affeldt-aist / infotheo Goto Github PK

Ubuntu 20.04.2 LTS
Release: 20.04

opam --version
2.0.5

coqc --version
The Coq Proof Assistant, version 8.13.1 (March 2021)
compiled on Mar 8 2021 11:40:26 with OCaml 4.08.1

opam list mathcomp
Name Installed Synopsis
coq-mathcomp-algebra 1.12.0 Mathematical Components Library on Algebra
coq-mathcomp-analysis 0.3.6 An analysis library for mathematical components
coq-mathcomp-bigenough 1.0.0 A small library to do epsilon - N reasonning
coq-mathcomp-field 1.12.0 Mathematical Components Library on Fields
coq-mathcomp-fingroup 1.12.0 Mathematical Components Library on finite groups
coq-mathcomp-finmap 1.5.1 Finite sets, finite maps, finitely supported functions
coq-mathcomp-solvable 1.12.0 Mathematical Components Library on finite groups (II)
coq-mathcomp-ssreflect 1.12.0 Small Scale Reflection

Running:
git clone https://github.com/affeldt-aist/infotheo.git
cd infotheo
make

Outputs:
make -f Makefile.coq all
make[1]: Entering directory '/home/user/Documents/infotheo'
COQC lib/ssrR.v
File "./lib/ssrR.v", line 5, characters 29-36:
Error: Unable to locate library Rstruct with prefix mathcomp.

make[2]: *** [Makefile.coq:720: lib/ssrR.vo] Error 1
make[1]: *** [Makefile.coq:343: all] Error 2
make[1]: Leaving directory '/home/user/Documents/infotheo'
make: *** [Makefile:2: all] Error 2

Could anyone help to figure out and solve the issue?

As discussed in coq/opam#1003, it's usually a good idea to have a top-level Makefile that issues the critical coq_makefile command for a build. The main advantage is that users (and other build systems such as OPAM and Nix) need only issue make to build the project from scratch - and one can even change to another build approach based on, say, dune, without changing this build command.

The typical Coq project top-level Makefile currently looks as follows:

all: Makefile.coq
        +$(MAKE) -f Makefile.coq all

clean: Makefile.coq
        +$(MAKE) -f Makefile.coq cleanall
        rm -f Makefile.coq Makefile.coq.conf

Makefile.coq: _CoqProject
        coq_makefile -f _CoqProject -o Makefile.coq

_CoqProject Makefile: ;

%: Makefile.coq
        +$(MAKE) -f Makefile.coq $@

.PHONY: all clean

Note that this mostly just defers actions to the makefile generated by coq_makefile.

If this sounds like a good idea, I can make a pull request.

Because of this conflict, these two files cannot be imported at the same time.

TODO: b \in X -> b \in B, etc.

get rid of the big_enumP warnings that will become error with the next MathComp release

Dear infotheo authors, I want to point out that my co-authors and I have a paper on the formalization of bounds on the trimmed mean algorithm that uses infotheo. It has been accepted at PPDP this year (https://ppdp2021.github.io/#accepted, the paper is called "Trimming Data Sets: a Verified Algorithm for Robust Mean Estimation", soon to be available) and you can find the source code of the formalization here: https://github.com/ieva-itu/robustmean/blob/main/robustmean.v

We are thankful for the all the development of probability theory that we used in our paper, and we think you might appreciate some lemmas that should belong to infotheo more than our development.
As we are all novice Coq programmers and not used to the mathcomp style, I'd appreciate if you could take a look at the code and see whether you're interested in integrating it here, and maybe help us match the style of the infotheo package. This is also why I'm not making a pull request yet.

it has been merged into MathComp-Analysis

Rstruct.R_eqType and ssrR.R_eqType

Lemma eqRstruct_eqR (m n : R) : (m == n :> Rstruct.R_eqType) = (m == n :> ssrR.R_eqType).
Proof.
Fail reflexivity.
case/boolP: (m == n).
by move/eqP ->; rewrite eqxx.
by move/eqP=> H; apply esym; rewrite -/(is_true _); apply/eqP.
Qed.

@t6s

Should be Mixin @t6s

should be subR_le0

Since we're favoring a structure with an inequality in bool for prob, the constructor mk_ might turn out to be superfluous after all. Investigate its removal.

Cc: @t6s

I tried to build infotheo using make:

COQC ecc_modern/ldpc_algo.v
File "./ecc_modern/ldpc_algo.v", line 175, characters 0-76:
Error: ConstructiveCauchyReals.CReal is not an inductive type.

mulRV : forall x : R, x != 0 -> x * / x = 1
invRM : forall r1 r2 : R, r1 <> 0 -> r2 <> 0 -> / (r1 * r2) = / r1 * / r2

@t6s

The following expression fails to be parsed after importing both proba.v (infotheo) and probability.v (mathcomp-analysis):

Local Open Scope form_scope.
Variables (d : measure_display) (T : measurableType d) (R : realType) (P : probability T R).
Variable (X : {RV P >-> R}).

>>> Error: Syntax error: '->' expected after [term] (in [term]).

A similar reserved notation in proba.v seems to be confusing the parser:

Reserved Notation "{ 'RV' d -> T }" (at level 0, d, T at next level,
  format "{ 'RV'  d  ->  T }").

I experienced this issue when trying to use prob_lt0. The lemma takes as its argument _ : p != 0 and it did not match my goal because of a mismatch between two eqType structures.

One solution would be to change the interface of prob to

Module Prob.
Record t := mk_ {
  p :> R ;
  Op1 : (0 <b= p <b= 1)%R }.
Definition O1 (p : t) : 0 <= p <= 1 :=
  match andP (Op1 p) with conj Op p1 => conj (leRP _ _ Op) (leRP _ _ p1) end.
Arguments O1 : simpl never.
Definition mk (q : R) (Oq1 : 0 <= q <= 1) : t.
Proof.
refine (@mk_ q (match Oq1 with conj Oq q1 => _ end)).
by move/leRP: Oq ->; move/leRP: q1 ->.
Defined.
Module Exports.
Notation prob := t.
Notation "q %:pr" := (@mk q (@O1 _)).
Canonical prob_subType := Eval hnf in [subType for p].
Definition prob_eqMixin := [eqMixin of prob by <:].
Canonical prob_eqType := Eval hnf in EqType _ prob_eqMixin.
End Exports.
End Prob.
Export Prob.Exports.
Coercion Prob.p : prob >-> R.

This seems to almost work, but failing at inferring the canonical structure for onem.

Hi!
I am excited to see a formal proof lib for information theory!

If I manage to find the time, I will try to apply it to some proofs about multi-user identification.
Therefore I nixified this: https://github.com/jorsn/infotheo/tree/nixify.
The most recent build from there is also cached in my cachix cache (run cachix use jorsn).

If you are interested in using nix, I can create a PR and perhaps write a usage note for the README.
If not, feel free to close this issue.
Whether I can maintain the nix stuff (and add it to nixpkgs) depends on whether I will expect to really use it for longer.

ltR_subl_addr: forall x y z : R, x - y < z <-> x < z + y
ltr_subl_addl: forall x y z : R, x - y < z <-> x < y + z

@t6s

fdists are currently defined over the R type of the standard library. Some developments would like to rely on this library but use structures from the mathcomp library. So we would like to have them generalized (maybe to numFieldType).

"op" should not appear in the lemma name, there are other instance of this problem in this file

it looks like this lemma should better be in MathComp-Analysis' classical_sets.v file

this should be cleaned and PRed to MathComp...

also fix notation?

The definitions of conv_set and the convex operation for necset_convType are essentially the same.
We should prepare more lemmas for conv_set and make necset_convType rely on them.

(I'm working on this issue in conv_set branch.)

We are missing the following: definition of multiplication of random variables and ring structure for RVs.

Definition mul_RV (U : finType) (P : {fdist U}) (X Y : {RV P -> R}) : {RV P -> R} := fun x => X x * Y x.
Notation "X `* Y" := (mul_RV X Y) : proba_scope.
Arguments mul_RV /.

and

Section RV_ring.
Variables (U : finType) (P : fdist U).
Import topology.
Import GRing.Theory.

Lemma add_RV_addr (X Y : {RV P -> R}) : X `+ Y = (X + Y)%ring.
Proof. reflexivity. Qed.

Lemma sub_RV_subr (X Y : {RV P -> R}) : X `- Y = (X - Y)%ring.
Proof. reflexivity. Qed.

Lemma trans_min_RV_subr (X : {RV P -> R}) (y : R) :
  X `-cst y = (X - cst y)%ring.
Proof. reflexivity. Qed.
Definition fdist_supp_choice : U.
by move/set0Pn/xchoose:(fdist_supp_neq0 P).
Defined.

Canonical fdist_supp_pointedType :=
  @classical_sets.Pointed.pack U fdist_supp_choice _ _ idfun.

Lemma mul_RV_mulr (X Y : {RV P -> R}) : X `* Y = (X * Y)%ring.
Proof. reflexivity. Qed.

Lemma sq_RV_sqrr (X : {RV P -> R}) : X `^2 = (X ^+ 2)%ring.
Proof. by rewrite /sq_RV/comp_RV; apply boolp.funext => u /=; rewrite mulR1. Qed.

Definition RV_ringE :=
  (add_RV_addr, sub_RV_subr, trans_min_RV_subr, mul_RV_mulr, sq_RV_sqrr).
End RV_ring.

Ubuntu 20.04.2 LTS
Release: 20.04

opam --version
2.0.5

coqc --version
The Coq Proof Assistant, version 8.13.1 (March 2021)
compiled on Mar 8 2021 11:40:26 with OCaml 4.08.1

opam list mathcomp

Name Installed Synopsis
coq-mathcomp-algebra 1.12.0 Mathematical Components Library on Algebra
coq-mathcomp-analysis 0.3.6 An analysis library for mathematical components
coq-mathcomp-bigenough 1.0.0 A small library to do epsilon - N reasonning
coq-mathcomp-field 1.12.0 Mathematical Components Library on Fields
coq-mathcomp-fingroup 1.12.0 Mathematical Components Library on finite groups
coq-mathcomp-finmap 1.5.1 Finite sets, finite maps, finitely supported functions
coq-mathcomp-solvable 1.12.0 Mathematical Components Library on finite groups (II)
coq-mathcomp-ssreflect 1.12.0 Small Scale Reflection

Running:
opam repo add coq-released https://coq.inria.fr/opam/released
opam install coq-infotheo

Outputs:

``
The following actions will be performed:
∗ install coq-infotheo 0.3.1

<><> Gathering sources ><><><><><><><><><><><><><><><><><><><><><><><><><><><><>
[coq-infotheo.0.3.1] found in cache

<><> Processing actions <><><><><><><><><><><><><><><><><><><><><><><><><><><><>
[ERROR] The compilation of coq-infotheo failed at "/home/user/.opam/opam-init/hooks/sandbox.sh build make -j1".

#=== ERROR while compiling coq-infotheo.0.3.1 =================================#
# context 2.0.5 | linux/x86_64 | ocaml-base-compiler.4.11.1 | https://coq.inria.fr/opam/released#2021-03-22 11:00
# path ~/.opam/with-coq/.opam-switch/build/coq-infotheo.0.3.1
# command ~/.opam/opam-init/hooks/sandbox.sh build make -j1
# exit-code 2
# env-file ~/.opam/log/coq-infotheo-51929-d2c37b.env
# output-file ~/.opam/log/coq-infotheo-51929-d2c37b.out
### output ###
# [...]
# Warning: filter_index_enum is deprecated; use big_enumP instead
# Warning: filter_index_enum is deprecated; use big_enumP instead
# Warning: filter_index_enum is deprecated; use big_enumP instead
# COQC toy_examples/expected_value_variance.v
# COQC toy_examples/expected_value_variance_ordn.v
# COQC toy_examples/expected_value_variance_tuple.v
# COQC toy_examples/conditional_entropy.v
# Killed
# make[2]: *** [Makefile.coq:720: toy_examples/conditional_entropy.vo] Error 137
# make[1]: *** [Makefile.coq:343: all] Error 2
# make[1]: Leaving directory '/home/user/.opam/with-coq/.opam-switch/build/coq-infotheo.0.3.1'
# make: *** [Makefile:2: all] Error 2

<><> Error report <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>
┌─ The following actions failed
│ λ build coq-infotheo 0.3.1
└─
╶─ No changes have been performed
# Run eval $(opam env) to update the current shell environment

``
Could anyone help to figure out and solve the issue?

mention that make is actually gmake in the readme

Prob.ge0 should be placed outside Module Prob and named prob_ge0.

rename convex_choice.v to convex.v @t6s

@t6s @garrigue

is lacking a space to print correctly