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MPC
1998
Springer
83views Mathematics» more  MPC 1998»
13 years 9 months ago
Nested Datatypes
A nested datatype, also known as a non-regular datatype, is a parametrised datatype whose declaration involves different instances of the accompanying type parameters. Nested datat...
Richard S. Bird, Lambert G. L. T. Meertens
CIE
2008
Springer
13 years 7 months ago
Recursion on Nested Datatypes in Dependent Type Theory
Nested datatypes are families of datatypes that are indexed over all types and where the datatype constructors relate different members of the family. This may be used to represent...
Ralph Matthes
SCP
2011
255views Communications» more  SCP 2011»
13 years 11 days ago
Map fusion for nested datatypes in intensional type theory
A definitional extension LNGMIt of the Calculus of Inductive Constructions (CIC), that underlies the proof assistant Coq, is presented that allows also to program with nested dat...
Ralph Matthes
FOSSACS
2003
Springer
13 years 10 months 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
LICS
2012
IEEE
11 years 7 months ago
Foundational, Compositional (Co)datatypes for Higher-Order Logic: Category Theory Applied to Theorem Proving
—Interactive theorem provers based on higher-order logic (HOL) traditionally follow the definitional approach, reducing high-level specifications to logical primitives. This al...
Dmitriy Traytel, Andrei Popescu, Jasmin Christian ...