Notes on Sconing and Relators
@inproceedings{Mitchell1992NotesOS, title={Notes on Sconing and Relators}, author={John C. Mitchell and Andre Scedrov}, booktitle={Annual Conference for Computer Science Logic}, year={1992} }
This paper describes a semantics of typed lambda calculi based on relations. The main mathematical tool is a category-theoretic method of sconing, also called glueing or Freyd covers. Its correspondence to logical relations is also examined.
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43 References
A relational approach to strictness analysis for higher-order polymorphic functions
- 1991
Computer Science
POPL '91
This paper defines the categorical notions of relators and transformations and shows that these concepts enable us to give a semantics for polymorphic, higher order functional programs and proves that strictness analysis is a polymorphic invariant.
Computational lambda-calculus and monads
- 1989
Computer Science
[1989] Proceedings. Fourth Annual Symposium on Logic in Computer Science
The author gives a calculus based on a categorical semantics for computations, which provides a correct basis for proving equivalence of programs, independent from any specific computational model.
An Extension of System F with Subtyping
- 1991
Mathematics
TACS
The main focus of the paper is the equational theory of F<:, which is related to PER models and the notion of parametricity, and some categorical properties of the theory when restricted to closed terms, including interesting categorical isomorphisms.
Categorical Semantics for Higher Order Polymorphic Lambda Calculus
- 1987
Computer Science
J. Symb. Log.
A categorical structure suitable for interpreting polymorphic lambda calculus (PLC) is defined, providing an algebraic semantics for PLC which is sound and complete and an equivalence between the theories and the categories.
Theorems for free!
- 1989
Mathematics
FPCA
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Categorical data types in parametric polymorphism
- 1994
Mathematics, Computer Science
Mathematical Structures in Computer Science
It is proved that Reynolds parametricity is a sufficient and necessary condition for the categorical data types to fulfill the universal properties of second order lambda calculus.
Proofs and types
- 1989
Philosophy
Sense, denotation and semantics natural deduction the Curry-Howard isomorphism the normalisation theorem Godel's system T coherence spaces denotational semantics of T sums in natural deduction system…
Types, Abstractions, and Parametric Polymorphism, Part 2
- 1991
Mathematics
MFPS
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