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 PGLA, can replace PGA as a carrier for program algebra by providing axioms for instruction sequence congruence, structural congruence and thread extraction. Finally, we provide three alternative projection semantics for PGLA that all coincide on PGLAcore.