Interactive Theorem Proving and Program Development

Author(s):  
Yves Bertot ◽  
Pierre Castéran
2009 ◽  
Vol 19 (5) ◽  
pp. 877-896 ◽  
Author(s):  
ANDREA ASPERTI ◽  
HERMAN GEUVERS ◽  
RAJA NATARAJAN

In a controversial paper (De Millo et al. 1979) at the end of the 1970's, R. A. De Millo, R. J. Lipton and A. J. Perlis argued against formal verifications of programs, mostly motivating their position by an analogy with proofs in mathematics, and, in particular, with the impracticality of a strictly formalist approach to this discipline. The recent, impressive achievements in the field of interactive theorem proving provide an interesting ground for a critical revisiting of their theses. We believe that the social nature of proof and program development is uncontroversial and ineluctable, but formal verification is not antithetical to it. Formal verification should strive not only to cope with, but to ease and enhance the collaborative, organic nature of this process, eventually helping us to master the growing complexity of scientific knowledge.


2011 ◽  
Vol 21 (4) ◽  
pp. 671-677 ◽  
Author(s):  
GÉRARD HUET

This special issue of Mathematical Structures in Computer Science is devoted to the theme of ‘Interactive theorem proving and the formalisation of mathematics’.The formalisation of mathematics started at the turn of the 20th century when mathematical logic emerged from the work of Frege and his contemporaries with the invention of the formal notation for mathematical statements called predicate calculus. This notation allowed the formulation of abstract general statements over possibly infinite domains in a uniform way, and thus went well beyond propositional calculus, which goes back to Aristotle and only allowed tautologies over unquantified statements.


2021 ◽  
Author(s):  
Steven Obua

This is a first sketch of the design of Practal, an interactive theorem proving system for practical logic.


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