Embedding first-order logic in a pure type system with parameters (Q2761749)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Embedding first-order logic in a pure type system with parameters |
scientific article; zbMATH DE number 1686293
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Embedding first-order logic in a pure type system with parameters |
scientific article; zbMATH DE number 1686293 |
Statements
7 January 2002
0 references
\(\beta\)-normal form
0 references
type theory
0 references
typed \(\lambda\)-calculus
0 references
first-order predicate logic
0 references
pure type system
0 references
Embedding first-order logic in a pure type system with parameters (English)
0 references
A standard way to code first-order predicate logic in a propositions-as-types style uses a type system that is a variant of the pure type system \(\lambda P\). Types in this system are not necessarily in \(\beta\)-normal form. Therefore, checking whether two types are \(\beta\)-equal is decidable, albeit sometimes costly in terms of time and/or memory. In this paper we present an alternative to Berardi's system, based on pure type systems with parameters. We show that all types in our system are in \(\beta\)-normal form, which is an advantage for implementations. Moreover, the syntactical structure of the system with parameters is similar to the syntax of first-order predicate logic. This is not the case for the system without parameters.
0 references
