Terminal algebra semantics and retractions for abstract data types

Algebraic approaches to nondeterminism—an overview

“…(3) It has also been pointed out [Hornung and Raulefs 1980;Broy and Wirsing 1981a,b] that, typically, initial structures are not fully abstract; they often distinguish elements that behave identically in all contexts, and additional axioms are needed if one wants to identify them.…”

The completeness of the algebraic specification methods for computable data types

“…But Guttag (1975), Guttag and Horning (1978) probably favour final algebra 186 0019-9958/82 $2.00 semantics: certainly Guttag and Horning (1978) contains a disclaimer about initial semantics and an approximate description of the objectives of the final algebra technique. An early rigorous account of final algebra semantics is Wand (1979) and other exact treatments of this far less well-understood alternative can be seen in Giarratana, Gimona, and Montanari (1976), Hornung and Raulefs (1980), Kamin (1980), Kaput (1980), the Munich Group, Broy et al (1979) and Wirsing and Broy (1980), and our own articles Tucker (1980a, 1983).…”

Initial and Final Algebra Semantics for Data Type Specifications: Two Characterization Theorems

“…Moreover, in the first paper to explicitly formulate final algebra semantics [23], Wand argues that it is indeed the denotational semantics of Guttag's theory of specifications.) Mathematically exact declarations in favor of the far less well-understood final algebra semantics can be seen in Hornung and Raulefs [13], Kamin [14], Kapur and Srivas [15], the Munich Group [8], [24] and Wand [23].…”