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73 commits

Author SHA1 Message Date
Leonardo de Moura
92b0a538c5 refactor(library/logic/wf): add well_founded class, and cleanup file 2014-11-07 10:18:24 -08:00
Leonardo de Moura
781f709bb4 feat(library/logic): import wf.lean in logic/default.lean 
We will use well-founded recursion in the definitional package
 2014-11-06 15:03:13 -08:00
Leonardo de Moura
194247f75b refactor(library/logic/wf): minimize dependencies 2014-11-06 14:59:03 -08:00
Leonardo de Moura
b177c84b06 feat(library/logic): add well-founded recursion 
It also removes the old well-founded induction theorem based on
classical principles
 2014-11-06 14:49:53 -08:00
Leonardo de Moura
d306c42a1f refactor(library/logic): cleanup some of the proofs in cast.lean, remove piext axiom 
Remark: the main motivation for piext was Lean 0.1 simplifier.
We are using a different approach in Lean 0.2.
The axiom is not needed anymore.
It is also not used in any part of the standard library
 2014-11-05 16:43:31 -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
591e566472 feat(frontends/lean): try to inject symmetry (if needed) in calc proofs, add calc_symm command for configuring the symmetry theorem for a given operator 
This is part of #268
 2014-10-30 23:24:09 -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
c7f6a6b94e feat(library/definitional/cases_on): automatically add 'cases_on' 2014-10-25 17:22:02 -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
Leonardo de Moura
6c7e23ecaa refactor(library): use 'reserve' notation in the standard library 2014-10-21 15:39:47 -07:00
Leonardo de Moura
40fb66bf07 feat(frontends/lean): change default precedence to 1 2014-10-20 18:40:55 -07:00
Leonardo de Moura
9edf780a00 feat(frontends/lean): elaborate inductive datatypes and introduction rules as a single elaboration problem 2014-10-13 18:35:11 -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
Floris van Doorn
c630b5ddb2 feat(library/algebra/category): use variables instead of parameters 2014-10-11 16:40:18 -07:00
Leonardo de Moura
d6d0593afb refactor(library): remove some unnecessary sections 2014-10-10 16:33:58 -07:00
Leonardo de Moura
a41850227a refactor(library/logic): use new K-like reduction to simplify some proofs 2014-10-10 14:52:21 -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
Floris van Doorn
abee75c5e9 feat(quantifiers.lean): change exists_unique to a constructively stronger formulation 
the previous formulation was constructively probably to weak to be useful
 2014-10-08 23:14:44 -07:00
Leonardo de Moura
744cee8dd8 feat(frontends/lean): force 'classes' to be declared before instances are declared, closes #228 2014-10-07 18:02:15 -07:00
Leonardo de Moura
e91a64fb38 chore(library/logic): fix comments 2014-10-05 11:11:48 -07:00
Leonardo de Moura
73aa024c31 refactor(library/logic): remove 'core' subdirectory 2014-10-05 10:50:13 -07:00
Leonardo de Moura
0f90d10a13 refactor(logic/core/eq): use sections 2014-10-05 10:19:50 -07:00
Leonardo de Moura
5a927b6db4 refactor(library/logic/cast): define heq using inductive datatypes 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-10-03 21:40:51 -07:00
Leonardo de Moura
a52b21c92d refactor(library): using section variables 2014-10-02 18:25:00 -07:00
Leonardo de Moura
d5cad765a0 feat(frontends/lean): enforce new semantics for section 'variables' 
The library file logic/core/connectives uses the new feature.
 2014-10-02 17:55:34 -07:00
Leonardo de Moura
f78d831de3 refactor(frontends/lean): remove hardcoded Type', and define it using notation 2014-10-02 14:29:51 -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
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
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
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
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
Jeremy Avigad
9988914189 refactor(library/logic): move files in classes directory to core 2014-09-16 13:13:01 -07:00
Leonardo de Moura
9ac5f28b03 refactor(library/logic/core/eq): cleanup 2014-09-09 19:15:11 -07:00
Leonardo de Moura
b4d765ff2e refactor(library/logic/core/cast): cleanup 2014-09-09 19:11:03 -07:00
Leonardo de Moura
9b9adf8831 refactor(library): replace decidable_eq with abbreviation 2014-09-09 16:09:05 -07:00
Leonardo de Moura
bd1bc336fb feat(library/coercion): add simple trick for defining coercions to function-class in a convenient way, closes #31 2014-09-09 14:36:36 -07:00
Leonardo de Moura
5087f03889 refactor(library/logic/classes/decidable): rename 'decidable_eq_to_decidable' theorem to 'of_decidable_eq' 2014-09-09 09:27:26 -07:00
Leonardo de Moura
b4793df653 feat(frontends/lean): rename '[fact]' to '[visible]' 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-09-08 07:47:42 -07:00
Leonardo de Moura
35e68fea76 feat(library/logic/classes/decidable): generalize 'by_cases' theorem 2014-09-08 00:16:20 -07:00
Leonardo de Moura
559dd586f2 feat(library): add 'decidable_eq' class 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
 2014-09-07 22:23:36 -07:00
Leonardo de Moura
48e5a2b6ad feat(library/classes/inhabited): add dfun_inhabited theorem 2014-09-07 19:08:31 -07:00