Restriction in Program Algebra

Program Algebra and Thread Algebra

Algebra of Program Termination

Well-foundedness and indu tive properties of relations are expressed in terms of xed points. A lass of xed point equations, alled \hylo" equations, is introdu ed. A methodology of re ursive program design based on the use of hylo equations is presented. Current resear h on generalisations of well-foundedness and indu tive properties of relations, making these properties relative to a datatype, ...

Apprentice Program: Linear Algebra

Definition 1.1. Let K be a field. (V,+, ·) is a vector space over K, if (V,+) is an Abelian group, and · : K × V → V (called scalar multiplication) is distributive, associative and multiplication by 1 is the identity on V . This compact definition unwinds to give us the following ten(!) axioms: (1) + : V × V → V (2) u+ (v + w) = (u+ v) + w. (3) u+ v = v + u. (4) ∃0 ∈ V such that v + 0 = 0 + v =...

Program Algebra with Repeat Instruction

In the setting of program algebra (PGA) we consider the repeat instruction. This special instruction is designed to represent infinite sequences of instructions as finite, linear programs. The resulting program notation is called PGLA and can be considered a string syntax for PGA. We redefine the repeat instruction by allowing its counter to be also zero. Then we show that PGLAcore, a kernel of...

Execution architectures for program algebra

We investigate the notion of an execution architecture in the setting of the program algebra PGA, and distinguish two sorts of these: analytic architectures, designed for the purpose of explanation and provided with a process-algebraic, compositional semantics, and synthetic architectures, focusing on how a program may be a physical part of an execution architecture. Then we discuss in detail t...