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Datei:
newman_yokouchi.pvs
Sprache: Lisp
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(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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