Skip to content

FormaSys kick‐off meeting topics

Cyril Cohen edited this page May 19, 2025 · 29 revisions

Topics and people interested

FormaSys

Yoshihiro

Jacques

  • link between monae and mca

Holger

  • ODE solving and integration of MCA in his dev
  • Mathcomp without deceq or with various levels of classicality

Reynald

  • Porting the inverted pendulum
  • Complex analysis and type inference issues
  • HB missing commands -> change of structures
  • QBS

Lucie

  • using trocq to change datatypes, e.g. reals or tuples

Quentin

  • HB change of structures
  • Remove articifial dependencies in classical axioms

Samy

Enrico

  • HB improvements

Yves

  • refinements of trajectories
  • proof that:
    • the paths do not have collisions
    • Dijstra algorithm
  • refinements with monads

Takafumi

  • complex analysis
  • manifolds
  • HB change of subject by application

Guillaume

  • available on Friday morning to formalize stuff
  • formalization of probabilistic semantics
  • long term goals: prove compiler passes
  • equivalence between kernel based and density based semantics
  • QBS and ωPAP spaces

Kazuhiko

  • Question: mathcomp school collocated with FormaSys?
  • Applications of relational parametricity
    • re-implementation of the internals of algebra tactics package: polynomials with commutative and non-commutative variables
    • cache the results of conversion

Working groups (Monday)

Group A (316 Centre)

Participants:

  • Holger
  • Yoshihiro
  • Quentin
  • Reynald
  • (Cyril)

Topics:

  • ODE solving and integration with MCA

Group B (Room M7)

Participants

  • Jacques
  • Lucie
  • Yves
  • Takafumi
  • (Kazuhiko)
  • (Cyril)

Topics:

  • Trocq for refinements to monadic programs

Tentative Working groups

Group C (From Tuesday)

Topics: Complex Analysis

Group B (From Thursday)

Participants:

  • Cyril (talk)
  • Kazuhiko
  • Reynald
  • Jacques
  • Lucie
  • Takafumi

Topics:

  • Trocq for mathcomp and MCA

Group

Topics

ODE solving and integration with MCA

Schedule:

Participants:

  • Holger
  • Yoshihiro
  • Quentin
  • (Cyril)

Trocq for refinements to monadic programs

Goals:

  • Algorithm refinement using naive functions
  • Data refinements to substitute naive functions with projections of a record.
  • Example: Fibonacci

Schedule:

Participants:

  • Jacques
  • Lucie
  • Yves
  • Takafumi
  • (Kazuhiko)
  • (Cyril)

Trocq for mathcomp and MCA

Goal:

  • change reals to canonical reals (see categoricity)[https://github.com/rocq-community/fourcolor/tree/master/theories/reals]
  • row vectors to tuples
  • polynomials of bounded size ⊂ polynomials

Schedule:

Participants:

  • Cyril (talk)
  • Kazuhiko
  • Reynald
  • Jacques
  • Lucie
  • Takafumi

HB

HB change of subject

Time constraints: from Wednesday

Participants:

  • Kazuhiko
  • Quentin
  • Enrico
  • Reynald
  • (Cyril)

Just wants to see the results:

  • Takafumi (PR review)

Program:

  1. State of affairs

Complete redesign HB commands

Goal: deprecate mixin and factory keywords, provide one go structure declaration

  • (Cyril)
  • Enrico
  • Lucie

Alias/tag usage for overlapping instances

Goals:

  • FAQ and doc of current users

  • Rethink how to infer alternative instances

  • Jacques

  • Takafumi

  • Reynald

  • (Cyril)

  • Kazuhiko

Lyapounov functions revival

  • (Reynald)
  • (Cyril)

Complex analysis

TODO: Schedule a meeting with Marie

Participants:

  • Reynald
  • Takafumi
  • Quentin
  • (Cyril)

Subtopic:

  • Manifolds

Topic queue

Merging Giry monads from MCA#1608 and Monae

Goals: comment on PR

Remark: better fitted for MC sharing days

TBD

  • Takafumi
  • Reynald
  • (Cyril)

Constructivising Mathcomp

Goal:

  • making decidable equality optional

  • adding various degrees of classicality (e.g. choice)

  • (Cyril)

  • Holger

  • (Quentin)

  • (Takafumi)

Quasi-Borel Spaces and ωPAP Spaces

Time constraints: Friday morning

  • Guillaume
  • Reynald
  • Yoshihiro
  • Takafumi
  • (Cyril)

Former contents

Complex analysis

  • Cyril
  • Reynald
  • Takafumi
  • Quentin

Drafting HB missing subject-change related commands

  • Cyril
  • Pierre
  • Reynald
  • Kazuhiko
  • Enrico
  • Quentin

Porting the inverted pendulum to mathcomp 2

  • Cyril
  • Reynald

Proving trajectories correct

  • Yves
  • Takafumi (especially the convexity part)

Important information is that the proof of correctness for the vertical cell decomposition algorithm is now complete. At this stage, it should be easy to show the two following facts:

  • every segment where both extremities are strictly inside the same cell is safe
  • every triangle with one point in one cell and one point in an adjacent cell, and the two segments intersecting with the same door is safe.

Refinements with imperative features.

LRA without Stdlib

  • Pierre

Parametricity and its consequences: free theorems, refinements, and induction principles

  • Kazuhiko
    • I can describe the recent version of A bargain for mergesorts (NB: the publicly-available preprint is outdated), which exploits a case where parametricity implies naturality (which is also an instance of free theorems) and the fact that parametricity implies induction principles on Church-encoded datatypes (which is perhaps related to the derive plugin of Rocq-Elpi).
    • I plan to establish RocqEAL-style refinements for commutative and non-commutative polynomials in monalg.v of multinomials, derive a reflexive decision procedure for non-commutative (semi)algebras over commutative (semi)rings (by exploiting the fact that mixed commutative and non-commutative polynomials are isomorphic to non-commutative polynomials over commutative polynomials), and later extend it to non-square matrices over commutative (semi)rings using untyping theorems
  • Enrico

Union-find based caching mechanism for conversion in reification in Rocq-Elpi

The idea is to reduce the calls of coq.unify-eq (and thus readback). It shouldn't be hard to implement, but the challenge would be not compromising the readability and maintainability of reification procedures, as we need to pass around the state. There is a related open issue of Algebra Tactics.

  • Kazuhiko
  • Enrico
    • how does this compare to tabling?
      • KS: The advantage of union-find is that it computes the symmetric and transitive closure of the set of known equations. Perhaps, we should try tabling first since it 1) looks like a lightweight yet very effective approach and 2) has the advantage that it automatically caches disequations.

Monads in mathcomp analysis

  • Jacques
  • Reynald
  • Cyril
  • Takafumi

Attending (please complete)

  • Cyril (whole week)
  • Pierre (Wed, Thu, Fri)
  • Yves (Mon, Tue, Wed)
  • Kazuhiko (whole week)
  • Reynald (whole week)
  • Holger (whole week)
  • Enrico (mon, tue, wed)
  • Jacques (whole week)
  • Quentin (whole week)
  • Takafumi (whole week)
Clone this wiki locally