Infix notation

Abstract: (1992). Two Notes on Notation. The American Mathematical Monthly: Vol. 99, No. 5, pp. 403-422.

Abstract: We investigate the use of the dot notation in the context of abstract types. The dot notation -- that is, a.f referring to the operation f provided by the abstraction a -- is used by programming languages such as Modula-2 and CLU. We compare this notation with the Mitchell-Plotkin approach, which draws a parallel between type abstraction and (weak) existential quantification in constructive logic. The basic operations on existentials coming from logic give new insights about the meaning of type abstraction, but differ completely from the more familiar dot notation. In this paper, we formalize simple calculi equipped with the dot notation, and relate them to a more classical calculus a la Mitchell and Plotkin. This work provides some theoretical foundations for the dot notation, and suggests some useful extensions.

Abstract: Described are a system and method for generating a search expression for use in searching heterogeneous repositories. An application program receives user-supplied input. A template is selected based on a structure of the input. The input is scanned and tokenized. Each token is substituted into one or more locations within the template designated for that token to produce a string-based search expression. The search expression can have logical OR and logical AND operations, parentheses to specify precedence of evaluation, and an infix notation. Templates are modifiable for changing the content of search expressions constructed for a given user input. User-specifiable and user-modifiable aspects include the selecting of particular attributes, operators, and evaluation precedence of template expressions, the tokenizing of user input, the mapping of token sequences to particular templates, and the designation of locations within a selected token expression in which to substitute tokens derived from the user input.