Notes on Sconing and Relators

@inproceedings{Mitchell1992NotesOS,
  title={Notes on Sconing and Relators},
  author={John C. Mitchell and Andre Scedrov},
  booktitle={CSL},
  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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References

SHOWING 1-10 OF 59 REFERENCES
A relational approach to strictness analysis for higher-order polymorphic functions
TLDR
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. Expand
Computational lambda-calculus and monads
  • E. Moggi
  • Mathematics, Computer Science
  • [1989] Proceedings. Fourth Annual Symposium on Logic in Computer Science
  • 1989
TLDR
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. Expand
Categorical Semantics for Higher Order Polymorphic Lambda Calculus
  • R. Seely
  • Mathematics, Computer Science
  • J. Symb. Log.
  • 1987
On definit une structure categorique adaptee a l'interpretation du lambda-calcul polymorphe, qui fournit une semantique algebrique solide et complete
Logical Relations and the Typed lambda-Calculus
  • R. Statman
  • Computer Science, Mathematics
  • Inf. Control.
  • 1985
TLDR
Demonstration des principaux resultats syntaxiques sur le calcul de type lambda a partir du theoreme fondamental des relations logiques. Expand
Theorems for free!
TLDR
From the type of a polymorphic function the authors can derive a theorem that it satisfies, courtesy of Reynolds’ abstraction theorem for the polymorphic lambda calculus, which provides a free source of useful theorems. Expand
Proofs and types
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 systemExpand
Extensional Models for Polymorphism
TLDR
The polymorphic extensional collapse method yields models that prove that the polymorphic lambda calculus can be conservatively added to arbitrary algebraic data type specifications, even with complete transfer of the computational power to the added data types. Expand
Types, Abstractions, and Parametric Polymorphism, Part 2
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, andExpand
On the Relation between Direct and Continuation Semantics
TLDR
This work gives two theorems which specify the relationship between the direct and the continuation semantic functions for a purely applicative language and shows that direct semantics are included in continuation semantics. Expand
An Extension of System F with Subtyping
TLDR
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. Expand
...
1
2
3
4
5
...