmes@41061:     (@{term word_sle}, "bvsle") ]
boehmes@41060: 
boehmes@41060: end
boehmes@41060: 
boehmes@41060: 
boehmes@41060: (* setup *)
boehmes@41060: 
boehmes@41060: val setup = 
boehmes@41072:   Context.theory_map (
blanchet@58058:     Old_SMTLIB_Interface.add_logic (20, smtlib_logic) #>
boehmes@41072:     setup_builtins)
boehmes@41060: 
boehmes@41060: end