Provable isomorphisms and domain equations in models of typed languages
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Proofs and types
Journal of Information Processing and Cybernetics
On the representation of data in lambda-calculus
CSL '89 Proceedings of the third workshop on Computer science logic
Recursive programming with proofs
Theoretical Computer Science - Special issue on discrete mathematics and applications to computer science
A framework for defining logics
Journal of the ACM (JACM)
Functions over free algebras definable in the simply typed lambda calculus
Theoretical Computer Science - A collection of contributions in honour of Corrado Bo¨hm on the occasion of his 70th birthday
On functors expressible in the polymorphic typed lambda calculus
Information and Computation
Isomorphisms of types: from &lgr;-calculus to information retrieval and language design
Isomorphisms of types: from &lgr;-calculus to information retrieval and language design
Proof-nets and the Hilbert space
Proceedings of the workshop on Advances in linear logic
The optimal implementation of functional programming languages
The optimal implementation of functional programming languages
A Note on Categorical Datatypes
Category Theory and Computer Science
Positive Recursive Type Assignment
Fundamenta Informaticae
Least and greatest fixed points in intuitionistic natural deduction
Theoretical Computer Science - Special issue on theories of types and proofs
Least and greatest fixed points in intuitionistic natural deduction
Theoretical Computer Science - Special issue on theories of types and proofs
Encoding Intensional Type Analysis
ESOP '01 Proceedings of the 10th European Symposium on Programming Languages and Systems
Monotone Inductive and Coinductive Constructors of Rank 2
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
Type-based termination of recursive definitions
Mathematical Structures in Computer Science
Minimality in a Linear Calculus with Iteration
Electronic Notes in Theoretical Computer Science (ENTCS)
On the building of affine retractions
Mathematical Structures in Computer Science
The visitor pattern as a reusable, generic, type-safe component
Proceedings of the 23rd ACM SIGPLAN conference on Object-oriented programming systems languages and applications
On Constructor Rewrite Systems and the Lambda-Calculus
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Deciding monadic theories of hyperalgebraic trees
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
Parigot's second order λµ-calculus and inductive types
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
On the stability by union of reducibility candidates
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
Monad translating inductive and coinductive types
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
Parametricity, type equality, and higher-order polymorphism
Journal of Functional Programming
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Positive recursive (fixpoint) types can be added to the polymorphic (Church-style) lambda calculus λ2 (System F) in several different ways, depending on the choice of the elimination operator. We compare several such definitions and we show that they fall into two equivalence classes with respect to mutual interpretability by means of beta-eta reductions. Elimination operators for fixpoint types are thus classified as either "iterators" or "recursors". This classification has an interpretation in terms of the Curry-Howard correspondence: types of iterators and recursors can be seen as images of induction axioms under different dependency-erasing maps. Systems with recursors are beta-eta equivalent to a calculus λ2U of recursive types with the operators Fold: σ[μα.σ/α]←μα.σ and Unfold: μα.σ←σ[μα.σ/α], where the composition Unfold or Fold reduces to identity.It is known that systems with iterators can be defined within λ2, by means of beta reductions. We conjecture that systems with recursors can not. In this paper we show that the system λ2U does not have such a property. For this we study the notion of polymorphic type embeddability (via (beta) left-invertible terms) and we show that if a type σ is embedded into another type τ then τ must be of depth at least equal to the depth of σ.