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# Computing with recursive types

## By: Cosmadakis, S.S.;

1989 / IEEE / 0-8186-1954-6

### Description

This item was taken from the IEEE Periodical ' Computing with recursive types ' A study is made of the complete adequacy for a lambda -calculus with simple recursive types. The set of types is built using the standard domain-theoretic constructors, namely, function space, sum, cartesian and strict product, and lifting. The recursive types allow the author to solve arbitrary systems of mutually recursive domain equations. Thus, he can define in this calculus types of integers, Booleans, lists and streams over these, and so on. The author can also define numerals, Boolean constants, simple arithmetic versions, of pure untyped terms. A precise description is given of the author's calculus, as well as some examples illustrating its expressiveness. A complete adequacy result for the lattice semantics is presented. The problem of designing a completely adequate evaluator for the CPO semantics is also examined.<

**Related Topics**

Formal Languages

Formal Logic

Cpo Semantics

Recursive Types

Lambda -calculus

Set Of Types

Domain-theoretic Constructors

Function Space

Sum

Cartesian

Strict Product

Lifting

Arbitrary Systems

Mutually Recursive Domain Equations

Integers

Booleans

Lists

Streams

Numerals

Boolean Constants

Simple Arithmetic Versions

Pure Untyped Terms

Lattice Semantics

Fixed-point Arithmetic

Lattices

Mathematical Programming

Impedance Matching

Testing

Equations

Calculus

Standards Development

Data Structures

Recursive Functions

Engineering