Editing Denotational semantics (section)

===Denotational semantics of state===
State (such as a heap) and simple [[imperative programming|imperative features]] can be straightforwardly modeled in the denotational semantics described above. The key idea is to consider a command as a partial function on some domain of states. The meaning of "{{code|1=x:=3}}" is then the function that takes a state to the state with {{code|3}} assigned to {{code|x}}. The sequencing operator "{{code|;}}" is denoted by composition of functions. Fixed-point constructions are then used to give a semantics to looping constructs, such as "{{code|while}}".

Things become more difficult in modelling programs with local variables. One approach is to no longer work with domains, but instead to interpret types as [[functor]]s from some category of worlds to a category of domains. Programs are then denoted by [[natural transformation|natural]] continuous functions between these functors.<ref>[[Peter W. O'Hearn]], John Power, [[Robert D. Tennent]], Makoto Takeyama. Syntactic control of interference revisited. ''Electron. Notes Theor. Comput. Sci.'' 1. 1995.</ref><ref>Frank J. Oles. ''A Category-Theoretic Approach to the Semantics of Programming''. PhD thesis, [[Syracuse University]], New York, USA. 1982.</ref>