Support try/catch on the happy (nothrow) path

test/compiler.jl

@@ -246,7 +246,7 @@ end
  @test only(g) ∈ (1., 2.)
 end
 
-function f_try_catch(x,y)
+function throws_and_catches_if_x_negative(x,y)
  z = x + y
  try
  if x < 0.
@@ -259,14 +259,49 @@ function f_try_catch(x,y)
  return 3z
 end
 
+function try_catch_finally(cond, x)
+
+ try
+ x = 2x
+ cond && throw(DomainError())
+ catch
+ x = 2x
+ finally
+ x = 3x
+ end
+
+ x
+end
+
+if VERSION >= v"1.8"
+ # try/catch/else is invalid syntax prior to v1.8
+ eval(Meta.parse("""
+ function try_catch_else(cond, x)
+ end
+ """))
+end
+
 @testset "try/catch" begin
  @testset "happy path (nothrow)" begin
- res, (dx,dy) = withgradient(f_try_catch, 1., 2.)
+ res, (dx,dy) = withgradient(throws_and_catches_if_x_negative, 1., 2.)
  @test res == 3 * (2 * (1. + 2.) + 1. + 2.)
  @test dx == 3. * (2. + 1.)
  @test dy == 3. * (2. + 1.)
  end
 
+ @testset "try/catch/finally" begin
+ res, (_, dx,) = withgradient(try_catch_finally, false, 1.)
+ @test res == 6.
+ @test dx == 6.
+
+ res, pull = pullback(try_catch_finally, true, 1.)
+ @test res == 12.
+ @test_throws ErrorException pull(1.)
+ err = try pull(1.) catch ex; ex end
+ @test occursin("Can't differentiate function execution in catch block",
+ string(err))
+ end
+
  function foo_try(f)
  y = 1
  try