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FOSSACS
2003
Springer
14 years 18 days ago
Generalized Iteration and Coiteration for Higher-Order Nested Datatypes
Abstract. We solve the problem of extending Bird and Paterson’s generalized folds for nested datatypes and its dual to inductive and coinductive constructors of arbitrarily high ...
Andreas Abel, Ralph Matthes, Tarmo Uustalu
ICFP
1997
ACM
13 years 11 months ago
Foundations for the Implementation of Higher-Order Subtyping
We show how to implement a calculus with higher-order subtyping and subkinding by replacing uses of implicit subsumption with explicit coercions. To ensure this can be done, a pol...
Karl Crary
CORR
2011
Springer
170views Education» more  CORR 2011»
12 years 11 months ago
A Modular Type-checking algorithm for Type Theory with Singleton Types and Proof Irrelevance
We define a logical framework with singleton types and one universe of small types. We give the semantics using a PER model; it is used for constructing a normalisation-by-evaluat...
Andreas Abel, Thierry Coquand, Miguel Pagano
LICS
2003
IEEE
14 years 20 days ago
Structural Subtyping of Non-Recursive Types is Decidable
We show that the first-order theory of structural subtyping of non-recursive types is decidable, as a consequence of a more general result on the decidability of term powers of d...
Viktor Kuncak, Martin C. Rinard
FSTTCS
1993
Springer
13 years 11 months ago
Induce-Statements and Induce-Expressions: Constructs for Inductive Programming
A for-loop is somewhat similar to an inductive argument. Just as the truth of a proposition P(n + 1) depends on the truth of P(n), the correctness of iteration n+1 of a for-loop de...
Theodore S. Norvell