Conference

# International Conference on Mathematical Foundations of Programming Semantics

About: International Conference on Mathematical Foundations of Programming Semantics is an academic conference. The conference publishes majorly in the area(s): Denotational semantics & Operational semantics. Over the lifetime, 105 publication(s) have been published by the conference receiving 2021 citation(s).

Topics: Denotational semantics, Operational semantics, Semantics (computer science), Typed lambda calculus, Bisimulation

##### Papers

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TL;DR: A new solution to the problem that arises and a standard approach to its solution is proposed, based on ideas taken from Girard's Logic of Unity, allowing for concise expression of programs.

Abstract: There is a standard syntax for Girard's linear logic, due to Abramsky, and a standard semantics, due to Seely. Alas, the former is incoherent with the latter: different derivations of the same syntax may be assigned different semantics. This paper reviews the standard syntax and semantics, and discusses the problem that arises and a standard approach to its solution. A new solution is proposed, based on ideas taken from Girard's Logic of Unity. The new syntax is based on pattern matching, allowing for concise expression of programs.

154 citations

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29 Mar 1989

TL;DR: It is shown that all primitive recursive functionals over these inductively defined types are also representable, and it is sketched some results that show that the extension of the Calculus of Construction by induction principles does not alter the set of functions in its computational fragment, F ω.

Abstract: We define the notion of an inductively defined type in the Calculus of Constructions and show how inductively defined types can be represented by closed types. We show that all primitive recursive functionals over these inductively defined types are also representable. This generalizes work by Bohm & Berarducci on synthesis of functions on term algebras in the second-order polymorphic λ-calculus (F 2). We give several applications of this generalization, including a representation of F 2-programs in F 3, along with a definition of functions reify, reflect, and eval for F 2 in F 3. We also show how to define induction over inductively defined types and sketch some results that show that the extension of the Calculus of Construction by induction principles does not alter the set of functions in its computational fragment, F ω. This is because a proof by induction can be realized by primitive recursion, which is already definable in F ω.

117 citations

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TL;DR: The concept of relations over sets is generalized to relations over an arbitrary category, and used to investigate the abstraction (or logical-relations) theorem, the identity extension lemma, and parametric polymorphism for Cartesian-closed-category models of the simply typed lambda calculus and PL-category model of the polymorphic typedlambda calculus.

Abstract: The concept of relations over sets is generalized to relations over an arbitrary category, and used to investigate the abstraction (or logical-relations) theorem, the identity extension lemma, and parametric polymorphism, for Cartesian-closed-category models of the simply typed lambda calculus and PL-category models of the polymorphic typed lambda calculus. Treatments of Kripke relations and of complete relations on domains are included.

111 citations

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11 Apr 1985

TL;DR: The aim of this note is to provide suitable levels of generality for Galois connections, which are no longer val id in the realm of adjoint situations and form an inappropriate level of generability.

Abstract: About 1830 E. Galois discovered and investigated a connection, for a given field extension K -* L, between the collection of all subfields of L containing K and the collection of all automorphisms of L leaving K pointwise fixed. The formal properties of this connection remain valid in more abstract settings. In 1940 G. Birkhoff [1] associated wi th any relation a connection, which he called a polarity. Generalizing this concept, O. Ore [8] introduced in 1944 Galois connexions between par t ia l ly ordered sets. These, as we l l as the polarities, have a contravariant form. Its covariant version was introduced in 1953 by J. Schmidt [11] under the name Galots connections of mixed type. Categorists observed that these connections are nothing else but adj0int s i tuations between par t ia l ly ordered sets, considered in the s tandard w a y as categories (see S. Mac Lane [7]). Unfor tuna te ly most properties of Galois connections, in fact a l l of the interesting ones, are no longer val id in the realm of adjoint situations. Hence, for Galois connections, adjoint functors form an inappropriate level of generality. The aim of this note is to provide suitable levels of generality.

98 citations

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TL;DR: A second-order type system over these operations supports both subtyping and polymorphism, and is provided with typechecking algorithms and limited semantic models.

Abstract: We define a simple collection of operations for creating and manipulating record structures, where records are intended as finite associations of values to labels. A second-order type system over these operations supports both subtyping and polymorphism. We provide typechecking algorithms and limited semantic models.

91 citations