Abstract syntax: N elem-of Nml = binary numerals N ::= I F I ::= B | I B F ::= .B | .B F B ::= 0 | 1 Semantic domain: Z = real numbers Semantic function: Nm: Nml -> Z Nm[[I F]] = Nm[[I]] + Nm[[.F]] Nm[[I B]] = 2*Nm[I] + Nm[[B]] Nm[[0]] = 0 Nm[[1]] = 1 Nm[[.B F]] = Nm[[.B]] + Nm[[.F]]/2 Nm[[.0]] = 0 Nm[[.1]] = 1/2 Test case: 1101.01 Nm[[1101.01]] \kw= Nm[[1101]] + Nm[[.01]] .ta \nwu = (2*Nm[[110]] + Nm[[1]]) + (Nm[[.0]] + Nm[[.1]]/2) = (2*(2*Nm[[11]] + Nm[[0]]) + Nm[[1]]) + (Nm[[.0]] + Nm[[.1]]/2) = (2*(2*(2*Nm[[1]] + Nm[[1]]) + Nm[[0]]) + Nm[[1]]) + (Nm[[.0]] + Nm[[.1]]/2 = (2*(2*(2*1 + 1) + 0) + 1) + (0 + (1/2)/2)