[Docs] Tweak the CL module

doc/modules/common_lisp.md

@@ -10,11 +10,24 @@ Not much to say here, as `lisp-mode` is configured in the "Lisp Base" module.
 
 ## SLIME
 
-This module bundles [SLIME](https://docs.cider.mx), a popular interactive
+This module bundles [SLIME](https://common-lisp.net/project/slime/), a popular interactive
 programming environment for SLIME, and enables many of its essential features.
 
+SLIME supports many Common Lisp implementations:
+
+* CMU Common Lisp (CMUCL)
+* Steel Bank Common Lisp (SBCL)
+* Clozure CL (a.k.a. OpenMCL)
+* LispWorks
+* Allegro CL
+* CLISP
+* Scieneer CL
+* ECL
+* Corman CL
+* ABCL
+
 The default config assumes the usage of [Clozure CL](https://github.com/Clozure/ccl) on macOS and
 of [SBCL](http://www.sbcl.org/) everywhere else. That's something you can easily
 tweak via `slime-default-lisp`.
 
-You can fire SLIME with `M-x slime`.
+You can start SLIME with `M-x slime`.