Add some more Effects system docs (#49652)

* add docs for `Base.infer_effects`
* add `show` decoder in `Effects` docs

Co-authored-by: Shuhei Kadowaki <40514306+aviatesk@users.noreply.github.com>

base/compiler/effects.jl

@@ -54,6 +54,37 @@ analyzed method (see the implementation of `merge_effects!`). Each effect proper
 initialized with `ALWAYS_TRUE`/`true` and then transitioned towards `ALWAYS_FALSE`/`false`.
 Note that within the current flow-insensitive analysis design, effects detected by local
 analysis on each statement usually taint the global conclusion conservatively.
+
+## Key for `show` output of Effects:
+
+The output represents the state of different effect properties in the following order:
+
+1. `consistent` (`c`):
+    - `+c` (green): `ALWAYS_TRUE`
+    - `-c` (red): `ALWAYS_FALSE`
+    - `?c` (yellow): `CONSISTENT_IF_NOTRETURNED` and/or `CONSISTENT_IF_INACCESSIBLEMEMONLY`
+2. `effect_free` (`e`):
+    - `+e` (green): `ALWAYS_TRUE`
+    - `-e` (red): `ALWAYS_FALSE`
+    - `?e` (yellow): `EFFECT_FREE_IF_INACCESSIBLEMEMONLY`
+3. `nothrow` (`n`):
+    - `+n` (green): `true`
+    - `-n` (red): `false`
+4. `terminates` (`t`):
+    - `+t` (green): `true`
+    - `-t` (red): `false`
+5. `notaskstate` (`s`):
+    - `+s` (green): `true`
+    - `-s` (red): `false`
+6. `inaccessiblememonly` (`m`):
+    - `+m` (green): `ALWAYS_TRUE`
+    - `-m` (red): `ALWAYS_FALSE`
+    - `?m` (yellow): `INACCESSIBLEMEM_OR_ARGMEMONLY`
+7. `noinbounds` (`i`):
+    - `+i` (green): `true`
+    - `-i` (red): `false`
+
+Additionally, if the `nonoverlayed` property is false, a red prime symbol (′) is displayed after the tuple.
 """
 struct Effects
     consistent::UInt8

base/reflection.jl

@@ -1525,6 +1525,42 @@ function return_types(@nospecialize(f), @nospecialize(types=default_tt(f));
     return rts
 end
 
+"""
+    infer_effects(f, types=default_tt(f); world=get_world_counter(), interp=Core.Compiler.NativeInterpreter(world))
+
+Compute the `Effects` of a function `f` with argument types `types`. The `Effects` represents the computational effects of the function call, such as whether it is free of side effects, guaranteed not to throw an exception, guaranteed to terminate, etc. The `world` and `interp` arguments specify the world counter and the native interpreter to use for the analysis.
+
+# Arguments
+- `f`: The function to analyze.
+- `types` (optional): The argument types of the function. Defaults to the default tuple type of `f`.
+- `world` (optional): The world counter to use for the analysis. Defaults to the current world counter.
+- `interp` (optional): The native interpreter to use for the analysis. Defaults to a new `Core.Compiler.NativeInterpreter` with the specified `world`.
+
+# Returns
+- `effects::Effects`: The computed effects of the function call.
+
+# Example
+
+```julia
+julia> function foo(x)
+           y = x * 2
+           return y
+       end;
+
+julia> effects = Base.infer_effects(foo, (Int,))
+(+c,+e,+n,+t,+s,+m,+i)
+```
+
+This function will return an `Effects` object with information about the computational effects of the function `foo` when called with an `Int` argument. See the documentation for `Effects` for more information on the various effect properties.
+
+!!! warning
+    The `infer_effects` function should not be used from generated functions;
+    doing so will result in an error.
+
+# See Also
+- [`Core.Compiler.Effects`](@ref): A type representing the computational effects of a method call.
+- [`Base.@assume_effects`](@ref): A macro for making assumptions about the effects of a method.
+"""
 function infer_effects(@nospecialize(f), @nospecialize(types=default_tt(f));
                        world = get_world_counter(),
                        interp = Core.Compiler.NativeInterpreter(world))