michael/lean2
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions
5129 commits 3 branches 0 tags 28 MiB
Commit graph

200 commits

Author SHA1 Message Date
Floris van Doorn
e8b076e460 feat(hott/types/sigma): port large part of the sigma library from the hott library 
most importantly, prove the characterization of paths in sigma types
 2014-11-22 17:44:12 -08:00
Leonardo de Moura
616f2d9b82 fix(library/data/nat/div): notation should be local 2014-11-22 17:33:42 -08:00
Leonardo de Moura
ab9c51bd4b refactor(library/data/nat/div): simplify 'gcd' definition 2014-11-22 17:19:24 -08:00
Leonardo de Moura
2af5ce364d feat(library/data/nat/decl): add 'measure' 2014-11-22 17:19:03 -08:00
Leonardo de Moura
d07481f60f feat(library/data/nat/div): remove some 'sorry's 2014-11-22 14:59:35 -08:00
Leonardo de Moura
9368b879bf refactor(library/data/nat/div): use well-founded library for defining div, mod and gcd 2014-11-22 13:26:55 -08:00
Leonardo de Moura
21b16fd97c feat(library/data/nat): add more basic theorems for definitional package 2014-11-22 13:25:46 -08:00
Leonardo de Moura
9c9f5bba1a refactor(library/data/nat): prove auxiliary theorems about < and sub asap for the definitional package 2014-11-22 09:36:33 -08:00
Leonardo de Moura
064ecd3e3d refactor(library/data/nat): declare lt and le asap using inductive definitions, and make key theorems transparent for definitional package 
We also define key theorems that will be used to generate the
automatically generated a well-founded subterm relation for inductive
datatypes.
We also prove decidability and wf theorems asap.
 2014-11-22 00:19:39 -08:00
Leonardo de Moura
dbb3b7c72a refactor(library/data/nat/sub): cleanup 'max' theorems 2014-11-18 17:56:42 -08:00
Leonardo de Moura
e77cd59368 refactor(library/logic): add basic definitions for relations at logic/relation.lean 
We need them for wf and definitional package
 2014-11-18 17:32:22 -08:00
Leonardo de Moura
99c30db805 feat(library/data/fin): add fin type 2014-11-17 23:44:57 -08:00
Leonardo de Moura
e2ceb86884 feat(library/data/nat/order): add calc_trans commands for lt and le 2014-11-17 23:44:27 -08:00
Leonardo de Moura
5dc42762de feat(library/data): define 'nat.addl' addition using recursion on the first argument, prove it to be equivalent to 'add', and use it to define vector.append 2014-11-17 22:03:39 -08:00
Leonardo de Moura
3cd3da5a84 refactor(library/data/prod/wf): remove duplication, and import wf's for sigma and prod 2014-11-16 21:19:10 -08:00
Leonardo de Moura
b7725c2949 feat(library/data/sigma/wf): define 'lex' for 'sigma' types and prove wf theorem 2014-11-16 20:08:52 -08:00
Leonardo de Moura
dd0b1ecdbf refactor(library/data/sigma): break file into smaller pieces to reduce dependencies 2014-11-16 18:22:03 -08:00
Leonardo de Moura
53ac754328 refactor(library/data/option): cleanup using 'no_confusion' 2014-11-16 17:56:51 -08:00
Leonardo de Moura
de209f929e feat(library/data/prod/wf): define relational product and prove wf theorem for it 2014-11-16 17:47:07 -08:00
Leonardo de Moura
bf5f48730c refactor(library/data/subtype): define subtype using 'structure' command 2014-11-16 15:01:14 -08:00
Leonardo de Moura
b5404cd979 refactor(library/data/vector): cleanup, use variables, add concat 2014-11-15 22:36:52 -08:00
Leonardo de Moura
85f24e4c80 feat(library/data/vector): add 'zip' and 'unzip' functions 2014-11-15 22:19:23 -08:00
Leonardo de Moura
a7adfde84f feat(library/data/vector): use 'mechanical' definitions, and add 'last' function 
The 'mechanical' definitions are "mimicking" what the definitional
package will do.
 2014-11-15 20:21:18 -08:00
Leonardo de Moura
e7a7458922 feat(library/general_notation): reserve unary minus 2014-11-13 22:08:20 -08:00
Leonardo de Moura
6bc89f0916 feat(library/definitional): define ibelow and below 
These are helper definitions for brec_on and binduction_on
 2014-11-12 16:38:46 -08:00
Leonardo de Moura
ef5a3e83ad feat(library/data/vector): expand 'vector' module 2014-11-11 22:33:47 -08:00
Leonardo de Moura
21b93bd2e5 chore(library/data/prod/wf): remove dependency on opaque theorem 2014-11-11 00:39:53 -08:00
Leonardo de Moura
54213b48dc feat(library/data/prod/wf): lex of well-founded relations is well-founded 2014-11-11 00:29:21 -08:00
Leonardo de Moura
76711d00c1 feat(library/data/nat/wf): define measure using inverse image 2014-11-11 00:28:46 -08:00
Leonardo de Moura
4623a62ec3 feat(library/data/nat/wf): predecessor relation is well-founded 2014-11-10 22:15:15 -08:00
Leonardo de Moura
189e5e6b48 refactor(library/data/nat/wf): mark theorem as transparent 
It doesn't really help since
        le_imp_lt_or_eq, succ_le_cancel, lt_imp_le_succ and or.elim
are still opaque
 2014-11-10 12:52:02 -08:00
Floris van Doorn
780e949992 feat(empty): define negation of types 2014-11-08 19:12:54 -08:00
Leonardo de Moura
b97d437011 refactor(library/data/nat/basic): use no_confusion construction to simplify proofs 2014-11-08 19:00:40 -08:00
Leonardo de Moura
ac5a963db3 refactor(library/data/sum): use no_confusion construction to simplify proofs 2014-11-08 18:58:56 -08:00
Leonardo de Moura
46149d0d50 refactor(library/data/prod): break into pieces to reduce dependencies 
prod is needed for some automatically generated constructions.
So, it is important it is loaded in the environment as early as possible.
 2014-11-08 10:19:29 -08:00
Leonardo de Moura
64d2cc60c2 feat(library/data/nat/wf): add nat.lt is well founded theorem 2014-11-07 10:48:31 -08:00
Leonardo de Moura
f16f215c2a refactor(data/num/string): break into pieces to reduce dependencies 2014-11-07 08:53:14 -08:00
Leonardo de Moura
fd34fd17de refactor(library/data/bool): break into pieces to reduce dependencies 2014-11-07 08:41:14 -08:00
Leonardo de Moura
e993486301 refactor(library/data/num): break into pieces to reduce dependencies 2014-11-07 08:24:29 -08:00
Leonardo de Moura
60eac0195d feat(frontends/lean/structure_cmd): generate projection over constructor theorems for structures 2014-11-04 09:10:25 -08:00
Leonardo de Moura
b24165dc7b feat(frontends/lean/structure_cmd): remove 'cases_on' for structures since it may confuse users, add 'destruct' as alternative name for 'rec_on' 2014-11-03 23:06:33 -08:00
Leonardo de Moura
d2b5af237e refactor(library): use new 'structure' command to define prod and sigma 2014-11-03 18:57:55 -08:00
Floris van Doorn
d8a616fa70 refactor(library): major changes in the library 
I made some major changes in the library. I wanted to wait with pushing
until I had finished the formalization of the slice functor, but for
some reason that is very hard to formalize, requiring a lot of casts and
manipulation of casts. So I've not finished that yet.

Changes:

- in multiple files make more use of variables

- move dependent congr_arg theorems to logic.cast and proof them using heq (which doesn't involve nested inductions and fewer casts).

- prove some more theorems involving heq, e.g. hcongr_arg3 (which do not
  require piext)

- in theorems where casts are used in the statement use eq.rec_on
  instead of eq.drec_on

- in category split basic into basic, functor and natural_transformation

- change the definition of functor to use fully bundled
categories. @avigad: this means that the file semisimplicial.lean will
also need changes (but I'm quite sure nothing major).  You want to
define the fully bundled category Delta, and use only fully bundled
categories (type and ᵒᵖ are notations for the fully bundled
Type_category and Opposite if you open namespace category.ops). If you
want I can make the changes.

- lots of minor changes
 2014-11-03 18:45:12 -08:00
Leonardo de Moura
ae9d11c9c4 refactor(library/data): rename prod_ext and dpair_ext to prod.eta and sigma.eta 
Reason: they will be generated automatically by definitional package.
 2014-11-03 08:29:05 -08:00
Leonardo de Moura
8d3e9fdc20 refactor(library/data/nat/basic): remove unnecessary {} 2014-10-31 09:49:45 -07:00
Leonardo de Moura
8a4d4409cd feat(frontends/lean/calc_proof_elaborator): add '{...⁻¹}' if needed in calc proofs, closes #268 
This commit also simplifies library/data/nat/basic.lean
 2014-10-31 01:02:49 -07:00
Leonardo de Moura
5f23179388 refactor(library/data/nat): remove unnecessary ! and eq.symm 
The calc command automatically adds them now.
 2014-10-30 23:28:35 -07:00
Leonardo de Moura
09c6c05e26 chore(library/data/quotient): replace 'let' with 'have' and cleanup 2014-10-30 18:44:05 -07:00
Leonardo de Moura
407e35692b feat(frontends/lean/calc): wrap calc proofs with 'proof-qed' annotation to identify places where proof influences what is being proved 
Later, we will add a custom annotation and elaborator for calc proofs.
This is the first step for issue #268.

Remark: we don't wrap the proof if it is of the form

   - `by tactic`
   - `begin tactic-seq end`
   - `{ expr }`
 2014-10-30 18:33:47 -07:00
Leonardo de Moura
ea739100b3 fix(library/unifier): broken optimization in the unifier 
See new comments and tests for details.
 2014-10-28 16:09:41 -07:00
Leonardo de Moura
777aa63660 fix(kernel/inductive): relax eliminator generation rules for empty types 
This commit also removes the workaround false.rec_type. It is not needed anymore
 2014-10-28 10:31:00 -07:00
Leonardo de Moura
aafdbf57f0 fix(library/data/unit): missing file 2014-10-25 18:34:41 -07:00
Leonardo de Moura
c7f6a6b94e feat(library/definitional/cases_on): automatically add 'cases_on' 2014-10-25 17:22:02 -07:00
Leonardo de Moura
758a17ab23 refactor(library/data/unit): break unit.lean into smaller pieces 
The unit datatype is used by automation.

We want to be able to access its declaration without having to access
all dependencies (e.g., decidable, subsingleton, inhabited, ...).

This is *not* an optimization, but a way to make sure we can "import" unit
before we import other declarations.
 2014-10-25 14:57:33 -07:00
Leonardo de Moura
354b50a1f5 refactor(library/data/unit): make unit universe polymorphic 
Motivation: we need it for "padding".
Example 1: defining a n-ary tuple type.
Example 2: defining cases-on for mutually recursive datatypes
 2014-10-25 13:55:03 -07:00
Leonardo de Moura
cdcde661ef feat(library/definitional/induction_on): automatically add 'induction_on' 2014-10-25 13:37:04 -07:00
Leonardo de Moura
a7a06ab0f8 feat(library/definitional/rec_on): automatically generate rec_on function for inductive datatypes 2014-10-25 13:08:59 -07:00
Soonho Kong
51125c1577 fix(library/data/quotient/default.lean): remove classical 2014-10-24 07:41:29 -07:00
Leonardo de Moura
e24225fabf feat(frontends/lean): validate infixl/infixr/postfix/prefix declarations against reserved notations 2014-10-21 15:39:47 -07:00
Leonardo de Moura
6c7e23ecaa refactor(library): use 'reserve' notation in the standard library 2014-10-21 15:39:47 -07:00
Leonardo de Moura
2e9141b7e1 refactor(library): remove unnecessary :max hack in notation declarations 
This hack is not needed anymore.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-10-20 18:45:52 -07:00
Leonardo de Moura
854e72e665 refactor(library/data/list): minimize dependencies and avoid 'sorry' warning 2014-10-20 15:32:42 -07:00
Leonardo de Moura
f63d47fef3 feat(frontends/lean/pp): support foldl/foldr notation in the pretty printer 2014-10-19 11:16:24 -07:00
Leonardo de Moura
85339c0cc1 fix(library/data/list/basic): mark :: as infixr 2014-10-19 08:58:52 -07:00
Leonardo de Moura
5c1d5133dd fix(library/data/prod): make the notation for tuples and product types consistent 2014-10-13 06:48:37 -07:00
Leonardo de Moura
a26618e0f2 feat(frontends/lean): add '[]' notation for marking arguments where class-instance resolution should be applied 2014-10-12 13:06:00 -07:00
Leonardo de Moura
d6d0593afb refactor(library): remove some unnecessary sections 2014-10-10 16:33:58 -07:00
Leonardo de Moura
8f1b6178a7 chore(*): minimize the use of parameters 2014-10-09 07:13:06 -07:00
Floris van Doorn
ae3419f82f feat(library): add definition of subsingleton and some other minor changes 2014-10-08 23:14:44 -07:00
Leonardo de Moura
c9e5e40477 refactor(library/data/num): cleanup 2014-10-05 13:47:51 -07:00
Leonardo de Moura
86591c7272 refactor(library/data/prod): cleanup 2014-10-05 13:38:08 -07:00
Leonardo de Moura
d56266c524 refactor(data/sum): use sections 2014-10-05 13:20:04 -07:00
Leonardo de Moura
15779c5d1e refactor(data/list): use '!' operator, and new name convention for declaration names 2014-10-05 13:10:35 -07:00
Leonardo de Moura
efaeeb0726 refactor(data/nat/sub): use new policy for marking implicit arguments and '!' operator 2014-10-05 12:39:13 -07:00
Leonardo de Moura
fa96596bf7 refactor(data/int/order): use '!' operator 2014-10-05 11:44:18 -07:00
Leonardo de Moura
a0d4d82f3f refactor(data/nat/order): use new policy for marking implicit arguments and '!' operator 2014-10-05 11:36:39 -07:00
Leonardo de Moura
73aa024c31 refactor(library/logic): remove 'core' subdirectory 2014-10-05 10:50:13 -07:00
Leonardo de Moura
317e910054 refactor(library/data/bool): use new style 2014-10-05 09:50:55 -07:00
Leonardo de Moura
4946f55290 refactor(frontends/lean): constant/axiom are top-level commands, parameter/variable/hypothesis/conjecture are section/context-level commands 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-10-02 17:55:34 -07:00
Leonardo de Moura
d42fd657fe refactor(library): is_inhabited "theorems" should be "definitions", they are "data" 2014-10-02 09:00:34 -07:00
Leonardo de Moura
153e3927ac feat(frontends/lean/elaborator): modify '!' semantics: it stops consuming arguments as soon it finds an argument that does not occur in the rest of the type. 2014-10-01 18:50:17 -07:00
Leonardo de Moura
e64d5c4a4a refactor(library/data/nat): use new operator '!' 2014-10-01 18:39:47 -07:00
Leonardo de Moura
a978e30c81 refactor(library/data/nat): rename to_nat to of_num 2014-10-01 17:52:33 -07:00
Leonardo de Moura
716cd4d651 refactor(library): rename namespace eq_ops to eq.ops 2014-10-01 17:51:17 -07:00
Leonardo de Moura
bc6ebf34be feat(library/data/bool): do not use ! as notation for bnot, rename band/bor -> and/or 2014-10-01 17:00:03 -07:00
Leonardo de Moura
3657d4c3ab feat(frontends/lean): coercion num -> int even when nat is not open, closes #219 
I also had to mark the coercions as reducible.
Otherwise, given the constraint

          ?M (int.of_num 0) =?= (int.of_nat (nat.to_nat 0))

the unifier will not generate the solution

          ?M := fun x, x
 2014-10-01 11:09:10 -07:00
Leonardo de Moura
3ca1264f61 refactor(library): mark 'decidable' theorems as definitions 
If we don't do that, then any 'if' term that uses one of these theorems
will get "stuck". That is, the kernel will not be able to reduce them
because theorems are always opaque
 2014-09-30 09:02:37 -07:00
Floris van Doorn
3a95734fae feat(library): changes in eq.lean sigma.lean and category.lean 
in eq.lean, make rec_on depend on the proof, and add congruence theorems for n-ary functions with n between 2 and 5
in sigma.lean, finish proving equality of triples
in category.lean, define the functor category, and make the proofs of the arrow and slice categories easier for the elaborator
 2014-09-26 19:45:23 -04:00
Floris van Doorn
05fb3aa060 feat(library/data/int): remove duplicate theorem, fix one sorry 2014-09-26 19:45:23 -04:00
Floris van Doorn
5396e422d2 feat(library): add constructions of categories, some changes in eq, sigma and path 
in eq, add theorem for proof irrelevance and congruence for binary functions
in sigma, add some support for triplets
in path, comment out two unneccesary definitions
in category, add Cat, slice, coslice, product and arrow categories, also add fully bundled approach
 2014-09-26 19:45:23 -04:00
Leonardo de Moura
86f06a54ea refactor(library/data/vector): rename 'vec' to 'vector' 2014-09-19 16:20:50 -07:00
Leonardo de Moura
e430dc8bab feat(frontends/lean): add 'irreducible' as syntax sugar for 'reducible [off]' 2014-09-19 15:54:32 -07:00
Leonardo de Moura
4e2377ddfc refactor(frontends/lean): replace '[protected]' modifier with 'protected definition' and 'protected theorem', '[protected]' is not a hint. 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-09-19 15:54:32 -07:00
Leonardo de Moura
5d8c7fbdf1 refactor(frontends/lean): replace '[private]' modifier with 'private 
definition' and 'private theorem', '[private]' is not a hint.
 2014-09-19 15:54:32 -07:00
Leonardo de Moura
97b1998def refactor(frontends/lean): replace '[opaque]' modifier with 'opaque 
definition', '[opaque]' is not a hint, but a kind of definition
 2014-09-19 15:54:32 -07:00
Leonardo de Moura
08ccd58eb6 feat(frontends/lean): add 'reducible' modifier for controlling which 
definitions are unfolded during elaboration

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-09-19 15:54:32 -07:00
Leonardo de Moura
baf4c01de8 feat(frontends/lean): definitions are opaque by default 2014-09-19 15:54:32 -07:00
Leonardo de Moura
93c2c30310 feat(frontends/lean): allow transient coercions, i.e., coercions that 
are not saved in .olean files
 2014-09-19 15:54:32 -07:00
Leonardo de Moura
e3e2370a38 feat(frontends/lean): split 'opaque_hint' command into 'opaque' and 'transparent' 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-09-16 18:03:40 -07:00
Jeremy Avigad
74cb289d48 refactor(library): rename algebra directory to struc, move categories.lean to algebra 2014-09-16 13:13:01 -07:00