Sequentiality and Piecewise-affinity in Segments of Real-PCF
Amin Farjudian · Electronic Notes in Theoretical Computer Science · 2004
Real PCF (RPCF) was proposed by Martín Escardó [8] as a language for Real number computation.One of the key -and most controversial -constants is parallel-if (pif I ), the existence of which causes a serious inefficiency in the language leading to RPCF being impractical.While search is being undertaken to replace pif I with a more efficient operator, one needs to be assured of the segment of RPCF without pif I being sequential.A positive answer to this question is the main result of this paper.On the other hand, we show that non-affine functions -such as f (x) := x 2 -are not definable in RPCF without pif I .