论文信息 - Mechanical procedure for proof construction via closed terms in typed λ calculus

Mechanical procedure for proof construction via closed terms in typed λ calculus

In this paper is presented an algorithm for constructing natural deduction proofs in the propositional intuitionistic and classical logics according to the analogy relating intuitionistic propositional formulas and natural deduction proofs, respectively, to types and terms of simple type theory. Proofs are constructed as closed terms in the simple typed λ calculus. The soundness and completeness of this method are proved.

Marek Zaionc

[1] Alonzo Church,et al. A formulation of the simple theory of types , 1940, Journal of Symbolic Logic.

[2] Gérard P. Huet,et al. A Unification Algorithm for Typed lambda-Calculus , 1975, Theor. Comput. Sci..

[3] Richard Statman,et al. Intuitionistic Propositional Logic is Polynomial-Space Complete , 1979, Theor. Comput. Sci..

[4] Marek Zaionc. The Set of Unifiers in Typed Lambda-Calculus as Regular Expression , 1985, RTA.

[5] W. Tait. Infinitely Long Terms of Transfinite Type , 1965 .

[6] Harold T. Hodes,et al. The | lambda-Calculus. , 1988 .

[7] Per Martin-Löf,et al. Intuitionistic type theory , 1984, Studies in proof theory.

[8] H. Friedman. Equality between functionals , 1975 .

[9] A. Church. The calculi of lambda-conversion , 1941 .

[10] R. Statman,et al. On the Existence of Closed Terms in the Typed lambda Calculus II: Transformations of Unification Problems , 1981, Theor. Comput. Sci..