There and back again

Abstract

Invertible programming occurs in the area of data conversion where it is required that the conversion in one direction is the inverse of the other. For that purpose, we introduce bidirectional arrows (biarrows). The bi-arrow class is an extension of Haskell's arrow class with an extra combinator that changes the direction of computation.The advantage of the use of bi-arrows for invertible programming is the preservation of invertibility properties using the biarrow combinators. Programming with bi-arrows in a polytypic or generic way exploits this the most. Besides bidirectional polytypic examples, including invertible serialization, we give the definition of a monadic bi-arrow transformer, which we use to construct a bidirectional parser/pretty printer.

Automatic Generation and Validation of Instruction Encoders and Decoders

“…Given a pattern P &P 2 , it satisfies disjointness if P 1 and P 2 match disjoint fields. 1 To understand this, suppose P 1 and P 2 relate different abstract arguments a 1 and a 2 to overlapping bits in a bit string l. Then, we cannot determine if the values in the overlapping bits are for a 1 or a 2 . Hence, the derived binary relation cannot possibly be a bijection.…”

“…Instruction decoding and encoding are special cases of parsing and pretty printing, respectively. Although there was early work on verifying that parsing and pretty-printing are inverses of each other by formulating them as bijections [1,10], this requirement was perceived as too strong [16]. Most of the recent work on verified parsing and pretty printing are dedicated to verify parser generators based on context-free grammars, regular expressions, parser combinators, or general data formats [3,11,17].…”

Refactoring pattern matching

“…This approach to invertible languages is not new. As a matter of fact, there have been a number of proposals for similar purposes [19,20,21,22,23]. On the other hand, reversible languages are usually domain-specific; it is hard to directly reuse them for different applications other than the ones for which they were designed.…”

“…The language rinv owes its origins to the rich literature on invertible programming [19,22], a programming paradigm where programs can be executed both forwards and backwards. Mu et al [19] concentrate their effort on designing a language that provides only injective functions.…”

“…The whole process is specified in terms of formats; the corresponding value-level transformations are induced. Invertible arrows [22] extend the arrow framework [51] (a generalization of monads) with a combinator that encodes pairs of functions being each other's inverses; the paper introducing invertible arrows [22] recognizes that, when full invertibility is not achievable (due to the non-isomorphic nature of the two sides), left-or right-biased semi-invertibility is nevertheless a useful approximation.…”