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chore(library/library.md): update documentation

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Leonardo de Moura 2017-08-16 14:17:26 -07:00
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README.md
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@ -17,7 +17,7 @@ About
- [Homepage](http://leanprover.github.io)
- [Theorem Proving in Lean](https://leanprover.github.io/theorem_proving_in_lean/index.html)
- [Standard Library](library/library.md)
- [Core library](library/library.md)
- [Emacs Mode](src/emacs/README.md)
- [Change Log](doc/changes.md)
- For HoTT mode, please use [Lean2](https://github.com/leanprover/lean2).

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library/library.md
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@ -1,20 +1,12 @@
The Lean Standard Library
The Lean Core Library
=========================
(This documentation is partially out-of-date.)
The Lean standard library is contained in the following files and directories:
The Lean core library is contained in the following files and directories:
* [init](init/) : constants and theorems needed for low-level system operations
* [init/logic.lean](init/logic.lean) : logical constructs and axioms
* [init/data](init/data/) : concrete datatypes and type constructors
* [init/algebra](init/algebra/) : algebraic structures
* [tools](tools/) : additional tools
The files in `init` are loaded by default, and hence do not need to be
imported manually. Other files can be imported individually, but the
following is designed to load most of the standard library:
* [standard](standard.lean) : constructive logic and datatypes
Lean's default logical framework is a version of the Calculus of
Constructions with:
@ -25,7 +17,7 @@ Constructions with:
* inductively defined types
* quotient types
Most of the `standard` library does not rely on any axioms beyond this
Most of the `core` library does not rely on any axioms beyond this
framework, and is hence fully constructive.
The following additional axioms are defined in `init`:
@ -38,12 +30,5 @@ excluded middle is derived from Hilbert choice. For Hilbert choice and
excluded middle, use `open classical`. The additional axioms are used
sparingly. For example:
* The constructions of finite sets and the rationals use quotients.
* The set library uses propext and funext, as well as excluded middle to prove
some classical identities.
* Hilbert choice is used to define the multiplicative inverse on the reals, and
also to define function inverses classically.
You can use `#print axioms foo` to see which axioms `foo` depends
on. Many of the theories in the `theories` folder are unreservedly
classical.
on.