228 See theory Big_Operators for canonical examples. |
230 See theory Big_Operators for canonical examples. |
229 Note that foundational constants comm_monoid_set.F and |
231 Note that foundational constants comm_monoid_set.F and |
230 semilattice_set.F correspond to former combinators fold_image |
232 semilattice_set.F correspond to former combinators fold_image |
231 and fold1 respectively. These are now gone. You may use |
233 and fold1 respectively. These are now gone. You may use |
232 those foundational constants as substitutes, but it is |
234 those foundational constants as substitutes, but it is |
233 preferable to interpret the above locales accordingly. |
235 preferable to interpret the above locales accordingly. |
234 - Dropped class ab_semigroup_idem_mult (special case of lattice, |
236 - Dropped class ab_semigroup_idem_mult (special case of lattice, |
235 no longer needed in connection with Finite_Set.fold etc.) |
237 no longer needed in connection with Finite_Set.fold etc.) |
236 - Fact renames: |
238 - Fact renames: |
237 card.union_inter ~> card_Un_Int [symmetric] |
239 card.union_inter ~> card_Un_Int [symmetric] |
238 card.union_disjoint ~> card_Un_disjoint |
240 card.union_disjoint ~> card_Un_disjoint |
239 INCOMPATIBILITY. |
241 INCOMPATIBILITY. |
240 |
242 |
241 * Locale hierarchy for abstract orderings and (semi)lattices. |
243 * Locale hierarchy for abstract orderings and (semi)lattices. |
242 |
244 |
243 * Discontinued theory src/HOL/Library/Eval_Witness. INCOMPATIBILITY. |
245 * Discontinued theory src/HOL/Library/Eval_Witness. INCOMPATIBILITY. |
244 |
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245 * Discontinued obsolete src/HOL/IsaMakefile (considered legacy since |
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246 Isabelle2013). Use "isabelle build" to operate on Isabelle sessions. |
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247 |
246 |
248 * Numeric types mapped by default to target language numerals: natural |
247 * Numeric types mapped by default to target language numerals: natural |
249 (replaces former code_numeral) and integer (replaces former code_int). |
248 (replaces former code_numeral) and integer (replaces former code_int). |
250 Conversions are available as integer_of_natural / natural_of_integer / |
249 Conversions are available as integer_of_natural / natural_of_integer / |
251 integer_of_nat / nat_of_integer (in HOL) and |
250 integer_of_nat / nat_of_integer (in HOL) and |
273 |
272 |
274 * Introduce type class linear_continuum as combination of |
273 * Introduce type class linear_continuum as combination of |
275 conditionally-complete lattices and inner dense linorders which have |
274 conditionally-complete lattices and inner dense linorders which have |
276 more than one element. INCOMPATIBILITY. |
275 more than one element. INCOMPATIBILITY. |
277 |
276 |
278 * Introduced type classes order_top and order_bot. The old classes top |
277 * Introduced type classes order_top and order_bot. The old classes top |
279 and bot only contain the syntax without assumptions. |
278 and bot only contain the syntax without assumptions. INCOMPATIBILITY: |
280 INCOMPATIBILITY: Rename bot -> order_bot, top -> order_top |
279 Rename bot -> order_bot, top -> order_top |
281 |
280 |
282 * Introduce type classes "no_top" and "no_bot" for orderings without |
281 * Introduce type classes "no_top" and "no_bot" for orderings without |
283 top and bottom elements. |
282 top and bottom elements. |
284 |
283 |
285 * Split dense_linorder into inner_dense_order and no_top, no_bot. |
284 * Split dense_linorder into inner_dense_order and no_top, no_bot. |
286 |
285 |
287 * Complex_Main: Unify and move various concepts from |
286 * Complex_Main: Unify and move various concepts from |
288 HOL-Multivariate_Analysis to HOL-Complex_Main. |
287 HOL-Multivariate_Analysis to HOL-Complex_Main. |
289 |
288 |
290 - Introduce type class (lin)order_topology and linear_continuum_topology. |
289 - Introduce type class (lin)order_topology and |
291 Allows to generalize theorems about limits and order. |
290 linear_continuum_topology. Allows to generalize theorems about |
292 Instances are reals and extended reals. |
291 limits and order. Instances are reals and extended reals. |
293 |
292 |
294 - continuous and continuos_on from Multivariate_Analysis: |
293 - continuous and continuos_on from Multivariate_Analysis: |
295 "continuous" is the continuity of a function at a filter. |
294 "continuous" is the continuity of a function at a filter. "isCont" |
296 "isCont" is now an abbrevitation: "isCont x f == continuous (at _) f". |
295 is now an abbrevitation: "isCont x f == continuous (at _) f". |
297 |
296 |
298 Generalized continuity lemmas from isCont to continuous on an arbitrary |
297 Generalized continuity lemmas from isCont to continuous on an |
299 filter. |
298 arbitrary filter. |
300 |
299 |
301 - compact from Multivariate_Analysis. Use Bolzano's lemma |
300 - compact from Multivariate_Analysis. Use Bolzano's lemma to prove |
302 to prove compactness of closed intervals on reals. Continuous functions |
301 compactness of closed intervals on reals. Continuous functions |
303 attain infimum and supremum on compact sets. The inverse of a continuous |
302 attain infimum and supremum on compact sets. The inverse of a |
304 function is continuous, when the function is continuous on a compact set. |
303 continuous function is continuous, when the function is continuous |
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304 on a compact set. |
305 |
305 |
306 - connected from Multivariate_Analysis. Use it to prove the |
306 - connected from Multivariate_Analysis. Use it to prove the |
307 intermediate value theorem. Show connectedness of intervals on |
307 intermediate value theorem. Show connectedness of intervals on |
308 linear_continuum_topology). |
308 linear_continuum_topology). |
309 |
309 |
310 - first_countable_topology from Multivariate_Analysis. Is used to |
310 - first_countable_topology from Multivariate_Analysis. Is used to |
311 show equivalence of properties on the neighbourhood filter of x and on |
311 show equivalence of properties on the neighbourhood filter of x and |
312 all sequences converging to x. |
312 on all sequences converging to x. |
313 |
313 |
314 - FDERIV: Definition of has_derivative moved to Deriv.thy. Moved theorems |
314 - FDERIV: Definition of has_derivative moved to Deriv.thy. Moved |
315 from Library/FDERIV.thy to Deriv.thy and base the definition of DERIV on |
315 theorems from Library/FDERIV.thy to Deriv.thy and base the |
316 FDERIV. Add variants of DERIV and FDERIV which are restricted to sets, |
316 definition of DERIV on FDERIV. Add variants of DERIV and FDERIV |
317 i.e. to represent derivatives from left or right. |
317 which are restricted to sets, i.e. to represent derivatives from |
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318 left or right. |
318 |
319 |
319 - Removed the within-filter. It is replaced by the principal filter: |
320 - Removed the within-filter. It is replaced by the principal filter: |
320 |
321 |
321 F within X = inf F (principal X) |
322 F within X = inf F (principal X) |
322 |
323 |
323 - Introduce "at x within U" as a single constant, "at x" is now an |
324 - Introduce "at x within U" as a single constant, "at x" is now an |
324 abbreviation for "at x within UNIV" |
325 abbreviation for "at x within UNIV" |
325 |
326 |
326 - Introduce named theorem collections tendsto_intros, continuous_intros, |
327 - Introduce named theorem collections tendsto_intros, |
327 continuous_on_intros and FDERIV_intros. Theorems in tendsto_intros (or |
328 continuous_intros, continuous_on_intros and FDERIV_intros. Theorems |
328 FDERIV_intros) are also available as tendsto_eq_intros (or |
329 in tendsto_intros (or FDERIV_intros) are also available as |
329 FDERIV_eq_intros) where the right-hand side is replaced by a congruence |
330 tendsto_eq_intros (or FDERIV_eq_intros) where the right-hand side |
330 rule. This allows to apply them as intro rules and then proving |
331 is replaced by a congruence rule. This allows to apply them as |
331 equivalence by the simplifier. |
332 intro rules and then proving equivalence by the simplifier. |
332 |
333 |
333 - Restructured theories in HOL-Complex_Main: |
334 - Restructured theories in HOL-Complex_Main: |
334 |
335 |
335 + Moved RealDef and RComplete into Real |
336 + Moved RealDef and RComplete into Real |
336 |
337 |
337 + Introduced Topological_Spaces and moved theorems about |
338 + Introduced Topological_Spaces and moved theorems about |
338 topological spaces, filters, limits and continuity to it |
339 topological spaces, filters, limits and continuity to it |
339 |
340 |
340 + Renamed RealVector to Real_Vector_Spaces |
341 + Renamed RealVector to Real_Vector_Spaces |
341 |
342 |
342 + Split Lim, SEQ, Series into Topological_Spaces, Real_Vector_Spaces, and |
343 + Split Lim, SEQ, Series into Topological_Spaces, |
343 Limits |
344 Real_Vector_Spaces, and Limits |
344 |
345 |
345 + Moved Ln and Log to Transcendental |
346 + Moved Ln and Log to Transcendental |
346 |
347 |
347 + Moved theorems about continuity from Deriv to Topological_Spaces |
348 + Moved theorems about continuity from Deriv to Topological_Spaces |
348 |
349 |