Scalar extension broadcasting and prototype type conformity

Scalar Extension and Type Promotion

In dyadic APL operations, scalar extension does not preserve the scalar's original prototype if it differs from the array operand. Instead, the language applies type promotion rules to ensure both operands are compatible before the operation is executed. The scalar is effectively coerced to the promoted type, and the resulting array adopts this promoted prototype.

Implementation Differences: Dyalog vs. GNU APL

While both systems follow the fundamental rule that a rank-0 scalar is replicated to match the shape of the non-scalar operand, their handling of prototype mismatches varies:

• Dyalog APL (18.0): Employs a strict promotion hierarchy. For numeric mismatches (e.g., 64-bit integer vs. 64-bit float), the system typically promotes the integer to a float to prevent precision loss. If prototypes are fundamentally incompatible (such as mixing character and numeric types in a numeric operation), Dyalog will trigger a DOMAIN ERROR.
• GNU APL: Follows similar shape rules but utilizes a different internal promotion strategy and error-handling mechanism. Portability is not guaranteed because GNU APL may handle specific numeric edge cases or type coercions differently than Dyalog.

Nested Arrays and Rank Elevation

When the scalar operand is a nested array rather than a simple numeric, the following consequences occur:

1. Shape: The result shape matches the non-scalar operand.
2. Content: The nested array is treated as a single entity (rank 0). Scalar extension replicates this entire nested structure into every cell of the resulting array.
3. Rank: The resulting array is a nested array where each element is the original nested scalar.

Note: Whether the nested structure is flattened or preserved during specific dyadic operations can be implementation-specific and should be verified per environment.

Verification Steps

To verify prototype behavior in your specific environment, execute the following scoped tests:

⍝ Test 1: Numeric Promotion (Integer Scalar + Float Vector)
res ← 1 + 1.1 2.1 3.1
⍝ Inspect result type to see if 1 was promoted to float

⍝ Test 2: Nested Scalar Extension
nested_scalar ← ⊂ 1 2 3
res_nested ← nested_scalar + 1 1 1
⍝ Verify if result is a vector of 3 nested arrays

Missing Diagnostic: To provide a more precise promotion mapping, please specify if you are using a specific Dyalog configuration (e.g., #C or #S) as this can influence how numeric types are handled.