Theory and Use of Conditional Composition

Abstract : In this note, tagged collections and tbeir compositions were introduced. Tbese collections can be viewed as quantified expressions and can be used to manipulate lists and functions using tbe existing properties of quantification and one additional axiom. These tagged collections were used to introduce tbe theory of conditional composition of functions, and tbe conditional replace operator. These concepts were used to describe tbe semantics of programming languages, and to introduce new programming language constructs. We described tbe semantics of partitioned state spaces, which vas tben used to describe tbe seniantics of exceptions, loop exits, and structured jumps. The conditional replace operator was used to describe operations in relational databases. Conditional composition was used to describe tbe operation of an embedded system with priority levels.