PhoX
Encyclopedia
In automated theorem proving
, PhoX is a proof assistant based on higher-order logic
which is eXtensible. The user gives PhoX an initial goal and guides it through subgoals and evidence to prove that goal; internally, it constructs natural deduction trees. Each previously proven formula can become a rule for later proofs.
PhoX was originally designed and implemented by Christophe Raffalli in the Objective Caml
programming language
. He has continued to lead the current development team, a joint effort of Savoy University and University Paris VII
.
The primary aim of the PhoX project creating a user friendly proof checker using the type system developed by Jean-Louis Krivine at University Paris VII. It is meant to be more intuitive than other systems while remaining extensible, efficient, and expressive. Compared to other systems, the proof-building syntax is simplified and closer to natural language. Other features include GUI-driven proof construction, rendering formatted output, and proof of correctness of programs in the ML programming language.
PhoX is currently used to teach logic at Savoy University. It is in an experimental but usable state.
Automated theorem proving
Automated theorem proving or automated deduction, currently the most well-developed subfield of automated reasoning , is the proving of mathematical theorems by a computer program.- Decidability of the problem :...
, PhoX is a proof assistant based on higher-order logic
Higher-order logic
In mathematics and logic, a higher-order logic is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and a stronger semantics...
which is eXtensible. The user gives PhoX an initial goal and guides it through subgoals and evidence to prove that goal; internally, it constructs natural deduction trees. Each previously proven formula can become a rule for later proofs.
PhoX was originally designed and implemented by Christophe Raffalli in the Objective Caml
Objective Caml
OCaml , originally known as Objective Caml, is the main implementation of the Caml programming language, created by Xavier Leroy, Jérôme Vouillon, Damien Doligez, Didier Rémy and others in 1996...
programming language
Programming language
A programming language is an artificial language designed to communicate instructions to a machine, particularly a computer. Programming languages can be used to create programs that control the behavior of a machine and/or to express algorithms precisely....
. He has continued to lead the current development team, a joint effort of Savoy University and University Paris VII
University of Paris VII: Denis Diderot
Paris Diderot University, also known as Université Paris Diderot - Paris 7, is a French leading University located in Paris, France. It is one of the heirs of the Faculty of Sciences of the University of Paris , which was one of the earliest established in Europe, founded in the mid 12th century...
.
The primary aim of the PhoX project creating a user friendly proof checker using the type system developed by Jean-Louis Krivine at University Paris VII. It is meant to be more intuitive than other systems while remaining extensible, efficient, and expressive. Compared to other systems, the proof-building syntax is simplified and closer to natural language. Other features include GUI-driven proof construction, rendering formatted output, and proof of correctness of programs in the ML programming language.
PhoX is currently used to teach logic at Savoy University. It is in an experimental but usable state.