Matita (means pencil in italian) is an experimental, interactive theorem prover.
An interactive prover is a software tool aiding the development of formal proofs by man-machine collaboration. It provides a formal language where mathematical definitions, executable algorithms and theorems cohexist, and an interactive environment keeping the current status of the proof, and updating it according to commands (usually called tactics) issued by the user.
Matita is based on a Dependent Type System known as the Calculus of Inductive Constructions.
It embeds key computational constructs of functional programming languages: functions can be defined by (well-founded) recursion, and are live entities that can be tested and executed.
At the same time, proofs are an integrated part of the formalism, allowing, via the Curry Howard isomorphism, a smooth interplay between specification, implementation and verification: proofs are objects of the language, and can be treated as normal data, naturally leading to a programming style akin to proof-carrying-code, where chunks of software come equipped with proofs of (some of) their properties.
Matita is part of HELM, an Hypertextual, Electronic Library of Mathematics, developed at the Computer Science Department, University of Bologna, Italy.
Website: github.com/LPCIC/matita
Support:
Developer: Andrea Asperti, Ferruccio Guidi, Luca Padovani, Enrico Tassi, Claudio Sacerdoti Coen, and Stefano Zacchiroli
License: GNU General Public License v2.0
Related Software
| Proof Assistants | |
|---|---|
| Coq | Formal proof management system |
| Isabelle | Generic proof assistant; express mathematical formulas in a formal language |
| Agda | Interactive system for writing and checking proofs |
| Lean | Programming language and theorem prover |
| Matita | Experimental, interactive theorem prover |
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