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# Iris proof style
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**Warning:** this document is still in development and rather incomplete.
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If you run across a question of style (for example, something comes
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up in an MR) and it's not on this list, please do reach out to us on Mattermost
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so we can add it.
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## Basic syntax
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### Binders
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**Good:** `(a : B)`
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**Bad:** `(a:B)`, `(a: B)`
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**TODO**: Prefer `(a : B)` to `a : B`
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This applies to Context, Implicit Types, and definitions
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### Unicode
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Always use Unicode variants of forall, exists, ->, <=, >=
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**Good:** `∀ ∃ → ≤ ≥`
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**Bad:** `forall exists -> <= >=`
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### Equivalent vernacular commands
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Use `Context`, never `Variable`
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**TODO:** Use `Implicit Types`, never `Implicit Type`
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Use `Lemma`, not `Theorem` (or the other variants: `Fact`, `Corollary`,
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`Remark`)
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**TODO:** Always add `Global` or `Local` to `Hint`, `Arguments`, and `Instance`.
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### Ltac
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We prefer `first [ t1 | fail 1 "..." ]` to `t1 || fail "..."` because the latter will fail if `t1` doesn't make progress. See https://gitlab.mpi-sws.org/iris/iris/-/issues/216. Note that `first [ t1 | fail "..."]` is simply incorrect; the failure message will never show up and will be replaced with a generic failure.
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### Coqdoc comments
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Module-level comments (covering the entire file) go at the top of the file, before the `Require`.
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### Uncategorized
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Indent the body of a match by one space:
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**Good:**
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```coq
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match foo with
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| Some x =>
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long line here using
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```
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*RJ*: This is odd, usually everything is in (multiples of) 2 spaces, I think.
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*Tej*: https://gitlab.mpi-sws.org/iris/iris/-/blob/920bc3d97b8830139045e1780f2aff4d05b910cd/iris_heap_lang/proofmode.v#L194
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Avoid using the extra square brackets around an Ltac match:
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**Good:**
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```coq
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match goal with
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| |- ?g => idtac g
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```
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**Bad:**
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```coq
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match goal with
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| [ |- ?g ] => idtac g
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```
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Use coqdoc syntax in comments for Coq identifiers and inline code, e.g. `[cmraT]`
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Put proofs either all on one line (`Proof. reflexivity. Qed.`) or split up the usual way with indentation.
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**Bad:**
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```coq
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Lemma foo : 2 + 2 = 4 ∧ 1 + 2 = 3.
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Proof. split.
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- reflexivity.
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- done.
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Qed.
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```
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Put the entire theorem statement on one line or one premise per line, indented by 2 spaces.
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**Bad:**
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```coq
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Lemma foo x y z :
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x < y → y < z →
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x < z.
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```
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**Good:**
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```coq
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Lemma foo x y z : x < y → y < z → x < z.
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```
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**Good:** (particularly if premises are longer)
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```coq
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Lemma foo x y z :
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x < y →
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y < z →
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x < z.
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```
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If the parameters before the `:` become too long, indent later lines by 4 spaces and always have a newline after `:`:
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**Bad:**
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```coq
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Lemma foo (very_long_name : has_a_very_long_type)
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(even_longer_name : has_an_even_longer_type) : x < y → y < z →
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x < z.
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```
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**Good:**
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```coq
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Lemma foo (very_long_name : has_a_very_long_type)
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(even_longer_name : has_an_even_longer_type) :
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x < y → y < z → x < z.
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```
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For definitions that don't fit into one line, put `:=` before the linebreak, not after.
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**Bad:**
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```coq
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Definition foo (arg1 arg2 arg3 : name_of_the_type)
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:= the body that is very long.
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```
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**Good:**
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```coq
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Definition foo (arg1 arg2 arg3 : name_of_the_type) :=
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the body that is very long.
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```
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**TODO:** Use `"[H1 H2]"` when possible otherwise do `"(H1 & H2 & H3)"`
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For tests with output put `Check "theorem name in a string"` before it so that the output from different tests is separated.
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For long `t1; t2; t3` and `t; [t1 | t2 | t3]` split them like this, and indent by 2 spaces:
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**Good:**
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```coq
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t;
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[t1
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|t2
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|t3].
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```
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```coq
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t;
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t1;
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t2.
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```
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**TODO:** Keep all `Require`, `Import` and `Export` at the top of the file.
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## File organization
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theories/algebra is for primitive ofe/RA/CMRA constructions
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theories/algebra/lib is for derived constructions
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theories/base_logic/lib is for constructions in the base logic (using own)
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## Naming
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* `*_ctx` for persistent facts (often an invariant) needed by everything in a library
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* `*_interp` for a function from some representation to iProp
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* If you have lemma `foo` which is an iff and you want single direction versions, name them `foo_1` (forward) and `foo_2` (backward)
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* If you have a lemma `foo` parametrized by an equivalence relation, you might want a version specialized to Leibniz equality for better rewrite support; name that version `foo_L` and state it with plain equality (e.g., `dom_empty_L` in stdpp). You might take an assumption `LeibnizEquiv A` if the original version took an equivalence (say the OFE equivalence) to assume that the provided equivalence is plain equality.
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* Lower-case theorem names, lower-case types, upper-case constructors
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* **TODO:** how should `f (g x) = f' (g' x)` be named?
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* `list_lookup_insert` is named by context (the type involved), then the two functions outside-in on the left-hand-side, so it has the type `lookup (insert …) = …` where the `insert` is on a list. Notations mean it doesn’t actually look like this and the insert is textually first.
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* Injectivity theorems are instances of `Inj` and then are used with `inj`
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* Suffixes `_l` and `_r` when we have binary `op x y` and a theorem related to the left or right. For example, `sep_mono_l` says bi_sep is monotonic in its left argument (holding the right constant).
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* Entailments at the top level are typically written `P -* Q`, which is notation
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for `P ⊢ Q`. If you have a theorem which has no premises you have to write ⊢ P
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explicitly (for example, it is common to have `⊢ |==> ∃ γ, …` for an allocation
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theorem)
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* Suffix `'` (prime) is used when `foo'` is a corollary of `foo`. Try to avoid
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these since the name doesn't convey how `foo'` is related to `foo`.
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* Given a polymorphic function/relation `f` (e.g., `eq`, `equiv`, `subseteq`), the instance of type `A` is called `A_f_instance`, and we add a lemma `A_f` that characterizes the instance. In case of many instances, this lemma is proved by unfolding the definition of the instance, e.g., `frac_op`, `frac_valid`. However, in some cases, e.g., `list_eq`, `map_eq`, `set_eq` this lemma might require non-trivial proof work.
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* For lemmas involving modalities, we usually follow this naming scheme:
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```
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M1_into_M2: M1 P ⊢ M2 P
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M1_M2_elim: M1 (M2 P) ⊣⊢ M1 P
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M1_elim_M2: M1 (M2 P) ⊣⊢ M2 P
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M1_M2: M1 (M2 P) ⊣⊢ M2 (M1 P)
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```
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### Naming algebra libraries
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**TODO:** describe any conclusions we came to with the `mono_nat` library
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## Parameter order and implicitness for lemmas
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* Parameter order is usually from more higher-order to less higher-order (types, functions, plain values), and otherwise follows the order in which variables appear in the lemma statement.
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* In new lemmas, arguments should be marked as implicit when they can be inferred by unification in all intended usage scenarios. (If an argument can *sometimes* be inferred, we do not have a clear guideline yet -- consider on a case-by-case basis, for now.)
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## Metavariables
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**TODO:** move these to the right place
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* `P` `Q` for bi:PROP (or specifically `iProp Σ`)
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* `Φ` and `Ψ` for (?A -> iProp), like postconditions
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* `φ` and `ψ` for `Prop`
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* `A` `B` for types, ofeT, or cmraT
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Suffixes like O, R, UR (already documented) |
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\ No newline at end of file |
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Moved to https://gitlab.mpi-sws.org/iris/iris/-/blob/master/docs/style_guide.md |
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\ No newline at end of file |