Commit 61761244 authored by Pierre Letouzey's avatar Pierre Letouzey
Browse files

Explicit license : CC0

parent 6132f13b
(** Alternative definitions of substs and alpha for named formulas *)
(** * Alternative definitions of substs and alpha for named formulas *)
(** The NatDed development, Pierre Letouzey, 2019.
This file is released under the CC0 License, see the LICENSE file *)
Require Import Defs NameProofs Nam.
Import ListNotations.
......
(** Equivalence between various substs and alpha for named formulas *)
(** * Equivalence between various substs and alpha for named formulas *)
(** The NatDed development, Pierre Letouzey, 2019.
This file is released under the CC0 License, see the LICENSE file *)
Require Import Defs NameProofs Nam Alpha Meta Equiv.
Import ListNotations.
......
(** * Ordering the Ascii datatype *)
(** The NatDed development, Pierre Letouzey, 2019.
This file is released under the CC0 License, see the LICENSE file *)
Require Import Bool Ascii BinNat Orders OrdersEx.
Local Open Scope char_scope.
......
Creative Commons Legal Code
CC0 1.0 Universal
CREATIVE COMMONS CORPORATION IS NOT A LAW FIRM AND DOES NOT PROVIDE
LEGAL SERVICES. DISTRIBUTION OF THIS DOCUMENT DOES NOT CREATE AN
ATTORNEY-CLIENT RELATIONSHIP. CREATIVE COMMONS PROVIDES THIS
INFORMATION ON AN "AS-IS" BASIS. CREATIVE COMMONS MAKES NO WARRANTIES
REGARDING THE USE OF THIS DOCUMENT OR THE INFORMATION OR WORKS
PROVIDED HEREUNDER, AND DISCLAIMS LIABILITY FOR DAMAGES RESULTING FROM
THE USE OF THIS DOCUMENT OR THE INFORMATION OR WORKS PROVIDED
HEREUNDER.
Statement of Purpose
The laws of most jurisdictions throughout the world automatically confer
exclusive Copyright and Related Rights (defined below) upon the creator
and subsequent owner(s) (each and all, an "owner") of an original work of
authorship and/or a database (each, a "Work").
Certain owners wish to permanently relinquish those rights to a Work for
the purpose of contributing to a commons of creative, cultural and
scientific works ("Commons") that the public can reliably and without fear
of later claims of infringement build upon, modify, incorporate in other
works, reuse and redistribute as freely as possible in any form whatsoever
and for any purposes, including without limitation commercial purposes.
These owners may contribute to the Commons to promote the ideal of a free
culture and the further production of creative, cultural and scientific
works, or to gain reputation or greater distribution for their Work in
part through the use and efforts of others.
For these and/or other purposes and motivations, and without any
expectation of additional consideration or compensation, the person
associating CC0 with a Work (the "Affirmer"), to the extent that he or she
is an owner of Copyright and Related Rights in the Work, voluntarily
elects to apply CC0 to the Work and publicly distribute the Work under its
terms, with knowledge of his or her Copyright and Related Rights in the
Work and the meaning and intended legal effect of CC0 on those rights.
1. Copyright and Related Rights. A Work made available under CC0 may be
protected by copyright and related or neighboring rights ("Copyright and
Related Rights"). Copyright and Related Rights include, but are not
limited to, the following:
i. the right to reproduce, adapt, distribute, perform, display,
communicate, and translate a Work;
ii. moral rights retained by the original author(s) and/or performer(s);
iii. publicity and privacy rights pertaining to a person's image or
likeness depicted in a Work;
iv. rights protecting against unfair competition in regards to a Work,
subject to the limitations in paragraph 4(a), below;
v. rights protecting the extraction, dissemination, use and reuse of data
in a Work;
vi. database rights (such as those arising under Directive 96/9/EC of the
European Parliament and of the Council of 11 March 1996 on the legal
protection of databases, and under any national implementation
thereof, including any amended or successor version of such
directive); and
vii. other similar, equivalent or corresponding rights throughout the
world based on applicable law or treaty, and any national
implementations thereof.
2. Waiver. To the greatest extent permitted by, but not in contravention
of, applicable law, Affirmer hereby overtly, fully, permanently,
irrevocably and unconditionally waives, abandons, and surrenders all of
Affirmer's Copyright and Related Rights and associated claims and causes
of action, whether now known or unknown (including existing as well as
future claims and causes of action), in the Work (i) in all territories
worldwide, (ii) for the maximum duration provided by applicable law or
treaty (including future time extensions), (iii) in any current or future
medium and for any number of copies, and (iv) for any purpose whatsoever,
including without limitation commercial, advertising or promotional
purposes (the "Waiver"). Affirmer makes the Waiver for the benefit of each
member of the public at large and to the detriment of Affirmer's heirs and
successors, fully intending that such Waiver shall not be subject to
revocation, rescission, cancellation, termination, or any other legal or
equitable action to disrupt the quiet enjoyment of the Work by the public
as contemplated by Affirmer's express Statement of Purpose.
3. Public License Fallback. Should any part of the Waiver for any reason
be judged legally invalid or ineffective under applicable law, then the
Waiver shall be preserved to the maximum extent permitted taking into
account Affirmer's express Statement of Purpose. In addition, to the
extent the Waiver is so judged Affirmer hereby grants to each affected
person a royalty-free, non transferable, non sublicensable, non exclusive,
irrevocable and unconditional license to exercise Affirmer's Copyright and
Related Rights in the Work (i) in all territories worldwide, (ii) for the
maximum duration provided by applicable law or treaty (including future
time extensions), (iii) in any current or future medium and for any number
of copies, and (iv) for any purpose whatsoever, including without
limitation commercial, advertising or promotional purposes (the
"License"). The License shall be deemed effective as of the date CC0 was
applied by Affirmer to the Work. Should any part of the License for any
reason be judged legally invalid or ineffective under applicable law, such
partial invalidity or ineffectiveness shall not invalidate the remainder
of the License, and in such case Affirmer hereby affirms that he or she
will not (i) exercise any of his or her remaining Copyright and Related
Rights in the Work or (ii) assert any associated claims and causes of
action with respect to the Work, in either case contrary to Affirmer's
express Statement of Purpose.
4. Limitations and Disclaimers.
a. No trademark or patent rights held by Affirmer are waived, abandoned,
surrendered, licensed or otherwise affected by this document.
b. Affirmer offers the Work as-is and makes no representations or
warranties of any kind concerning the Work, express, implied,
statutory or otherwise, including without limitation warranties of
title, merchantability, fitness for a particular purpose, non
infringement, or the absence of latent or other defects, accuracy, or
the present or absence of errors, whether or not discoverable, all to
the greatest extent permissible under applicable law.
c. Affirmer disclaims responsibility for clearing rights of other persons
that may apply to the Work or any use thereof, including without
limitation any person's Copyright and Related Rights in the Work.
Further, Affirmer disclaims responsibility for obtaining any necessary
consents, permissions or other rights required for any use of the
Work.
d. Affirmer understands and acknowledges that Creative Commons is not a
party to this document and has no duty or obligation with respect to
this CC0 or use of the Work.
(** * Explicit enumeration of countable types *)
(** The NatDed development, Pierre Letouzey, 2019.
This file is released under the CC0 License, see the LICENSE file *)
Require Import Ascii NArith Defs Mix NameProofs Meta.
Import ListNotations.
Local Open Scope bool_scope.
......
(** * Initial definitions for Natural Deduction *)
(** The NatDed development, Pierre Letouzey, 2019.
This file is released under the CC0 License, see the LICENSE file *)
Require Export Setoid Morphisms RelationClasses Arith Omega Bool String
MSetRBT StringOrder List Utils.
Require DecimalString.
......@@ -31,7 +36,11 @@ Bind Scope string_scope with name.
(** Signatures *)
(** Just in case, a signature that could be infinite *)
(** A signature is a set of function symbols and predicate symbols
(with their arities). These sets are usually finite, but we'll
use an infinite signature at least once (during the proof of
the completeness theorem).
Note : Functions of arity zero are also called constants. *)
Definition function_symbol := name.
Definition predicate_symbol := name.
......@@ -45,7 +54,7 @@ Record signature :=
{ funsymbs : function_symbol -> option arity;
predsymbs : predicate_symbol -> option arity }.
(** A finite version *)
(** A finite version (using lists) *)
Module Finite.
......@@ -118,9 +127,6 @@ Fixpoint fresh_loop (names:Names.t) (id:string) n : variable :=
Definition fresh names := fresh_loop names "x" (Names.cardinal names).
(* Compute fresh (Names.add "x" (Names.add "y" (Names.singleton "xx"))). *)
(** Misc types : operators, quantificators *)
Inductive op := And | Or | Impl.
......
(** Conversion from Named formulas to Locally Nameless formulas *)
(** * Conversion from Named formulas to Locally Nameless formulas *)
(** The NatDed development, Pierre Letouzey, 2019.
This file is released under the CC0 License, see the LICENSE file *)
Require Import Defs NameProofs.
Require Nam Mix.
......
(** Conversion from Named derivations to Locally Nameless derivations *)
(** * Conversion from Named derivations to Locally Nameless derivations *)
(** The NatDed development, Pierre Letouzey, 2019.
This file is released under the CC0 License, see the LICENSE file *)
Require Import RelationClasses Arith Omega.
Require Import Defs NameProofs Equiv Alpha Alpha2 Meta.
......
This NatDed development is free software: you can redistribute
it and/or modify it under the terms of the Creative Commons Zero 1.0
License (CC0 1.0).
This work is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY to the greatest extent permissible under
applicable law. See the CC0 1.0 for more details.
You should have received a copy of the CC0 1.0 License along with
this library (see file COPYING). If not, see
<https://creativecommons.org/publicdomain/zero/1.0/legalcode>
-- Pierre Letouzey, 2019
\ No newline at end of file
(** Some Meta-properties (proved on the Mix encoding) *)
(** * Some meta-properties of the Mix encoding *)
(** The NatDed development, Pierre Letouzey, 2019.
This file is released under the CC0 License, see the LICENSE file *)
Require Import Defs NameProofs Mix.
Import ListNotations.
......
(** Natded again, with a Locally Nameless encoding *)
(** * Natural deduction, with a Locally Nameless encoding *)
(** The NatDed development, Pierre Letouzey, 2019.
This file is released under the CC0 License, see the LICENSE file *)
Require Import Defs.
Require DecimalString.
......
(** * Models of theories *)
(** The NatDed development, Pierre Letouzey, 2019.
This file is released under the CC0 License, see the LICENSE file *)
Require Import Eqdep_dec Defs Mix NameProofs Meta Theories PreModels.
Import ListNotations.
Local Open Scope bool_scope.
......
(** * Natded : a toy implementation of Natural Deduction *)
(** Pierre Letouzey, © 2019-today *)
(** A signature : a list of function symbols (with their arity)
and a list of predicate symbols (with their arity).
Functions of arity zero are also called constants.
Note : in theory a signature could be infinite and hence not
representable by some lists, but we'll never do this in practice.
*)
(** The NatDed development, Pierre Letouzey, 2019.
This file is released under the CC0 License, see the LICENSE file *)
Require Import Defs.
Require DecimalString.
......
(** * Proofs about name sets *)
(** The NatDed development, Pierre Letouzey, 2019.
This file is released under the CC0 License, see the LICENSE file *)
Require Import Ascii MSetFacts MSetProperties StringUtils Defs.
Local Open Scope bool_scope.
Local Open Scope lazy_bool_scope.
......
(** * Pre-models of theories *)
(** The NatDed development, Pierre Letouzey, 2019.
This file is released under the CC0 License, see the LICENSE file *)
Require Import Defs Mix NameProofs Meta.
Import ListNotations.
Local Open Scope bool_scope.
......@@ -6,6 +12,12 @@ Local Open Scope eqb_scope.
Set Implicit Arguments.
(** A pre-model (also called a Σ-structure) is a non-empty domain M
alongside some interpretations for function symbols and predicate
symbols. For a full model of a theorie, we'll need the axioms
of the theories, and the facts that their interpretations are
valid. *)
Fixpoint arity_fun A n B :=
match n with
| O => B
......@@ -29,10 +41,6 @@ Record PreModel (M:Type)(sign:signature) :=
predsOk : forall s, sign.(predsymbs) s = get_arity (preds s)
}.
(** A premodel is also called a Σ-structure. For a full model
of a theorie, we'll need the axioms of the theories, and
the facts that their interpretations are valid. *)
(** Note: actually, we're not using [sign], [funsOk], [predsOK]
anywhere in this file (yet?) !! *)
......
(** * Ordering of the String datatype *)
(** The NatDed development, Pierre Letouzey, 2019.
This file is released under the CC0 License, see the LICENSE file *)
Require Import Bool Orders Ascii AsciiOrder String.
Local Open Scope string_scope.
......
(** * Utilities about the String datatypes *)
(** The NatDed development, Pierre Letouzey, 2019.
This file is released under the CC0 License, see the LICENSE file *)
Require Import Ascii String.
Local Open Scope string_scope.
......
(** Notion of 1st order theories *)
(** * First-order theories *)
(** The NatDed development, Pierre Letouzey, 2019.
This file is released under the CC0 License, see the LICENSE file *)
Require Import Defs NameProofs Mix Meta Countable.
Import ListNotations.
......
(** * Utilities : boolean equalities, list operators, ... *)
(** The NatDed development, Pierre Letouzey, 2019.
This file is released under the CC0 License, see the LICENSE file *)
Require Import Bool Arith Omega Ascii String AsciiOrder StringOrder List.
Import ListNotations.
Open Scope lazy_bool_scope.
......@@ -24,7 +30,7 @@ Proof.
reflexivity.
Qed.
(** A bit of overloading of notations (via Coq Classes) *)
(** Generic boolean equalities (via Coq Classes) *)
Delimit Scope eqb_scope with eqb.
Local Open Scope eqb_scope.
......@@ -73,6 +79,7 @@ Proof.
- apply eqb_neq. auto.
Qed.
(** List stuff *)
Fixpoint list_assoc {A B}`{Eqb A} x (l:list (A*B)) :=
match l with
......
Markdown is supported
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment