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Contribution Guide for the mathcomp-analysis library (WIP)

The purpose of this file is to document coding styles to be used when contributing to mathcomp-analysis. It comes as an addition to mathcomp's contribution guide.

Policy for Pull Requests

Always submit a pull request for code and wait for the CI to pass before merging. Text markup files may be edited directly though, should you have commit rights.

--> vs. cvg vs. lim

  • F --> x means F tends to x. This is the preferred way of stating a convergence. Lemmas about it use the string cvg.
  • lim F is the limit of F, it makes sense only when F converges and defaults to a distinguished point otherwise. It should only be used when there is no other expression for the limit. Lemmas about it use the string lim.
  • cvg F is defined as F --> lim F, and is equivalent through cvgP and cvg_ex to the existence of some x such that F --> x. When the limit is known, F --> x should be preferred. Lemmas about it use the string is_cvg.

near tactics vs. filterS, filterS2, filterS3 lemmas

When dealing with limits, mathcomp-analysis favors filters phrasing, as in

\forall x \near \oo, P x.

In the presence of such goals, the near tactics can be used to recover epsilon-delta reasoning (see this paper).

However, when the proof does not require changing the epsilon it is might be worth using filter combinators, i.e. lemmas such as

filterS : forall T (F : set (set T)), Filter F -> forall P Q : set T, P `<=` Q -> F P -> F Q

and its variants (filterS2, filterS3, etc.).

Landau notations

Landau notations can be written in four shapes:

  • f =o_F e (i.e. functional with a simple right member, thus a binary notation)
  • f = g +o_F e (i.e. functional with an additive right member, thus ternary)
  • f x =o_(x \near F) (e x) (i.e. pointwise with a simple right member, thus binary)
  • f x = g x +o_(x \near F) (e x) (i.e. pointwise with an additive right member, thus ternary)

The outcome is an expression with the normal Leibniz equality = and term 'o_F which is not parsable. See this paper for more explanation and the header of the file landau.v.

Deprecation

Deprecations are introduced for breaking changes. For a simple renaming, the pattern is:

#[deprecated(since="analysis X.Y.Z", note="Use new_definition instead.")]
Notation old_definition := new_definition (only parsing).

Note that this needs to be at the top-level (i.e., not inside a section).

When a lemma lem is scheduled for deletion, it ought better be renamed __deprecated__lem (so that it can be blacklisted). The deprecation command then becomes:

#[deprecated(since="analysis X.Y.Z", note="Use another_lemma instead.")]
Notation lem := __deprecated__lem (only parsing).

The (only parsing) format is needed so that Coq does not print back the deprecated name (for example when displaying error messages, that would be confusing).

Naming convention

homo and mono notations

Statements of {homo ...} or {mono ...} shouldn't be named after homo, or mono (just as for {morph ...} lemmas). Instead use the head of the unfolded statement (for homo) or the head of the LHS of the equality (for mono), as in

Lemma le_contract : {mono contract : x y / (x <= y)%O}.

When a {mono ...} lemma subsumes {homo ...}, it gets priority for the short name, and, if really needed, the corresponding {homo ...} lemma can be suffixed with W. If the {mono ...} lemma is only valid on a subdomain, then the {homo ...} lemma takes the short name, and the {mono ...} lemma gets the suffix in.

Suffixes for names of lemmas

  • The construction _ !=set0 corresponds to suffix nonempty
  • The construction _ != set0 corresponds to suffix neq0