Assistant of proof

In Data-processing (or Mathematical assisted by data processing), a assistant of proof is a Logiciel allowing the writing and the checking of mathematical evidence, either on Théorème S in the usual sense of mathematics, or on assertions relating to the execution of computer programs.

The writing of entirely formal evidence is an extremely tiresome activity; many stages which would be jumped, because considered as obvious for the reader familiar of mathematics, must be peeled in the greatest details. However, the assistant of proof can more or less provide automation to limit the work of the human user. Certain assistants of proof, such as special minutes, have procedures of decision in fields often used and décidables (such as the Arithmétique of Presburger); often, procedures of semi-decision are added to them (which do not finish inevitably successfully).

An objection with the use of assistants of proof is that, in any event, the safety of the evidence obtained rests on the good performance of the assistant. Indeed, the assistants of evidence are large complex software, which one can suspect that they are them-even bugs. An assistant of proof bug can allow to show the Absurde. Certain assistants of proof, like Cock, produce a term of proof whose checking can be deputy with a software much simpler than a complete assistant; thus, Coq produces terms of the Calcul of Constructions (inductive, now), a Lambda-calculation typified of a higher nature, which one can relatively easily check if they are correctly typified. Cock, moreover, itself was proven in Coq, which returns confidence that one can have in this software a little more legitimate.

Note on the terminology: the use of proof in the place of demonstration is, in any rigor, an Anglicism, as a direct translation of the word “proof”, but the use of the word “proof” now forms part of the language of the specialists and this article yields with this use. The difficulty is all the more large as the word “demonstration” has a different everyday usage in English.

Assistants of proof

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Automatic and interactive Prouveurs A prouvor is a automatic Démonstrateur of theorems or a interactive Démonstrateur of theorems. The term is a Anglicisme coming from English prover . The term is of everyday usage in the field.

For the Method B

Workshop B with its prouvor and PP, the prouvor of predicate
the balbulette (http://www.b4free.com/)
to also see proB (stimulating and model-checker) www.ecs.soton.ac.uk/~mal/systems/prob.html

Boyer-Moore (http://www.cs.utexas.edu/users/boyer/ftp/nqthm/ and http://www.cs.utexas.edu/users/moore/best-ideas/nqthm/)
ACL http://www.cs.utexas.edu/users/moore/acl2/
special minutes http://pvs.csl.sri.com/
Affirm (University off. Southern California)
Gypsy prover (GTP)
EVES and NEVER (ORA, Canada) http://www.ora.on.ca/eves/welcome.html
Larch http://www.sds.lcs.mit.edu/spd/larch/
Lean http://i12www.ira.uka.de/leantap/
Lego http://www.dcs.ed.ac.uk/home/lego/
Cock http://coq.inria.fr/coq-fra.html
HOL http://www.cl.cam.ac.uk/Research/HVG/HOL/
IMPS http://imps.mcmaster.ca/
Isabelle http://www.cl.cam.ac.uk/Research/HVG/Isabelle/
Otter http://www-unix.mcs.anl.gov/AR/otter/
TPS http://gtps.math.cmu.edu/tps.html
Mona http://www.brics.dk/mona/
LoTREC http://www.irit.fr/ACTIVITES/LILaC/Lotrec/-- >

See too

Pasigraphie
Décidabilité and indecidability

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