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A TeX macro associates a TeX control sequence with a replacement list of TeX tokens, possibly containing parameters. During TeX expansion, arguments are substituted into that list. Character tokens retain their TeX category codes, so this mechanism has more structure than unrestricted replacement of raw text strings.^[ref]

For a simple example, \def\dup#1{#1+#1} defines a macro with one parameter. In mathematics, $\dup{x}$ yields the token sequence for $x+x$. With $\dup{u+v}$, the expansion gives $u+v+u+v$. The replacement duplicates the supplied tokens; it does not evaluate or simplify the mathematical expression.

This makes TeX macros useful for reusable notation. A document can express an intention through one command and change the associated presentation centrally. The actual printed result still depends on subsequent execution, computer fonts and mathematical typesetting.

A TeX parameter token marks an argument position in a TeX macro definition. With ordinary category assignments, #1 through #9 name the available positions. During TeX expansion, the supplied argument tokens replace the corresponding placeholders.^[ref]

For an original example, \def\twice#1{#1:#1} followed by \twice{ab} expands to ab:ab. The braces delimit one argument containing two character tokens; they are not copied into the replacement at each placeholder. Calling \twice7 instead gives 7:7. Thus #1 identifies an argument slot rather than instructing TeX to print the digit 1.

The definition's replacement list can be inspected before execution. Its placeholders remain distinct from ordinary digit tokens, even when an actual argument happens to be a digit. This separation makes token substitution useful for reusable notation.

A TeX primitive is an operation supplied by TeX itself, such as defining a TeX macro, changing a register or constructing a typesetting box. A TeX control sequence can name a primitive or a macro. The distinction concerns the current meaning of the command, rather than the appearance of its name.^[ref]

For example, \hbox constructs a horizontal typesetting box. The assignment \let\mkbox=\hbox gives another name to its current meaning. Defining a macro with \def\label{sample} creates a replacement list instead. Some primitives participate in TeX expansion, while others perform operations during later processing; primitive does not mean unexpandable. This distinction helps explain why a command can appear in an expansion trace without immediately drawing a glyph.

A TeX token is an internal syntactic unit used by TeX. Ordinary character tokens pair a TeX character code with a TeX category code; TeX control sequence tokens identify commands. Macro processing also uses TeX parameter tokens.^[ref]

For example, an a read with category 11 and an a read with category 12 are different character tokens, even though both can select the same printed glyph in ordinary text. Changing a category assignment later does not retokenize a previously stored TeX macro replacement list. A stored control-sequence token can, however, acquire a different current meaning through redefinition.

The TeX input processor performs the relevant lexical analysis. The later TeX expansion stage operates on the resulting tokens. This separation explains why changing the spelling of input and changing the meaning of an existing command are different operations.

Victor Eijkhout is a computing researcher and author of TeX by Topic by Victor Eijkhout, a technical reference explaining how TeX processes input, expands macros and builds typeset material. Its subject-based organization makes the distinction between TeX tokens, TeX expansion and later layout operations explicit.^[ref]

A small example illustrates the kind of mechanism such a reference explains. Define a TeX macro with \def\double#1{#1#1}. The call \double{ab} substitutes the argument's two letter tokens twice, producing the expanded letter-token sequence abab. In contrast, \double ab takes only the next unbraced letter token as its argument; the remaining b follows the replacement, giving aab. These are own illustrative calls under ordinary tokenization, not quotations from the book.^[ref]

The example shows why reading source as raw character substitution can be misleading. Argument boundaries and tokenization are part of the computation; the eventual visual layout is a later concern. That separation connects a practical typesetting problem with more general ideas about programming language processing.

His institutional profile also identifies work in numerical linear algebra, scientific computing and parallel computing, and links his computing textbooks. These are professional contributions beyond the TeX reference, rather than evidence inferred from a similarly named person.^[ref]