Incorporating Quotation and Evaluation Into Church's Type Theory

Incorporating Quotation and Evaluation into Church's Type Theory: Syntax and Semantics

cttqe is a version of Church’s type theory that includes quotation and evaluation operators that are similar to quote and eval in the Lisp programming language. With quotation and evaluation it is possible to reason in cttqe about the interplay of the syntax and semantics of expressions and, as a result, to formalize syntax-based mathematical algorithms. We present the syntax and semantics of c...

Theory Morphisms in Church's Type Theory with Quotation and Evaluation

cttqe is a version of Church’s type theory with global quotation and evaluation operators that is engineered to reason about the interplay of syntax and semantics and to formalize syntax-based mathematical algorithms. cttuqe is a variant of cttqe that admits undefined expressions, partial functions, and multiple base types of individuals. It is better suited than cttqe as a logic for building n...

HOL Light QE

We are interested in algorithms that manipulate mathematical expressions in mathematically meaningful ways. Expressions are syntactic, but most logics do not allow one to discuss syntax. cttqe is a version of Church’s type theory that includes quotation and evaluation operators, akin to quote and eval in the Lisp programming language. Since the HOL logic is also a version of Church’s type theor...

Simple Type Theory with Undefinedness, Quotation, and Evaluation

This paper presents a version of simple type theory called Q uqe 0 that is based on Q0, the elegant formulation of Church’s type theory created and extensively studied by Peter B. Andrews. Q uqe 0 directly formalizes the traditional approach to undefinedness in which undefined expressions are treated as legitimate, nondenoting expressions that can be components of meaningful statements. Q uqe 0...

Ingredients for Good Health Policy-Making: Incorporating Power and Politics into the Mix