Floris van Doorn
9e492a8771
feat(category): more about adjoint functors
...
This commit has multiple unfinished proofs (commented out)
2015-11-16 21:32:09 -08:00
Floris van Doorn
f866f71491
feat(algebra/e_closure): add some support for dependent elimination of two_quotients
2015-11-16 21:32:09 -08:00
Floris van Doorn
206bcd4b2a
feat(algebra/homotopy_group): define homotopy groups
2015-11-16 21:32:09 -08:00
Floris van Doorn
47be1e3a15
feat(types/pointed): change definition of loop space
2015-11-16 21:32:09 -08:00
Floris van Doorn
d402b67d25
feat(hott/function): show that a function is embedding iff it has propositional fibers
2015-11-16 21:32:09 -08:00
Floris van Doorn
5c1bf1e777
fix(hott): delete empty file
2015-11-16 21:32:09 -08:00
Floris van Doorn
e00ccff6de
fix(hott): make sure the HoTT library compiles with --to_axiom
2015-11-16 21:32:09 -08:00
Leonardo de Moura
4d68e2a520
feat(library,hott): add eq.mpr and eq.mp lemmas
2015-11-14 15:40:47 -08:00
Leonardo de Moura
5ceac83b6a
feat(frontends/lean/elaborator): restrict the number of places where coercions are considered
...
We do not consider coercions around meta-variables anymore.
2015-11-11 12:37:19 -08:00
Leonardo de Moura
9bedbbb739
refactor(library,hott): remove coercions between algebraic structures
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They are classes, and mixing coercion with type class resolution is a
recipe for disaster (aka counterintuitive behavior).
2015-11-11 11:57:44 -08:00
Ulrik Buchholtz
0eb070e183
fix(hott/book.md): align with previous commit
2015-11-08 14:21:27 -08:00
Ulrik Buchholtz
aebb88d42b
feat(hott/homotopy): connectedness, including HoTT Thm 8.2.1
2015-11-08 14:21:16 -08:00
Leonardo de Moura
a07598a3ec
feat(hott/init/logic): congr_fun was missing in the HoTT library, blast assumes it is part of the environment
2015-11-08 14:05:03 -08:00
Leonardo de Moura
01259a2d1c
feat(library/app_builder): add helper functions for creating eq.rec applications
2015-11-08 14:05:01 -08:00
Floris van Doorn
4828afa781
fix(hott): small fixes after rebasing
2015-11-08 14:04:59 -08:00
Floris van Doorn
5e4441cb43
fix(functor.equivalence): comment out sorry's
2015-11-08 14:04:59 -08:00
Floris van Doorn
49cb516c71
feat(category.limit): prove that the limit functor is right adjoint to the diagonal map
2015-11-08 14:04:59 -08:00
Floris van Doorn
36dfb61a3e
feat(category.limits): prove that yoneda preserves limits
2015-11-08 14:04:59 -08:00
Floris van Doorn
46dba4ee5e
refactor(category): move some files to subfolders, and create file with basic functors
2015-11-08 14:04:59 -08:00
Floris van Doorn
e14754a337
feat(category): start on proof of yoneda preserves limits and limit functor is left adjoint
2015-11-08 14:04:59 -08:00
Floris van Doorn
a99a99f047
feat(hit/quotient): prove the flattening lemma
2015-11-08 14:04:59 -08:00
Floris van Doorn
aa9f32a3bd
fix(init/equiv): make transport not an instance
2015-11-08 14:04:59 -08:00
Floris van Doorn
f2d07ca23c
feat(category): various small changes in category theory
2015-11-08 14:04:59 -08:00
Floris van Doorn
de1c47eda9
feat(categories): add exponential laws for categories
...
also give nicer rules to construct equalities between (pre)categories
2015-11-08 14:04:59 -08:00
Floris van Doorn
0e7b7af1da
refactor(category): add new folder functor, split adjoint file into separate files
2015-11-08 14:04:59 -08:00
Floris van Doorn
3f0d8c0a8c
feat(category.adjoint): prove more about functors
2015-11-08 14:04:58 -08:00
Floris van Doorn
18ec5f8b85
feat(categories): prove introduction rule for equivalences
2015-11-08 14:04:58 -08:00
Floris van Doorn
448178a045
feat(category.functor2): prove that the category of functors is complete and cocomplete if the codomain is
2015-11-08 14:04:58 -08:00
Floris van Doorn
3b7afad6ad
feat(category.hset): prove that the category of sets is cocomplete
2015-11-08 14:04:58 -08:00
Floris van Doorn
c7fd29f854
feat(category): start with the introduction rule for equivalences
2015-11-08 14:04:58 -08:00
Leonardo de Moura
50186e2db3
feat(library/class_instance_resolution): add old type class resolution procedure back to be able to compile HoTT library
2015-11-08 14:04:58 -08:00
Leonardo de Moura
d1e111fd6c
fix(hott,frontends/lean,library,library/tactic): make sure we can still compile the HoTT library
2015-11-08 14:04:55 -08:00
Leonardo de Moura
8ee214f133
checkpoint: new numeral encoding
2015-11-08 14:04:55 -08:00
Leonardo de Moura
744d1cba3d
feat(library,hott,frontends/lean): avoid keywords with hyphen
2015-11-08 14:04:54 -08:00
Jakob von Raumer
d508ceccec
feat(hott/homotpy) add join operator, and prove two basic lemmas
2015-10-13 09:59:24 -07:00
Floris van Doorn
115dedbd1c
fix(hott): notation spacing and markdown files
2015-10-02 16:26:10 -07:00
Leonardo de Moura
ede23a3267
feat(hott,library): add additional spacing hints
2015-09-30 17:41:44 -07:00
Floris van Doorn
aac13a2ee7
fix(hott): minor changes to merge ulrik and my commits
2015-09-28 09:09:22 -07:00
Floris van Doorn
2264759060
feat(category): define colimits as dual of limits
2015-09-28 09:09:22 -07:00
Floris van Doorn
df73931a6d
feat(category.opposite): prove that the opposite of a univalent category is univalent
2015-09-28 09:09:22 -07:00
Floris van Doorn
099bd95ebd
feat(category.limits): prove that being complete is a mere proposition for categories
2015-09-28 09:09:22 -07:00
Floris van Doorn
51edd0ad1d
feat(category.constructions.hset): prove that the category of sets is complete
2015-09-28 09:09:22 -07:00
Floris van Doorn
f82d1bd566
feat(category): add limits in a category
2015-09-28 09:09:22 -07:00
Floris van Doorn
6e23305c5d
feat(category): define terminal, initial, indiscrete and sum category
2015-09-28 09:09:21 -07:00
Floris van Doorn
3c4c722afd
feat(hott): port more from chapters 4 and 6 of the book
2015-09-28 09:09:21 -07:00
Ulrik Buchholtz
c6f3f6f3f4
feat(hott): prove HoTT book 7.5.4 and 7.5.5
2015-09-28 09:09:21 -07:00
Ulrik Buchholtz
25ed9d6e5a
feat(hott): prove HoTT book Theorem 4.7.7
2015-09-28 09:09:21 -07:00
Ulrik Buchholtz
ed1029641a
fix(hott/*): update book.md and clean up homotopy.connectedness
2015-09-28 09:09:21 -07:00
Ulrik Buchholtz
2c22501084
feat(hott): prove HoTT book Theorem 4.7.6
2015-09-28 09:09:21 -07:00
Leonardo de Moura
33f46fd137
feat(library/blast): parse blast tactic and invoke stub
2015-09-25 12:45:16 -07:00
Leonardo de Moura
4a6ff8058d
fix(hott): import commands (some files have been moved to different directories)
2015-09-25 09:39:45 -07:00
Ulrik Buchholtz
384a366e0f
refactor(hott): move homotopy hits to new homotopy folder
2015-09-24 22:52:33 -04:00
Floris van Doorn
732897340d
fix(types): change some definitions to theorems
2015-09-11 23:35:21 -07:00
Floris van Doorn
fb364f8bc7
feat(types): add more equivalences between combinations of type constructors
2015-09-11 23:35:21 -07:00
Floris van Doorn
e84b22864f
feat(hott): various changes in the HoTT library
2015-09-11 23:35:21 -07:00
Floris van Doorn
bd3aa9cf54
feat(category): prove Theorem 9.5.9 from the HoTT book
2015-09-11 23:35:21 -07:00
Floris van Doorn
1a3b363467
feat(category): prove that the yoneda embedding is an embedding
2015-09-11 23:35:21 -07:00
Floris van Doorn
fd89aa77a3
feat(hott): prove Yoneda lemma
2015-09-11 23:35:21 -07:00
Floris van Doorn
817d691237
fix(hott/init/nat): also define ℕ in the top-level in HoTT
2015-09-11 23:35:21 -07:00
Leonardo de Moura
cae2271818
refactor(hott/algebra/category/adjoint): rewrite expensive proof
...
see #815
2015-09-01 16:59:14 -07:00
Floris van Doorn
a8964adb9c
fix(hott): make sure there are no sorry's visible
2015-09-01 15:17:46 -07:00
Floris van Doorn
7e52c49dce
feat(hott): many changes is the HoTT library
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Prove that 'is_left_adjoint F' is a mere proposition, although this proof is commented out because it takes ~10 seconds
2015-09-01 15:17:46 -07:00
Floris van Doorn
f555120428
feat(types/eq): add general encode-decode method
2015-09-01 15:17:46 -07:00
Floris van Doorn
f4892db432
feat(types.trunc): prove the principle of unique choice
2015-09-01 15:17:46 -07:00
Floris van Doorn
c24fd508b6
feat(hott/types): add more about pathovers in type constructors, prove that double negation elimination doesn't hold universally
2015-09-01 15:17:46 -07:00
Floris van Doorn
cfddfdfa84
feat(hott/types): add characterization of lift, prove that Type.{u} is not an hset
2015-09-01 15:17:46 -07:00
Leonardo de Moura
582dbecfd0
feat(library,hott): add notation T1 : T2 as syntax sugar for (focus (T1; all_goals T2))
...
closes #775
2015-08-08 10:16:25 -07:00
Floris van Doorn
ad5cda48a8
refactor(hott): move cubical folder and files eq2, function and hprop_trunc from types/ to the root HoTT directory
2015-08-07 13:34:41 -07:00
Floris van Doorn
e51ba09a27
feat(hott): add types.sum, greatly expand types.prod, minor changes in types.sigma and types.pi
2015-08-07 13:34:41 -07:00
Floris van Doorn
3d2a6a08a4
feat(hott/nat): add characterization of equality in nat
2015-08-07 13:34:41 -07:00
Floris van Doorn
189293b5d4
fix(init.path): rename transport_compose to tr_compose
2015-08-07 13:34:41 -07:00
Floris van Doorn
d111607890
feat(hott): add file which maps sections of the HoTT book to the HoTT library
2015-08-07 13:34:41 -07:00
Floris van Doorn
f3ba81a19d
fix(init.path): a couple of small simplifications
2015-08-07 13:34:40 -07:00
Floris van Doorn
0ec525a8ee
feat(two_quotient): finish proof of elim_incl2
2015-08-07 13:34:40 -07:00
Floris van Doorn
11b1f416f6
feat(nat): add unfold attributes to add, mul, sub and of_num in namespace nat_esimp in both libraries
2015-08-04 13:23:20 +02:00
Floris van Doorn
747d12a385
feat(hott): prove characterization of a pathover in a pathover-type
2015-08-04 13:01:12 +02:00
Floris van Doorn
e198be318f
feat(circle): show that x = x in the circle is always Z
2015-08-04 13:01:11 +02:00
Floris van Doorn
7a780b1b60
feat(hott): various minor changes in the HoTT library
2015-08-04 13:01:11 +02:00
Leonardo de Moura
b3cd3efbb4
refactor(hott): fix "sorry"s at int/basic.hlean, and comment the remaining "sorry"s
2015-07-27 08:34:11 -07:00
Leonardo de Moura
e969c7a8d6
refactor(library): remove 'simp' hack
2015-07-22 10:13:19 -07:00
Leonardo de Moura
267545ca0c
feat(frontends/lean): parse 'with_options' tactical
...
see issue #492
2015-07-13 19:13:41 -04:00
Leonardo de Moura
6ab5cf214c
feat(library,hott): add simp tactic reference
2015-07-13 18:01:40 -04:00
Leonardo de Moura
38d5c361df
refactor(hott/types/trunc): remove unnecessary fold
...
The new unfold tactic performs the fold automatically for us.
see issue #692
2015-07-12 13:07:18 -04:00
Leonardo de Moura
584f9e3f49
fix(library/tactic/unfold_rec): support indexed families at unfold_rec
...
This commit also removes many (now unnecessary) folds from the HoTT
library.
See issue #692
We still have to implement support for recursive definitions based on
brec_on that recurse over inductive families.
2015-07-12 12:32:58 -04:00
Leonardo de Moura
a9515ac7a4
feat(library/tactic/rewrite_tactic): try to fold nested recursive applications after unfolding a recursive function
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See issue #692 .
The implementation still has some rough spots.
It is not clear what the right semantic is.
Moreover, the folds in e_closure could not be eliminated automatically.
2015-07-08 21:19:18 -04:00
Leonardo de Moura
4b1b3e277f
feat(frontends/lean): rename '[unfold-c]' to '[unfold]' and '[unfold-f]' to '[unfold-full]'
...
see issue #693
2015-07-07 16:37:06 -07:00
Leonardo de Moura
68785b8bed
fix(library/tactic/generalize_tactic): fixes #711
2015-06-26 19:35:30 -07:00
Leonardo de Moura
de90926eed
refactor(hott): adjust HoTT library to new support for projections
2015-06-26 17:18:30 -07:00
Floris van Doorn
69f91bfd86
fix(types/nat/hott): workaround failed inductions
2015-06-25 23:13:47 -04:00
Floris van Doorn
24762fe843
feat(hit): add hits with 2-path constructors
...
In hit.two_quotient we define a general construction to define hits with 2-dimensional path constructors, similar to quotients.
We can add 2-paths between any two 'words', where a word consists of 1-path constructors, concatenation and inverses.
We use this to define the torus, reflexive quotients and the reduced suspension.
There is still one 'sorry' in the construction
2015-06-25 22:31:41 -04:00
Floris van Doorn
df3ce2b00b
feat(types/eq2): add theorem about eq_of_con_inv_eq_idp
2015-06-25 22:31:41 -04:00
Floris van Doorn
c8eee66c5b
feat(hott/relation): add equivalence closure of a relation
2015-06-25 22:31:41 -04:00
Floris van Doorn
b94b66243e
feat(hott/types): add some theorems about operations of 2-paths
2015-06-25 22:31:41 -04:00
Floris van Doorn
ea0f57aef5
feat(hott): various clean-up and small additions
2015-06-25 22:31:40 -04:00
Floris van Doorn
2748525c21
feat(hit/susp): finish the proof that loop space is adjoint to the suspension
2015-06-25 22:31:40 -04:00
Floris van Doorn
124c9d3d8a
feat(hott): various cleanup and fixes, rename \~ to ~, expand types.pointed
2015-06-25 22:31:40 -04:00
Floris van Doorn
ac03bf7a4a
feat(hott/nat): prove computation rule for cases by inequality
2015-06-25 22:31:40 -04:00
Floris van Doorn
0b9c8e14a4
fix(*/init/nat): fix occurrences where both theorem and [unfold-c] were used
2015-06-25 22:31:40 -04:00
Floris van Doorn
fa1979c128
feat(datatypes): let the type of unit be the lowest non-Prop universe
...
The definitional package (brec_on and cases_on) now use poly_unit instead of unit
closes #698
2015-06-25 17:33:46 -07:00
Leonardo de Moura
cfafc90cc0
refactor(hott,library): make sure files compile even without using "projection macros"
2015-06-22 12:22:11 -07:00
