🎓 Chapter 6: Dynamic Functions (Dfns) & Control Flow
In modern APL (Dyalog and mAPL), user-defined functions are written using Dfns (Dynamic Functions) enclosed in curly braces {...}.
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1. Dfn Argument Symbols
Inside a dfn:
⍵(Omega): Represents the Right Argument.⍺(Alpha): Represents the Left Argument (in dyadic calls).
Simple Monadic Dfn:
```apl
Square ← { ⍵ × ⍵ }
Square 9 ⍝ Returns 81
```
⍝ Define a monadic squaring dfn
Square ← { ⍵ × ⍵ }
Square 9---
2. Dyadic Dfns (Two Arguments)
A dyadic dfn uses both ⍺ (left) and ⍵ (right):
```apl
Hypot ← { ( (⍺*2) + (⍵*2) ) * 0.5 }
3 Hypot 4 ⍝ Returns 5
```
⍝ Hypotenuse function √(a² + b²)
Hypot ← { ((⍺*2) + (⍵*2)) * 0.5 }
3 Hypot 4---
3. Guards & Early Return (condition : expression)
A Guard (:) provides conditional control flow inside a dfn.
If condition evaluates to 1 (True), the dfn returns expression immediately and terminates execution.
⍝ Safe division dfn: returns 0 if denominator is 0
SafeDiv ← { ⍵ = 0 : 0 ⋄ ⍺ ÷ ⍵ }
10 SafeDiv 2 ⋄ 10 SafeDiv 0---
4. Self-Recursion (∇)
Inside a dfn, the symbol ∇ (Del) refers to the dfn itself, allowing clean recursive function definitions!
⍝ Recursive Factorial dfn using self-reference (∇)
Fact ← { ⍵ ≤ 1 : 1 ⋄ ⍵ × ∇ (⍵ - 1) }
Fact 6← Chapter 5: Outer Products (∘.) & Table Math Chapter 7: Each (¨) & The Rank Operator (⍤) →