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There is no way you can tell that's valid Common Lisp without actually compiling and executing the code in the json-reader.lisp file. When the compiler gets to (enable-json-syntax), it sees that it is a macro so it executes its code at compile-time. That code then redefines the meaning of the { and [ characters to be the start of JSON objects/arrays (instead of their normal meaning in Common Lisp), and installs code telling Common Lisp how to parse JSON syntax, which is triggered when those characters are encountered in input. The example-object function shows an example of using it. Finally, (disable-json-syntax) is another macro, also executed at compile time, which undoes those changes to the Common Lisp syntax.
Common Lisp did not invent the idea of allowing a program to dynamically alter the language syntax as it was being parsed; I believe the idea was first introduced in Maclisp, and from there spread to other LISP dialects (such as Franz Lisp and Interlisp) before finally being standardised in Common Lisp. The originators of Scheme intentionally decided to leave this feature out, but some implementations/descendants of Scheme have added it back in, such as Racket [1], Guile [2], and Chicken Scheme [3]. Other Lisp-family languages (such as Clojure or Emacs Lisp) have resisted calls to add it, despite encouragement from certain quarters.
Earlier you spoke of "Tcl's lack of a grammar up against Scheme, Lisp", but if runtime-extensible syntax is a form of "lack of a grammar", then many Lisp family languages lack grammar too.
Another language for which this is true (albeit to a significantly lesser degree), is Java. With Java, you can run arbitrary code at compile time by defining an annotation processor. The annotation processor code is run when the annotation is encountered. The annotation processor is allowed to issue compilation errors. It can also generate more source code for additional classes, which gets added to the compilation process, and your program may refer some of those generated classes, and hence need that generated code to compile–for an example see [4] from the Google AutoValue docs, where the "AutoValue_Animal" class being constructed in the create() method is dynamically generated by a processor which is triggered by the @AutoValue annotation. So, if your Java program contains annotations with an associated processor, and if you define "syntactically correct" as "compiles without any errors", then you can't know if the Java program is syntactically correct without executing arbitrary Java code.
[0] https://gist.github.com/chaitanyagupta/9324402
[1] https://docs.racket-lang.org/reference/Reader_Extension.html
[2] https://www.gnu.org/software/guile/manual/html_node/Reader-E...
[3] https://wiki.call-cc.org/man/5/Module%20(chicken%20read-synt...
[4] https://github.com/google/auto/blob/master/value/userguide/i...