Denotational Semantics of Call-by-name Normalization in Lambda-mu Calculus

We study normalization in the simply typed lambda-mu calculus, an extension of lambda calculus with control flow operators. Using an enriched version of the Yoneda embedding, we obtain a categorical normal form function for simply typed lambda-mu terms, which gives a special kind of a call-by-name denotational semantics particularly useful for deciding equalities in the lambda-mu calculus.

[1]  Peter Selinger,et al.  Control categories and duality: on the categorical semantics of the lambda-mu calculus , 2001, Mathematical Structures in Computer Science.

[2]  Ulrich Berger,et al.  An inverse of the evaluation functional for typed lambda -calculus , 1991, [1991] Proceedings Sixth Annual IEEE Symposium on Logic in Computer Science.

[3]  Martin Hofmann,et al.  Normalization by evaluation for typed lambda calculus with coproducts , 2001, Proceedings 16th Annual IEEE Symposium on Logic in Computer Science.

[4]  Timothy G. Griffin,et al.  A formulae-as-type notion of control , 1989, POPL '90.

[5]  J. Lambek,et al.  Introduction to higher order categorical logic , 1986 .

[6]  Martin Hofmann,et al.  Completeness of Continuation Models for lambda-mu-Calculus , 2002, Inf. Comput..

[7]  Thomas Streicher,et al.  Classical logic, continuation semantics and abstract machines , 1998, Journal of Functional Programming.

[8]  Charles S. Peirce,et al.  Studies in Logic , 2008 .

[9]  Peter Dybjer,et al.  Normalization and the Yoneda Embedding , 1998, Math. Struct. Comput. Sci..

[10]  Ichiro Ogata.  A Proof Theoretical Account of Continuation Passing Style , 2002, CSL.

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

[12]  C.-H. Luke Ong,et al.  A semantic view of classical proofs: type-theoretic, categorical, and denotational characterizations , 1996, Proceedings 11th Annual IEEE Symposium on Logic in Computer Science.

[13]  G. M. Kelly,et al.  BASIC CONCEPTS OF ENRICHED CATEGORY THEORY , 2022, Elements of ∞-Category Theory.

[14]  Michel Parigot,et al.  Lambda-Mu-Calculus: An Algorithmic Interpretation of Classical Natural Deduction , 1992, LPAR.

[15]  S. Lane.  Categories for the Working Mathematician , 1971 .