feat(tactic/norm_num_command): add user command to run norm_num on an…

… expression (#12550)

For example,
```
#norm_num 2^100 % 10
-- 6
```

src/tactic/norm_num.lean

@@ -1493,6 +1493,8 @@ add_tactic_doc
 
 end tactic.interactive
 
+/-! ## `conv` tactic -/
+
 namespace conv.interactive
 open conv interactive tactic.interactive
 open norm_num (derive)
@@ -1512,3 +1514,86 @@ conv.interactive.simp ff (simp_arg_type.except ``one_div :: hs) []
   { discharger := tactic.interactive.norm_num1 (loc.ns [none]) }
 
 end conv.interactive
+
+/-!
+## `#norm_num` command
+A user command to run `norm_num`. Mostly copied from the `#simp` command.
+-/
+
+namespace tactic
+
+setup_tactic_parser
+
+/--
+The basic usage is `#norm_num e`, where `e` is an expression,
+which will print the `norm_num` form of `e`.
+
+Syntax: `#norm_num` (`only`)? (`[` simp lemma list `]`)? (`with` simp sets)? `:`? expression
+
+This accepts the same options as the `#simp` command.
+You can specify additional simp lemmas as usual, for example using
+`#norm_num [f, g] : e`, or `#norm_num with attr : e`.
+(The colon is optional but helpful for the parser.)
+The `only` restricts `norm_num` to using only the provided lemmas, and so
+`#norm_num only : e` behaves similarly to `norm_num1`.
+
+Unlike `norm_num`, this command does not fail when no simplifications are made.
+
+`#norm_num` understands local variables, so you can use them to
+introduce parameters.
+-/
+@[user_command] meta def norm_num_cmd (_ : parse $ tk "#norm_num") : lean.parser unit :=
+do
+  no_dflt ← only_flag,
+  hs ← simp_arg_list,
+  attr_names ← with_ident_list,
+  o ← optional (tk ":"),
+  e ← texpr,
+
+  /- Retrieve the `pexpr`s parsed as part of the simp args, and collate them into a big list. -/
+  let hs_es := list.join $ hs.map $ option.to_list ∘ simp_arg_type.to_pexpr,
+
+  /- Synthesize a `tactic_state` including local variables as hypotheses under which `expr.simp`
+     may be safely called with expected behaviour given the `variables` in the environment. -/
+  (ts, mappings) ← synthesize_tactic_state_with_variables_as_hyps (e :: hs_es),
+
+  /- Enter the `tactic` monad, *critically* using the synthesized tactic state `ts`. -/
+  simp_result ← lean.parser.of_tactic $ λ _, do
+  { /- Resolve the local variables added by the parser to `e` (when it was parsed) against the local
+       hypotheses added to the `ts : tactic_state` which we are using. -/
+    e ← to_expr e,
+
+    /- Replace the variables referenced in the passed `simp_arg_list` with the `expr`s corresponding
+       to the local hypotheses we created.
+
+       We would prefer to just elaborate the `pexpr`s encoded in the `simp_arg_list` against the
+       tactic state we have created (as we could with `e` above), but the simplifier expects
+       `pexpr`s and not `expr`s. Thus, we just modify the `pexpr`s now and let `simp` do the
+       elaboration when the time comes.
+
+       You might think that we could just examine each of these `pexpr`s, call `to_expr` on them,
+       and then call `to_pexpr` afterward and save the results over the original `pexprs`. Due to
+       how functions like `simp_lemmas.add_pexpr` are implemented in the core library, the `simp`
+       framework is not robust enough to handle this method. When pieces of expressions like
+       annotation macros are injected, the direct patten matches in the `simp_lemmas.*` codebase
+       fail, and the lemmas we want don't get added.
+       -/
+    let hs := hs.map $ λ sat, sat.replace_subexprs mappings,
+
+    /- Try simplifying the expression, like in `#simp`  -/
+    e ← prod.fst <$> e.simp {fail_if_unchanged := ff} failed no_dflt attr_names hs,
+    /- Try applying `norm_num` with the default `norm_num` set, allowing it to fail to simplify. -/
+    e ← prod.fst <$> norm_num.derive e <|> return e,
+    return e } ts,
+
+  /- Trace the result. -/
+  when (¬ is_trace_enabled_for `silence_simp_if_true ∨ simp_result ≠ expr.const `true [])
+    (trace simp_result)
+
+add_tactic_doc
+{ name                     := "#norm_num",
+  category                 := doc_category.cmd,
+  decl_names               := [`tactic.norm_num_cmd],
+  tags                     := ["simplification", "arithmetic", "decision procedure"] }
+
+end tactic