Quellcode-Bibliothek IEEE_854_defs.prf Sprache: Lisp

(IEEE_854_defs
(fp_add_TCC1 0
  (fp_add_TCC1-1 nil 3321206130
   ("" (skosimp*) (("" (assert) nil nil)) nil) nil nil))
(fp_add_TCC2 0
  (fp_add_TCC2-1 nil 3321206130
   ("" (skosimp*) (("" (grind) nil nil)) nil) nil nil))
(fp_add_x_correct 0
  (fp_add_x_correct-1 nil 3321206130
   ("" (skosimp*)
    (("" (expand "fp_add")
      (("" (expand "fp_add_x")
        (("" (lift-if)
          (("" (expand "fp_nan")
            (("" (expand "fp_nan_x")
              (("" (expand "fp_add_inf")
                (("" (expand "fp_add_inf_x")
                  (("" (ground)
                    (("" (expand "fp_op")
                      (("" (expand "fp_op_x")
                        (("" (expand "real_to_fp_x")
                          (("" (expand "fp_round")
                            (("" (expand "fp_round_x")
                              ((""
                                (lift-if)
                                ((""
                                  (expand "round_exceptions")
                                  ((""
                                    (propax)
                                    nil))))))))))))))))))))))))))))))))
    nil)
   ((fp_add const-decl "fp_num" IEEE_854_defs nil)
    (fp_nan_x const-decl "[fp_num, exception]" NaN_ops nil)
    (fp_add_inf_x const-decl "[fp_num, exception]" infinity_arithmetic
     nil)
    (fp_op const-decl "fp_num" arithmetic_ops nil)
    (real_to_fp_x const-decl "[fp_num, exception]" real_to_fp nil)
    (fp_round_x const-decl "[real, exception]" real_to_fp nil)
    (round_exceptions const-decl "real" real_to_fp nil)
    (fp_round const-decl "real" real_to_fp nil)
    (fp_op_x const-decl "[fp_num, exception]" arithmetic_ops nil)
    (fp_add_inf const-decl "fp_num" infinity_arithmetic nil)
    (fp_nan const-decl "fp_num" NaN_ops nil)
    (fp_add_x const-decl "[fp_num, exception]" IEEE_854_defs nil))
   nil))
(fsub_alt_def 0
  (fsub_alt_def-1 nil 3321206130
   ("" (skosimp*)
    (("" (expand "fp_sub")
      (("" (expand "fp_add")
        (("" (rewrite "toggle_finite")
          (("" (rewrite "toggle_NaN")
            (("" (lift-if)
              (("" (assert)
                (("" (split)
                  (("1" (flatten)
                    (("1" (expand "fp_op")
                      (("1" (expand "apply")
                        (("1" (rewrite "value_toggle")
                          (("1" (assert)
                            (("1" (lift-if)
                              (("1"
                                (assert)
                                (("1"
                                  (ground)
                                  (("1"
                                    (expand "signed_zero")
                                    (("1"
                                      (case
                                       "forall fp: zero?(toggle_sign(fp)) iff zero?(fp)")
                                      (("1"
                                        (inst?)
                                        (("1"
                                          (replace -1)
                                          (("1"
                                            (case
                                             "forall (fin1,fin2: (finite?)): (sign(fin1) = sign(toggle_sign(fin2))) iff (sign(fin1) /= sign(fin2))")
                                            (("1"
                                              (inst?)
                                              (("1"
                                                (replace -1)
                                                (("1" (propax) nil)))))
                                             ("2"
                                              (hide -1 -2 -3 -4 2 3 4)
                                              (("2"
                                                (skosimp*)
                                                (("2"
                                                  (expand
                                                   "toggle_sign")
                                                  (("2"
                                                    (typepred
                                                     "sign(fin1!1)")
                                                    (("2"
                                                      (typepred
                                                       "sign(fin2!1)")
                                                      (("2"
                                                        (ground)
                                                        nil)))))))))))
                                             ("3"
                                              (hide -1 -2 -3 -4 2 3 4)
                                              (("3"
                                                (skosimp*)
                                                (("3"
                                                  (rewrite
                                                   "toggle_finite")
                                                  nil)))))))))))
                                       ("2"
                                        (hide -1 -2 -3 2 3 4)
                                        (("2"
                                          (skosimp*)
                                          (("2"
                                            (expand "zero?")
                                            (("2"
                                              (rewrite "toggle_finite")
                                              (("2"
                                                (rewrite
                                                 "value_toggle")
                                                (("2"
                                                  (ground)
                                                  nil)))))))))))))))))))))))))))))))
                   ("2" (flatten)
                    (("2" (rewrite "fp_sub_inf_def")
                      (("1" (ground) nil)
                       ("2" (ground) nil))))))))))))))))))))
    nil)
   ((fp_sub const-decl "fp_num" IEEE_854_defs nil)
    (toggle_finite formula-decl nil IEEE_854_values nil)
    (fp_num type-decl nil IEEE_854_values nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (> const-decl "bool" reals nil)
    (above nonempty-type-eq-decl nil integers nil)
    (b formal-const-decl "above(1)" IEEE_854_defs nil)
    (p formal-const-decl "above(1)" IEEE_854_defs nil)
    (integer nonempty-type-from-decl nil integers nil)
    (E_max formal-const-decl "integer" IEEE_854_defs nil)
    (E_min formal-const-decl "{i: integer | E_max > i}" IEEE_854_defs
     nil)
    (fp_op const-decl "fp_num" arithmetic_ops nil)
    (finite? adt-recognizer-decl "[fp_num -> boolean]" IEEE_854_values
     nil)
    (value_toggle formula-decl nil IEEE_854_values nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (IFF const-decl "[bool, bool -> bool]" booleans nil)
    (zero? const-decl "bool" IEEE_854_values nil)
    (toggle_sign const-decl "fp_num" IEEE_854_values nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (/= const-decl "boolean" notequal nil)
    (sign adt-accessor-decl "[(finite?) -> sign_rep]" IEEE_854_values
          nil)
    (sign_rep type-eq-decl nil enumerated_type_defs nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (signed_zero const-decl "{fin | zero?(fin)}" arithmetic_ops nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (apply const-decl "real" arithmetic_ops nil)
    (fp_sub_inf_def formula-decl nil infinity_arithmetic nil)
    (infinite? adt-recognizer-decl "[fp_num -> boolean]"
     IEEE_854_values nil)
    (toggle_NaN formula-decl nil IEEE_854_values nil)
    (fp_add const-decl "fp_num" IEEE_854_defs nil))
   nil))
(fp_div_TCC1 0
  (fp_div_TCC1-1 nil 3321206130 ("" (skosimp*) (("" (assert) nil)) nil)
   nil nil))
(fp_div_TCC2 0
  (fp_div_TCC2-1 nil 3321206136 ("" (subtype-tcc) nil nil) nil nil))
(fp_sqrt_TCC1 0
  (fp_sqrt_TCC1-1 nil 3321206130
   ("" (skosimp*)
    (("" (lemma "value_positive") (("" (inst?) (("" (assert) nil))))))
    nil)
   ((E_min formal-const-decl "{i: integer | E_max > i}" IEEE_854_defs
     nil)
    (E_max formal-const-decl "integer" IEEE_854_defs nil)
    (integer nonempty-type-from-decl nil integers nil)
    (p formal-const-decl "above(1)" IEEE_854_defs nil)
    (b formal-const-decl "above(1)" IEEE_854_defs nil)
    (above nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (value_positive formula-decl nil IEEE_854_values nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (finite? adt-recognizer-decl "[fp_num -> boolean]" IEEE_854_values
     nil)
    (fp_num type-decl nil IEEE_854_values nil))
   nil))
(fp_sqrt_TCC2 0
  (fp_sqrt_TCC2-1 nil 3321206130 ("" (tcc) nil nil)
   ((expt def-decl "real" exponentiation nil)
    (^ const-decl "real" exponentiation nil)
    (E_min formal-const-decl "{i: integer | E_max > i}" IEEE_854_defs
     nil)
    (E_max formal-const-decl "integer" IEEE_854_defs nil)
    (integer nonempty-type-from-decl nil integers nil)
    (p formal-const-decl "above(1)" IEEE_854_defs nil)
    (b formal-const-decl "above(1)" IEEE_854_defs nil)
    (above nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (value const-decl "real" IEEE_854_values nil)
    (zero? const-decl "bool" IEEE_854_values nil)
    (minus_int_is_int application-judgement "int" integers nil)
    (posnat_expt application-judgement "posnat" exponentiation nil)
    (posint_times_posint_is_posint application-judgement "posint"
     integers nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (int_expt application-judgement "int" exponentiation nil)
    (nzreal_expt application-judgement "nzreal" exponentiation nil)
    (nzint_times_nzint_is_nzint application-judgement "nzint" integers
     nil))
   nil)))

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