منابع مشابه
Refining Inductive Types
Dependently typed programming languages allow sophisticated properties of data to be expressed within the type system. Of particular use in dependently typed programming are indexed types that refine data by computationally useful information. For example, the N-indexed type of vectors refines lists by their lengths. Other data types may be refined in similar ways, but programmers must produce ...
متن کاملQuotient inductive-inductive types
Higher inductive types (HITs) in Homotopy Type Theory (HoTT) allow the definition of datatypes which have constructors for equalities over the defined type. HITs generalise quotient types, and allow to define types which are not sets in the sense of HoTT (i.e. do not satisfy uniqueness of equality proofs) such as spheres, suspensions and the torus. However, there are also interesting uses of HI...
متن کاملRefining algebraic data types
Our purpose is to formalize two potential refinements of single-sorted algebraic data types – subalgebras and algebras which satisfy equivalence relations – by considering their categorical interpretation. We review the usual categorical formalization of singleand multi-sorted algebraic data types as initial algebras, and the correspondence between algebraic data types and endofunctors. We intr...
متن کاملA Syntax for Higher Inductive-Inductive Types∗
Higher inductive-inductive types (HIITs) generalise inductive types of dependent type theories in two directions. On the one hand they allow the simultaneous definition of multiple sorts that can be indexed over each other. On the other hand they support equality constructors, thus generalising higher inductive types of homotopy type theory. Examples that make use of both features are the Cauch...
متن کاملOrder-Sorted Inductive Types
System F ! is an extension of system F ! with subtyping and bounded quantiication. Order-sorted algebra is an extension of many-sorted algebra with overloading and subtyping. We combine both formalisms to obtain IF ! , a higher-order typed-calculus with subtyping, bounded quan-tiication and order-sorted inductive types, i.e. data types with built-in subtyping and overloading. Moreover we show t...
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ژورنال
عنوان ژورنال: Logical Methods in Computer Science
سال: 2012
ISSN: 1860-5974
DOI: 10.2168/lmcs-8(2:9)2012