Access Restriction

Author Wiedijk, Freek
Source CiteSeerX
Content type Text
File Format PDF
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Declarative Style ♦ Logical Foundation ♦ Declarative System ♦ Declarative Language ♦ Interactive Theorem Provers ♦ Easy Access ♦ Full Set ♦ Hol Light ♦ Isabelle Isar ♦ Procedural Style Strong Automation ♦ Proof Interface ♦ Intermediate Step ♦ Procedural Proof ♦ Industrial Strength ♦ Matita System ♦ Procedural Style ♦ Hol Light Interactive Theorem Prover ♦ Declarative Counterpart ♦ Proof Language ♦ Declarative Proof Style ♦ Formal Proof ♦ Miz3 Interface ♦ Mizar System ♦ Proof Style ♦ Formal Library ♦ Slight Variant ♦ Procedural Interactive Theorem Prover ♦ Interactive Theorem Prover Regardless ♦ Interactive Theorem Proving ♦ Normal Mathematical Text ♦ Straightforward Way ♦ Controlled Natural Language
Abstract Abstract. We propose a synthesis of the two proof styles of interactive theorem proving: the procedural style (where proofs are scripts of commands, like in Coq) and the declarative style (where proofs are texts in a controlled natural language, like in Isabelle/Isar). Our approach combines the advantages of the declarative style – the possibility to write formal proofs like normal mathematical text – and the procedural style – strong automation and help with shaping the proofs, including determining the statements of intermediate steps. Our approach is new, and differs significantly from the ways in which the procedural and declarative proof styles have been combined before in the Isabelle, Ssreflect and Matita systems. Our approach is generic and can be implemented on top of any procedural interactive theorem prover, regardless of its architecture and logical foundations. To show the viability of our proposed approach, we fully implemented it as a proof interface called miz3, on top of the HOL Light interactive theorem prover. The declarative language that this interface uses is a slight variant of the language of the Mizar system, and can be used for any interactive theorem prover regardless of its logical foundations. The miz3 interface allows easy access to the full set of tactics and formal libraries of HOL Light, and as such has ‘industrial strength’. Our approach gives a way to automatically convert any procedural proof to a declarative counterpart, where the converted proof is similar in size to the original. As all declarative systems have essentially the same proof language, this gives a straightforward way to port proofs between interactive theorem provers. 1.
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article