Boomborg-PC: A Proof-Checker of Calculus of Constructions

Boomborg-PC is a proof-checker of Calculus of Constructions that runs on a bu er of GNU Emacs. Calculus of Constructions, proposed by Thierry Coquand and G erard Huet [2], is one of the so-called higher-order typed -calculi [1]. A typed -calculus is a formal system for writing typed -terms, and Boomborg-PC is a program that typechecks -terms written by the rules of Calculus of Constructions. A typed -calculus is called higher-order, if it has variables ranging over types. Higher-order typed -calculi, including Calculus of Constructions, are also called general logic or logical framework, because they can be used as a general framework to implement various kinds of logical system such as rst-order predicate calculus. This means that representing a proposition of a logical system as a type and a proof as a -term by the Curry-Howard correspondence, one can implement the logical system on a higherorder typed -calculus. Consequently, by typechecking a -term, one can check a proof that is represented by the -term. In recent years, many proof-checkers based on higher-order typed -calculi have been developed [11, 3, 9], and higher-order typed -calculi have become a standard framework for writing formal proofs. Extended Calculus of Constructions [6], proposed by Zhaohui Luo, is an extension of Calculus of Constructions by -types and a type hierarchy. Boomborg-PC can also typecheck -terms in a subsystem of Extended Calculus of Constructions. On the other hand, GNU Emacs is a general-purpose text editor developed by Richard Stallman [10], and has become a standard text editor on workstations. Nemacs, the Japanese version of GNU Emacs, developed by Ken'ichi Handa et al., and its descendant Mule, the multilingual enhancement to GNU Emacs, are also widely used as a Japanese text editor [5, 8]. Boomborg-PC is a typechecker in which one can typecheck -terms of Calculus of Constructions on a bu er of Mule or Nemacs. The characteristic features of Boomborg-PC as a proof-checker can be summarized as follows.