Algebraic semantics

Adequacy for Algebraic Effects

“…This result is very much in the spirit of Mezei and Wright [19], and Theorem 4.26 of [8] is a similar result for recursive program schemes. Such results say that the denotational semantics of a program is that of the result of a preliminary symbolic computation.…”

Formal Tree Series

“…The definitions and results on commutative monoids are mainly due-sometimes in the framework of semiring theory-to Eilenberg [17], Goldstern [28], Karner [33], Krob [34], Kuich [35,36], Kuich, Salomaa [45], Manes, Arbib [47], Sakarovitch [53]. Our notion of continuous monoid is a specialization of the continuous algebras as defined, e. g., in Guessarian [31], Goguen, Thatcher, Wagner, Wright [27], Adamek, Nelson, Reiterman [2].…”

“…The set D X of all functions X → D is also a continuous distributive Σ-algebra by the pointwise operations and ordering as is the the set of all continuous functions D X → D. Moreover, it is equipped with the pointwise scalar multiplication which again satisfies (1)- (6) Proof. It is known that when t ∈ T Σ (X), then the function t D : D X → D induced by t is continuous, since it can be constructed from continuous functions (namely, the projections and the continuous operations of D corresponding to the symbols in Σ) by function composition, see, e.g., Guessarian [31]. Since scalar multiplication and + are continuous, so is any function induced by a series in A T Σ (X) .…”

CCS without τ's

“…We use A I-T _< U to indicate that T -< U can be derived from the axioms in Table 3.1 and Table 3.2 by using (o-induction, and other natural properties of substitutive partial orders, [Hen85a] and [Gue81].…”