Abstract

We present a proof that the canonical models of the untyped λ-calculus -- with call-by-value and lazy call-by-name evaluation -- in the category of bidomains and continuous and stable functions are fully abstract. This is achieved by showing that bidomains yield a fully abstract model of a version of Plotkin's FPC in which the constructor for sum types is restricted to its unary form -- lifting. It is shown that full abstraction for this model can be reduced to denability for the fragment corresponding to "unary PCF". An algorithm devised by Schmidt-Schau is used to show that the bidomain model of this fragment is fully abstract.

Citations