Specification and verification in higher order algebra: A case study of convolution

A Completeness Theorem for the Expressive Power of Higher-Order Algebraic Specifications

“…Our results establish that this type of nonconstructive specification is not possible in a purely first-order algebraic framework, but becomes possible in a second-order framework. This theme is pursued further in [17], where a case study of a nonconstructive second-order equational specification of the Hamming stream problem is given. Further discussion of this theme can be found in [16,21].…”

“…Its proof also gives deeper insight into the role of the quantifier functional and, thus, into the relationship between constructive and nonconstructive higher-order specifications. This theme forms one of the cornerstones of the theory of higher-order algebraic specification and is taken up elsewhere in [16,17].…”

Correctness of dataflow and systolic algorithms using algebras of streams

“…Our example of a systolic algorithm is a well known convolution algorithm adapted from [18]. We will extend the results presented in [32] regarding the correctness of this algorithm. Our example of a dataflow algorithm is an algorithm for computing the Hamming stream.…”

“…In particular, higher-order algebraic specifications have been shown to be substantially more expressive than first-order algebraic specification methods (see [17] and [28]). The use of second-order algebra as a mathematical framework for hardware design was first considered in [32] and [43] by means of case studies. The advantages of second-order algebra as a framework are both strong expressive power and a simple proof theory, together with an initial algebra semantics for specifications.…”

Higher-order algebra with transfinite types

“…For an introduction to higher{order algebraic methods see Moller [1987], Moller et al [1988] and Meinke [1992], while for examples of their applications see for example Meinke and Steggles [1994], Meinke [1994] and Steggles [1995].…”