All syntactic elements, including variables and basic operators, appear as such procedures.
Subsequent "extensions" to the standard Algol68 allowed the to syntactic element to be replaced with upto and downto to achieve a small optimization.
The forms of judgment are syntactic elements; the categories are semantic elements.
To derive the latter from the former was to derive semantic elements from syntactic elements.
But in generative grammar, which sees meaning as separate from grammar, they are categories that define the distribution of syntactic elements.
Proofs proceed by applying the rules (which remove or add syntactic elements to or from diagrams) sequentially.
The difficulty is with explaining how syntactic elements give rise to the semantic result and in a way that generalizes consistently with all other language use.
The following are brief descriptions of possible syntactic elements of a clause:
An independent subject precedes the other syntactic elements except the sentence connective.
When the language designer decides that a syntactic element should be included for a method concept, candidate symbols are designed and evaluated.