Abstract

ion If we have box B containing free parameter symbols, so that it represents some parametric object b(X; Y; Z; : : :) (possibly with a restriction) we indicate that some of its parameters have been abstracted over by putting the corresponding parameter symbols in a small box at the top right of the box B representing b. Thus for example, we can bind the parameter symbols X and Z by creating the box: (7) X;Z b(X; Y; Z; : : :) If we want to apply this abstract to some objects, say those denoted by a; c, we would write (8) X;Z b(X; Y; Z; : : :) [a; c] According to the semantics we will give, this will denote the same object as (9) b(a; Y; c; : : :) In certain cases, an abstract like this may denote the sort of thing one can predicate of objects. In this case, we will provide ourselves with a variant notation, to show that the abstract can be used as a predicate. The variant is: (10) X;Z b(X; Y; Z; : : :) Our notation will allow us ways to indicate predication that is different from...

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