721 |
721 |
722 * Theory Real: new method ferrack implements quantifier elimination |
722 * Theory Real: new method ferrack implements quantifier elimination |
723 for linear arithmetic over the reals. The quantifier elimination |
723 for linear arithmetic over the reals. The quantifier elimination |
724 feature is used only for decision, for compatibility with arith. This |
724 feature is used only for decision, for compatibility with arith. This |
725 means a goal is either solved or left unchanged, no simplification. |
725 means a goal is either solved or left unchanged, no simplification. |
|
726 |
|
727 * Real: New axiomatic classes formalize real normed vector spaces and |
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728 algebras, using new overloaded constants scaleR :: real => 'a => 'a |
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729 and norm :: 'a => real. |
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730 |
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731 * Real: New constant of_real :: real => 'a::real_algebra_1 injects from |
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732 reals into other types. The overloaded constant Reals :: 'a set is now |
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733 defined as range of_real; potential INCOMPATIBILITY. |
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734 |
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735 * Hyperreal: Several constants that previously worked only for the reals |
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736 have been generalized, so they now work over arbitrary vector spaces. Type |
|
737 annotations may need to be added in some cases; potential INCOMPATIBILITY. |
|
738 |
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739 Infinitesimal :: ('a::real_normed_vector) star set" |
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740 HFinite :: ('a::real_normed_vector) star set" |
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741 HInfinite :: ('a::real_normed_vector) star set" |
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742 approx :: ('a::real_normed_vector) star => 'a star => bool |
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743 monad :: ('a::real_normed_vector) star => 'a star set |
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744 galaxy :: ('a::real_normed_vector) star => 'a star set |
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745 (NS)LIMSEQ :: [nat, 'a::real_normed_vector, 'a] => bool |
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746 (NS)convergent :: (nat => 'a::real_normed_vector) => bool |
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747 (NS)Bseq :: (nat => 'a::real_normed_vector) => bool |
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748 (NS)Cauchy :: (nat => 'a::real_normed_vector) => bool |
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749 (NS)LIM :: ['a::real_normed_vector => 'b::real_normed_vector, 'a, 'b] => bool |
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750 is(NS)Cont :: ['a::real_normed_vector => 'b::real_normed_vector, 'a] => bool |
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751 deriv :: ['a::real_normed_field => 'a, 'a, 'a] => bool |
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752 |
|
753 * Complex: Some complex-specific constants are now abbreviations for |
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754 overloaded ones: complex_of_real = of_real, cmod = norm, hcmod = hnorm. |
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755 Other constants have been entirely removed in favor of the polymorphic |
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756 versions (INCOMPATIBILITY): |
|
757 |
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758 approx <-- capprox |
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759 HFinite <-- CFinite |
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760 HInfinite <-- CInfinite |
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761 Infinitesimal <-- CInfinitesimal |
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762 monad <-- cmonad |
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763 galaxy <-- cgalaxy |
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764 (NS)LIM <-- (NS)CLIM, (NS)CRLIM |
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765 is(NS)Cont <-- is(NS)Contc, is(NS)contCR |
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766 (ns)deriv <-- (ns)cderiv |
726 |
767 |
727 |
768 |
728 *** ML *** |
769 *** ML *** |
729 |
770 |
730 * Pure/table: |
771 * Pure/table: |