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Formalization of Constructive Mathematics

Objective

The general theme is to explore the connections between reasoning and computations in mathematics. There are two main research directions. The first research direction is a refomulation of Hilbert's program, using ideas from formal, or pointfree topology. We have shown, with multiple examples, that this allows a partial realization of this program in commutative algebra, and a new way to formulate constructive mathematics. The second research direction explores the computational content using type theory and the Curry-Howard correspondence between proofs and programs. Type theory allows us to represent constructive mathematics in a formal way, and provides key insight for the design of proof systems helping in the analysis of the logical structure of mathematical proofs. The interest of this program is well illustrated by the recent work of G. Gonthier on the formalization of the 4 color theorem.

Field of science

  • /natural sciences/mathematics/pure mathematics/algebra
  • /natural sciences/mathematics/pure mathematics/algebra/commutative algebra
  • /natural sciences/mathematics/pure mathematics/topology
  • /natural sciences/mathematics

Call for proposal

ERC-2009-AdG
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Funding Scheme

ERC-AG - ERC Advanced Grant
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Host institution

GOETEBORGS UNIVERSITET
Address
Vasaparken
405 30 Goeteborg
Sweden
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 1 912 288
Principal investigator
Thierry Coquand (Prof.)
Administrative Contact
Ludde Edgren (Dr.)

Beneficiaries (1)

GOETEBORGS UNIVERSITET
Sweden
EU contribution
€ 1 912 288
Address
Vasaparken
405 30 Goeteborg
Activity type
Higher or Secondary Education Establishments
Principal investigator
Thierry Coquand (Prof.)
Administrative Contact
Ludde Edgren (Dr.)