CS 611 Lecture 34 Curry - Howard Isomorphism November 15 , 2000
نویسنده
چکیده
The Curry-Howard isomorphism is a correspondence between logical formulas and types. The central idea is that each type τ corresponds to a logical formula φ, and that a proof that some expression e is well-formed with respect to type τ , (i.e., e : τ) corresponds to a proof that the logical formula φ is logically valid. Many variations of classical logic have been developed, especially in the last century. We’re most interested in establishing an isomorphism between types and logical formulas in constructive, or intuitionistic logic. In constructive logic, formulas of the form φ ∨ ¬φ and ¬¬φ ⇔ φ, for example, are not valid. To demonstrate that a formula is valid in constructive logic, it is not enough to demonstrate that its negation is not valid.
منابع مشابه
Constructive Classical Logic as CPS-Calculus
We establish the Curry-Howard isomorphism between constructive classical logic and CPS-calculus. CPS-calculus exactly means the target language of Continuation Passing Style(CPS) transforms. Constructive classical logic we refer to are LKT and LKQ introduced by Danos et al.(1993).
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