2.7.4.2 Semantics

Declarations in silly should be understood in the obvious way as preprocessor directives to perform parenthetic textual substitutions (similar to #define id (exp) in C). All identifiers in expressions are thereby eliminated during the preprocessing phase.

The overall meaning of the program is the meaning of the expression in the last declaration. A denotational semantics for expressions is given by the following equations, where [[x]] should be read as “the meaning of x”, and x, y and z are metavariables. (That is, they stand for any source code fragment that could fit there subject to the constraint, informally speaking, that it has to correspond to a connected subtree of the parse tree as enforced by the unambiguous grammar in the context of the rest of the program.)

[[()]] = nil

[[(x)]] = [[x]]

[[(x,y)]] = cons([[x]],[[y]])

[[x y]] = [[x(y)]] = [[x]] [[y]]

[[x (y,z)]] = [[x(y,z)]] = [[x]] [[(y,z)]]

Toy languages like this are among the few situations a denotational semantics stands a chance of clarifying more than it obfuscates, so the reader is invited to take a moment to savor it.

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