In computer science, Programming Computable Functions (PCF) is a typed functional language introduced by Gordon Plotkin in 1977,[1] based on previous unpublished material by Dana Scott.
[2] However, since Milner's model was essentially based on the syntax of PCF it was considered less than satisfactory.
These models are based on game semantics[4][5] and Kripke logical relations.
However, Ralph Loader demonstrated that no effectively presentable fully abstract model could exist, since the question of program equivalence in the finitary fragment of PCF is not decidable.
One then defines typing judgments of terms-in-context in the usual way for the following syntactical constructs: A relatively straightforward semantics for the language is the Scott model.