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Try doing some basic maths questions in the Lean Theorem Prover. Functions, real numbers, equivalence relations and groups. Click on README.md and then on "Open in CoCalc with one click".
Project: Xena
Views: 18536License: APACHE
/- Copyright (c) 2019 Robert Y. Lewis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robert Y. Lewis -/ /-! # Library notes At various places in mathlib, we leave implementation notes that are referenced from many other files. To keep track of these notes, we use the command `library_note`. This makes it easy to retrieve a list of all notes, e.g. for documentation output. An example from `meta.expr`: ``` library_note "open expressions" "Some declarations work with open expressions, i.e. an expr that has free variables. Terms will free variables are not well-typed, and one should not use them in tactics like `infer_type` or `unify`. You can still do syntactic analysis/manipulation on them. The reason for working with open types is for performance: instantiating variables requires iterating through the expression. In one performance test `pi_binders` was more than 6x quicker than `mk_local_pis` (when applied to the type of all imported declarations 100x)." ``` These notes can be referenced in mathlib with the syntax `Note [note id]`. Often, these references will be made in code comments (`--`) that won't be displayed in docs. If such a reference is made in a doc string or module doc, it will be linked to the corresponding note in the doc display. Since these notes are used in files imported by `tactic.core`, this file has no imports. ## Implementation details `library_note note_id note_msg` creates a declaration `` `library_note.i `` for some `i`. This declaration is a pair of strings `note_id` and `note_msg`, and it gets tagged with the `library_note` attribute. -/ /-- A rudimentary hash function on strings. -/ def string.hash (s : string) : ℕ := s.fold 1 (λ h c, (33*h + c.val) % unsigned_sz) /-- A user attribute `library_note` for tagging decls of type `string × string` for use in note output. -/ @[user_attribute] meta def library_note_attr : user_attribute := { name := `library_note, descr := "Notes about library features to be included in documentation" } open tactic /-- Creates a name to store `note_id`. -/ private meta def get_name_for (note_id : string) : name := `library_note <.> ("_" ++ to_string note_id.hash) /-- If `note_name` and `note` are `pexpr`s representing strings, `add_library_note note_name note` adds a declaration of type `string × string` and tags it with the `library_note` attribute. -/ meta def tactic.add_library_note (note_name note : pexpr) : tactic unit := do note_name ← to_expr note_name, note ← to_expr note, let decl_name := get_name_for (to_string note_name), body ← to_expr ``((%%note_name, %%note) : string × string), add_decl $ mk_definition decl_name [] `(string × string) body, library_note_attr.set decl_name () tt none open lean lean.parser interactive /-- A command to add library notes. Syntax: ``` library_note "note id" "note content" ``` -/ @[user_command] meta def library_note (_ : parse (tk "library_note")) : parser unit := do name ← parser.pexpr, note ← parser.pexpr, of_tactic $ tactic.add_library_note name note /-- Collects all notes in the current environment. Returns a list of pairs `(note_id, note_content)` -/ meta def tactic.get_library_notes : tactic (list (string × string)) := attribute.get_instances `library_note >>= list.mmap (λ dcl, mk_const dcl >>= eval_expr (string × string))