Summary: Faithful Ideal Models for
Recursive Polymorphic Types \Lambda
Mart'in Abadi y Benjamin Pierce z Gordon Plotkin x
We explore ideal models for a programming language with recur
sive polymorphic types, variants of the model studied by MacQueen,
Plotkin, and Sethi. The use of suitable ideals yields a close fit be
tween models and programming language. Two of our semantics of
type expressions are faithful, in the sense that programs that behave
identically in all contexts have exactly the same types.
Often, a formal semantics assigns different values to programs that behave
identically in all contexts [Mil77, Plo77, Sto88]. In other words, the seman
tics of programminglanguage expressions is not fully abstract. This mis
match between model and programming language elicits diverse reactions.
Some propose extensions to the programming language, while others prefer
modifying the semantics. Both of these attitudes have suggested fruitful lines
\Lambda A preliminary version of this paper was presented at the 4th IEEE Symposium on
Logic in Computer Science in June 1989.
y Digital Equipment Corporation, Systems Research Center, 130 Lytton Avenue, Palo