lean2/library/data/data.md

data
====

Various data types.

Basic types:

* [empty](empty.lean) : the empty type
* [unit](unit.lean) : the singleton type
* [bool](bool.lean) : the boolean values
* [num](num.lean) : generic numerals
* [string](string.lean) : ascii strings
* [nat](nat/nat.md) : the natural numbers
* [fin](fin.lean) : finite ordinals
* [int](int/int.md) : the integers
* [rat](rat/rat.md) : the rationals
* [pnat](pnat.lean) : the positive natural numbers
* [real](real/real.md) : the real numbers
* [complex](complex.lean) : the complex numbers

Constructors:

* [prod](prod.lean) : cartesian product
* [sum](sum.lean)
* [sigma](sigma.lean) : the dependent product
* [uprod](uprod.lean) : unordered pairs
* [option](option.lean)
* [subtype](subtype.lean)
* [squash](squash.lean) : propositional truncation
* [list](list/list.md)
* [finset](finset/finset.md) : finite sets
* [stream](stream.lean)
* [set](set/set.md)
* [vector](vector.lean)

Types with extra information:

* [fintype](fintype/fintype.md) : finite types
* [encodable](encodable.lean) : types with a coding to nat
feat(library/standard): add markdown documentation 2014-08-01 10:37:55 -07:00			`data`
			`====`

feat(library/standard): add sigma types and subtypes, make inhabited constructive 2014-08-14 20:12:54 -07:00			`Various data types.`
feat(library/standard): add markdown documentation 2014-08-01 10:37:55 -07:00
			`Basic types:`

refactor(library/standard): integrate hott with standard library 2014-08-11 17:35:25 -07:00			`* [empty](empty.lean) : the empty type`
feat(library/standard): add markdown documentation 2014-08-01 10:37:55 -07:00			`* [unit](unit.lean) : the singleton type`
refactor(library/data): remove folders with a single file 2014-12-23 15:35:06 -05:00			`* [bool](bool.lean) : the boolean values`
			`* [num](num.lean) : generic numerals`
feat(library/standard): add markdown documentation 2014-08-01 10:37:55 -07:00			`* [string](string.lean) : ascii strings`
			`* [nat](nat/nat.md) : the natural numbers`
refactor(library): clean up headers and markdown files 2014-12-22 15:33:29 -05:00			`* [fin](fin.lean) : finite ordinals`
feat(library/standard): add markdown documentation 2014-08-01 10:37:55 -07:00			`* [int](int/int.md) : the integers`
feat(library/data/less_than.lean): add finite ordinals from Haitao Zhang 2015-06-05 20:34:49 +10:00			`* [rat](rat/rat.md) : the rationals`
feat(library/algebra/ordered_ring): add theorems used for rational upper bounds 2015-06-16 12:48:57 +10:00			`* [pnat](pnat.lean) : the positive natural numbers`
feat(library/data/complex): add complex numbers 2015-11-12 20:35:05 -05:00			`* [real](real/real.md) : the real numbers`
			`* [complex](complex.lean) : the complex numbers`
feat(library/standard): add markdown documentation 2014-08-01 10:37:55 -07:00
			`Constructors:`

feat(library/standard): add sigma types and subtypes, make inhabited constructive 2014-08-14 20:12:54 -07:00			`* [prod](prod.lean) : cartesian product`
			`* [sum](sum.lean)`
			`* [sigma](sigma.lean) : the dependent product`
feat(library/data): update defaults and markdown files 2015-05-08 20:23:15 +10:00			`* [uprod](uprod.lean) : unordered pairs`
feat(library/standard): add markdown documentation 2014-08-01 10:37:55 -07:00			`* [option](option.lean)`
feat(library/standard): add sigma types and subtypes, make inhabited constructive 2014-08-14 20:12:54 -07:00			`* [subtype](subtype.lean)`
feat(library/data): update defaults and markdown files 2015-05-08 20:23:15 +10:00			`* [squash](squash.lean) : propositional truncation`
feat(library/standard): add markdown documentation 2014-08-01 10:37:55 -07:00			`* [list](list/list.md)`
feat(library/data): update defaults and markdown files 2015-05-08 20:23:15 +10:00			`* [finset](finset/finset.md) : finite sets`
refactor(library/*): do various renamings 2015-05-25 22:13:23 +10:00			`* [stream](stream.lean)`
refactor(library/data/set): expand set.lean to set directory 2015-04-05 09:27:15 -04:00			`* [set](set/set.md)`
feat(library/data): update defaults and markdown files 2015-05-08 20:23:15 +10:00			`* [vector](vector.lean)`

			`Types with extra information:`

feat(library/data/fintype,finset): add cardinality for finite types from Haitao Zhang 2015-06-05 19:32:42 +10:00			`* [fintype](fintype/fintype.md) : finite types`
feat(library/data): update defaults and markdown files 2015-05-08 20:23:15 +10:00			`* [encodable](encodable.lean) : types with a coding to nat`