Compiling a Subset of APL Into a Typed Intermediate Language

Abstract

We present a compiler and a typed intermediate language for a subset of APL. The intermediate language treats all numeric data as multi-dimensional arrays and the type system makes explicit the ranks of arrays. Primitive operators are polymorphic in rank and in the type of the underlying data operated on.The frontend of the APL compiler deals with much of the gory details of the APL language, including infix resolution, resolution of identity items for reduce operations, resolution of default element values for empty arrays, scalar extensions, and resolution of certain kinds of overloading.We demonstrate the usefulness of the intermediate language by showing that it can be compiled efficiently, using known techniques, such as delayed arrays, into a C-like language. We also demonstrate that the language is sufficiently expressive that some primitive operators, such as APL's inner product operator, which works on arrays of arbitrary dimensions, can be compiled using more primitive operators.

Compiling APL to accelerate through a typed array intermediate language

“…Figure 3 shows the TAIL syntax supported by the compiler. The syntax deviates somewhat from the grammar described in [11], which has been updated to work with character and boolean arrays.…”

“…Our previous work on APLTAIL [11] compiles a subset of APL into a typed array intermediate language called TAIL. In this paper, we present a compiler from TAIL to Haskell source code, which employs the Accelerate library [6].…”

“…The compiler is based on the APLTAIL compiler, which compiles APL programs into a typed array intermediate language, called TAIL [11]. We translate TAIL programs into Haskell source code, employing Accelerate [6], a Haskell-library for general purpose GPU-programming.…”

Bounds Checking

“…Finally, another approach, taken by languages in the APL family, is to extend the language operators in a way that guarantees that out-of-bounds indices cannot occur [7]. This typically introduces non-affine indexing that might hinder subsequent optimizations.…”

Size slicing

“…A somewhat orthogonal approach has been to extend the language operators such that size and bounds checking invariants always hold [12], the downfall being that non-affine indexing might appear. The Futhark strategy is instead to rely on advanced program analysis and compilation techniques to implement a pay-as-you-go scheme for programming massively parallel architectures.…”