The paper discusses semalltics of encodings in logical frameworkswhere equalities in object calculi are represented by families of types as the case inELF. The notion of Leibniz equality in a category is introduced. T...The paper discusses semalltics of encodings in logical frameworkswhere equalities in object calculi are represented by families of types as the case inELF. The notion of Leibniz equality in a category is introduced. Two morphisms ina category are Leibniz equal if they are seen so by an internal category. The usualcategorical properties are then relativized to r-properties by requiring mediatingmorphisms to be unique up to some Leibniz equality. Using these terminologies,it is shown, by an example, that the term model of the encoding of an adequatelyrepresented object calculus is r-isomorphic to the term model of the object language.展开更多
文摘The paper discusses semalltics of encodings in logical frameworkswhere equalities in object calculi are represented by families of types as the case inELF. The notion of Leibniz equality in a category is introduced. Two morphisms ina category are Leibniz equal if they are seen so by an internal category. The usualcategorical properties are then relativized to r-properties by requiring mediatingmorphisms to be unique up to some Leibniz equality. Using these terminologies,it is shown, by an example, that the term model of the encoding of an adequatelyrepresented object calculus is r-isomorphic to the term model of the object language.
