feat: (↑) notation for coercions (#199)

See leanprover-community/mathport#116 (comment)

The notation is a bit problematic for the pretty-printer, as it doesn't automatically insert parentheses to disambiguate it from the built-in coercion notation.  Alternatives:
 1. Use a different token.
 2. Magically define `(↑ ∙)` to be the eta-reduction of `fun x => ↑x`.

PS: the old macro for `↑ x` was redundant since it's been moved to core some time ago.

Mathlib/Data/Subtype.lean

@@ -84,7 +84,7 @@ f x
 lemma restrict_apply {α} {β : α → Type _} (f : ∀x, β x) (p : α → Prop) (x : Subtype p) :
   restrict f p x = f x.1 := rfl
 
-lemma restrict_def {α β} (f : α → β) (p : α → Prop) : restrict f p = f ∘ CoeHead.coe := rfl
+lemma restrict_def {α β} (f : α → β) (p : α → Prop) : restrict f p = f ∘ (↑) := rfl
 
 lemma restrict_injective {α β} {f : α → β} (p : α → Prop) (h : injective f) :
   injective (restrict f p) :=

Mathlib/Tactic/Coe.lean

@@ -5,20 +5,24 @@ Author: Gabriel Ebner
 -/
 import Lean
 
-open Lean Elab Term
+open Lean Elab Term Meta
 
 /-!
-Redefine the ↑-notation to elaborate in the same way as type annotations
-(i.e., unfolding the coercion instance).
+Define a `(↑)` notation for coercions equivalent to the eta-reduction of `(↑ ·)`.
 -/
 
 namespace Lean.Elab.Term.CoeImpl
 
-scoped elab "coe%" x:term : term <= expectedType => do
-  tryPostponeIfMVar expectedType
-  let x ← elabTerm x none
-  synthesizeSyntheticMVarsUsingDefault
-  ensureHasType expectedType x
-
-macro_rules
-  | `(↑ $x) => `(coe% $x)
+elab "(" "↑" ")" : term <= expectedType => do
+  let expectedType ← instantiateMVars expectedType
+  let Expr.forallE _ a b .. := expectedType | do
+    tryPostpone
+    throwError "(↑) must have a function type, not{indentExpr expectedType}"
+  if b.hasLooseBVars then
+    tryPostpone
+    throwError "(↑) must have a non-dependent function type, not{indentExpr expectedType}"
+  if a.hasExprMVar then tryPostpone
+  if b.hasExprMVar then tryPostpone
+  let f ← withLocalDeclD `x a fun x => do
+    mkLambdaFVars #[x] (← mkCoe b a x)
+  return f.etaExpanded?.getD f