Direct Definition -- Why Not Tradfns

Traditional function definition

Traditional APL function definition uses ∇-headers, line numbers, and the Del editor:

∇ R←MEAN X
[1] R←(+/X)÷⍴X
∇

This style dates from the 1960s when APL ran on line-oriented terminals. It relies on dynamic scope, mutable line numbers, and → (branch) for flow control.

Dfns: the modern alternative

Dfns (direct functions), were first proposed by Ken Iverson. John Scholes introduced them in Dyalog APL in 1996. Here's the mean declares as a dfn.

      mean ← {(+/⍵)÷⍴⍵}

Key differences:

• Lexical scope -- a dfn sees the variables that existed where it was defined, not where it's called. This makes code easier to reason about and eliminates accidental name collisions.
• Closures -- dfns capture their defining environment, so they compose naturally with operators.
• Guards instead of branching -- condition : result replaces →label. No line numbers, no labels, no branch targets.
• First-class values -- dfns are values that can be assigned, passed to operators, and returned from other dfns.

Why MARPLE uses dfns exclusively

MARPLE does not support traditional ∇-header definitions. The reasons are both practical and philosophical:

Simplicity. One way to define functions means one set of scoping rules, one mental model, and less to learn.

Composability. Dfns work naturally with the rank operator and other higher-order constructs. A dfn is a value; a tradfn is a named procedure. Values compose; procedures don't.

No branch. The → primitive is the source of many bugs in traditional APL. Guards (condition : result) are clearer and less error-prone.

Modern expectations. Lexical scope, closures, and first-class functions are standard in modern programming. Dynamic scope and line-number-based flow control are not.

What you lose

Tradfns can be easier to read for long, step-by-step procedures. They support local variables declared in the header and multi-line editing in the Del editor. If you're coming from Dyalog or GNU APL and rely heavily on tradfns, you'll need to restructure your code as dfns -- though most APL programmers who try dfns prefer them.