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+ Matita is a new document-centric interactive theorem prover that - integrates several Mathematical Knowledge - Management tools and techniques.
++ Matita (that means pencil in italian) is an experimental, + interactive theorem prover under development at the + Computer Science Department of the + University of Bologna. +
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- Matita is traditional. Its logical foundation is the
- Calculus of (Co)Inductive Constructions (CIC). It can re-use
- mathematical concepts produced by other proof assistants like
- Coq and encoded in an
- XML encoding of CIC. The interaction
- paradigm of Matita is familiar, being inspired by CtCoq and
- Proof General. Its
- proof language is procedural in the same spirit of LCF.
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 innovative:
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- the user interface sports high quality bidimensional rendering of
- proofs and formulae transformed on-the-fly to MathML markup, on which direct
- manipulation of the underlying CIC terms is still possible;
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- the knowledge base is distributed: every authored concepts can be
- published becoming part of the Matita library which can be browsed as an hypertext
- (locally or on the World Wide Web) and searched by means of
- content-based queries;
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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.
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- + Matita is based on a Dependent Type System known as the Calculus of Inductive Constructions.
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- 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.
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- 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. +
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