University of Cambridge Computer Laboratory; New Museums Site

SVM HeaderParse 0.2

AUTHOR ADDR

Pembroke Street; Cambridge CB2 3QG

SVM HeaderParse 0.1

AUTHOR NAME

A Research

SVM HeaderParse 0.1

AUTHOR AFFIL

worker at the University of Cambridge Computer Laboratory, New Museums

SVM HeaderParse 0.2

AUTHOR ADDR

Site, Pembroke Street, Cambridge, CB2 3QG, England. The software

SVM HeaderParse 0.1

ABSTRACT

ion is in a precise sense a converse operation to application. Given 49 50 CHAPTER 5. PRIMITIVE BASIS OF HOL LIGHT a variable x and a term t, which may or may not contain x, one can construct the so-called lambda-abstraction x: t, which means `the function of x that yields t'. (In HOL's ASCII concrete syntax the backslash is used, e.g. \x. t.) For example, x: x + 1 is the function that adds one to its argument. Abstractions are not often seen in informal mathematics, but they have at least two merits. First, they allow one to write anonymous function-valued expressions without naming them (occasionally one sees x 7! t[x] used for this purpose), and since our logic is avowedly higher order, it's desirable to place functions on an equal footing with rstorder objects in this way. Secondly, they make variable dependencies and binding explicit; by contrast in informal mathematics one often writes f(x) in situations where one really means x: f(x). We should give some idea of how ordina...