doc: document all the convs

src/Init/Conv.lean

@@ -31,43 +31,125 @@ Basic forms:
 -/
 syntax (name := conv) "conv " (" at " ident)? (" in " term)? " => " convSeq : tactic
 
+/-- Traverses into the left subterm of a binary operator.
+(In general, for an `n`-ary operator, it traverses into the second to last argument.) -/
 syntax (name := lhs) "lhs" : conv
+
+/-- Traverses into the right subterm of a binary operator.
+(In general, for an `n`-ary operator, it traverses into the last argument.) -/
 syntax (name := rhs) "rhs" : conv
+
+/-- Reduces the target to Weak Head Normal Form. This reduces definitions
+in "head position" until a constructor is exposed. For example, `List.map f [a, b, c]`
+weak head normalizes to `f a :: List.map f [b, c]`. -/
 syntax (name := whnf) "whnf" : conv
+
 /-- Expand let-declarations and let-variables. -/
 syntax (name := zeta) "zeta" : conv
+
 /-- Put term in normal form, this tactic is ment for debugging purposes only -/
 syntax (name := reduce) "reduce" : conv
+
+/-- Performs one step of "congruence", which takes a term and produces
+subgoals for all the function arguments. For example, if the target is `f x y` then
+`congr` produces two subgoals, one for `x` and one for `y`. -/
 syntax (name := congr) "congr" : conv
+
+/--
+* `arg i` traverses into the `i`'th argument of the target. For example if the
+  target is `f a b c d` then `arg 1` traverses to `a` and `arg 3` traverses to `c`.
+* `arg @i` is the same as `arg i` but it counts all arguments instead of just the
+  explicit arguments. -/
 syntax (name := arg) "arg " "@"? num : conv
+
+/-- `ext x` traverses into a binder (a `fun x => e` or `∀ x, e` expression)
+to target `e`, introducing name `x` in the process. -/
 syntax (name := ext) "ext " (colGt ident)* : conv
+
+/-- `change t'` replaces the target `t` with `t'`,
+assuming `t` and `t'` are definitionally equal. -/
 syntax (name := change) "change " term : conv
+
+/-- `delta foo` unfolds all occurrences of `foo` in the target.
+Like the `delta` tactic, this ignores any definitional equations and uses
+primitive delta-reduction instead, which may result in leaking implementation details.
+Users should prefer `unfold` for unfolding definitions. -/
 syntax (name := delta) "delta " ident : conv
+
+/-- `unfold foo` unfolds all occurrences of `foo` in the target.
+Like the `unfold` tactic, this uses equational lemmas for the chosen definition
+to rewrite the target. For recursive definitions,
+only one layer of unfolding is performed. -/
 syntax (name := unfold) "unfold " ident : conv
+
+/-- `pattern pat` traverses to the first subterm of the target that matches `pat`. -/
 syntax (name := pattern) "pattern " term : conv
+
+/-- `rw [thm]` rewrites the target using `thm`. See the `rw` tactic for more information. -/
 syntax (name := rewrite) "rewrite " (config)? rwRuleSeq : conv
+
+/-- `simp [thm]` performs simplification using `thm` and marked `@[simp]` lemmas.
+See the `simp` tactic for more information. -/
 syntax (name := simp) "simp " (config)? (discharger)? (&"only ")? ("[" (simpStar <|> simpErase <|> simpLemma),* "]")? : conv
-syntax (name := simpMatch) "simp_match " : conv
+
+/-- `simp_match` simplifies match expressions. For example,
+```
+match [a, b] with
+| [] => 0
+| hd :: tl => hd
+```
+simplifies to `a`. -/
+syntax (name := simpMatch) "simp_match" : conv
+
 
 /-- Execute the given tactic block without converting `conv` goal into a regular goal -/
 syntax (name := nestedTacticCore) "tactic'" " => " tacticSeq : conv
+
 /-- Focus, convert the `conv` goal `⊢ lhs` into a regular goal `⊢ lhs = rhs`, and then execute the given tactic block. -/
 syntax (name := nestedTactic) "tactic" " => " tacticSeq : conv
+
+/-- `{ convs }` runs the list of `convs` on the current target, and any subgoals that
+remain are trivially closed by `skip`. -/
 syntax (name := nestedConv) convSeqBracketed : conv
+
+/-- `(convs)` runs the `convs` in sequence on the current list of targets.
+This is pure grouping with no added effects. -/
 syntax (name := paren) "(" convSeq ")" : conv
+
+/-- `conv => cs` runs `cs` in sequence on the target `t`,
+resulting in `t'`, which becomes the new target subgoal. -/
 syntax (name := convConvSeq) "conv " " => " convSeq : conv
 
 /-- `· conv` focuses on the main conv goal and tries to solve it using `s` -/
 macro dot:("·" <|> ".") s:convSeq : conv => `({%$dot ($s) })
-macro "rw " c:(config)? s:rwRuleSeq : conv => `(rewrite $[$c]? $s)
-macro "erw " s:rwRuleSeq : conv => `(rw (config := { transparency := Meta.TransparencyMode.default }) $s)
 
+/-- `rw [rules]` applies the given list of rewrite rules to the target.
+See the `rw` tactic for more information. -/
+macro "rw " c:(config)? s:rwRuleSeq : conv => `(rewrite $[$c]? $s)
+
+/-- `erw [rules]` is a shorthand for `rw (config := { transparency := .default }) [rules]`.
+This does rewriting up to unfolding of regular definitions (by comparison to regular `rw`
+which only unfolds `@[reducible]` definitions). -/
+macro "erw " s:rwRuleSeq : conv => `(rw (config := { transparency := .default }) $s)
+
+/-- `args` traverses into all arguments. Synonym for `congr`. -/
 macro "args" : conv => `(congr)
+/-- `left` traverses into the left argument. Synonym for `lhs`. -/
 macro "left" : conv => `(lhs)
+/-- `right` traverses into the right argument. Synonym for `rhs`. -/
 macro "right" : conv => `(rhs)
+/-- `intro` traverses into binders. Synonym for `ext`. -/
 macro "intro " xs:(colGt ident)* : conv => `(conv| ext $xs*)
 
 syntax enterArg := ident <|> ("@"? num)
+
+/-- `enter [arg, ...]` is a compact way to describe a path to a subterm.
+It is a shorthand for other conv tactics as follows:
+* `enter [i]` is equivalent to `arg i`.
+* `enter [@i]` is equivalent to `arg @i`.
+* `enter [x]` (where `x` is an identifier) is equivalent to `ext x`.
+For example, given the target `f (g a (fun x => x b))`, `enter [1, 2, x, 1]`
+will traverse to the subterm `b`. -/
 syntax "enter " "[" (colGt enterArg),+ "]": conv
 macro_rules
   | `(conv| enter [$i:num]) => `(conv| arg $i)
@@ -75,14 +157,26 @@ macro_rules
   | `(conv| enter [$id:ident]) => `(conv| ext $id)
   | `(conv| enter [$arg, $args,*]) => `(conv| (enter [$arg]; enter [$args,*]))
 
+/-- `skip` closes one conv goal "trivially", by using reflexivity
+(that is, no rewriting). -/
 macro "skip" : conv => `(tactic => rfl)
+
+/-- `done` succeeds iff there are no goals remaining. -/
 macro "done" : conv => `(tactic' => done)
+
+/-- `trace_state` prints the current goal state. -/
 macro "trace_state" : conv => `(tactic' => trace_state)
+
+/-- The `apply thm` conv tactic is the same as `apply thm` the tactic.
+There are no restrictions on `thm`, but strange results may occur if `thm`
+cannot be reasonably interpreted as proving one equality from a list of others. -/
+-- TODO: error if non-conv subgoals?
 macro "apply " e:term : conv => `(tactic => apply $e)
 
 /-- `first | conv | ...` runs each `conv` until one succeeds, or else fails. -/
 syntax (name := first) "first " withPosition((colGe "|" convSeq)+) : conv
 
+/-- `repeat convs` runs the sequence `convs` repeatedly until it fails to apply. -/
 syntax "repeat " convSeq : conv
 macro_rules
   | `(conv| repeat $seq) => `(conv| first | ($seq); repeat $seq | skip)