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+ @@ -21,6 +25,8 @@ University of Bologna.
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@@ -30,64 +36,36 @@ - Matita is based on the - Calculus of (Co)Inductive Constructions, and is compatible, at some - extent, with Coq. - It is a reasonably small and simple application, whose - architectural and software complexity is meant to be mastered by - students, providing a tool particularly suited for testing innovative - ideas and solutions. - Matita adopts a tactic based editing mode; (XML-encoded) proof objects - are produced for storage and exchange. +
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.
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- The graphical interface has been inspired by CtCoq and
- Proof General.
- It supports high quality bidimensional rendering of
- proofs and formulae transformed on-the-fly to
- MathML markup
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- The knowledge base can be
- browsed as an hypertext
- (locally or on the World Wide Web) and
- searched by means of
- content-based queries;
+ Matita is based on a Dependent Type System known as the Calculus of Inductive Constructions.
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- The tactical language, part of the proof language, has
- step-by-step semantics, enabling inspection and replaying of deeply
- structured proof scripts.
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 and reasoning: 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 currently adopted in the European Union "Certified Complexity" Project + CerCo for the formal verification of a + complexity-preserving compiler from a large subset of C to a microcontroller + assembly of the kind traditionally used in embedded systems. +
+ -