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Propositional G&#x00F6;del logic G extends intuitionistic logic with the non-constructive principle of linearity (A &#x2192; B) &#x2228; (B &#x2192; A). We introduce a Curry-Howard correspondence for G and show that a simple natural deduction calculus can be used as a typing system. The resulting functional language extends the simply typed &#x03BB;-calculus via a synchronous communication mechanism between parallel processes, which increases its expressive power. The normalization proof employs original termination arguments and proof transformations implementing forms of code mobility. Our results provide a computational interpretation of G, thus proving A. Avron's 1991 thesis.

Gödel logic: From natural deduction to parallel computation