Dependent Types and Explicit Substitutions
نویسنده
چکیده
We present a dependent-type system for a λ-calculus with explicit substitutions. In this system, meta-variables, as well as substitutions, are first-class objects. We show that the system enjoys properties like type uniqueness, subject reduction, soundness, confluence and weak normalization.
منابع مشابه
On the Syntax of Dependent Types and the Coherence Problem (working Draft)
We discuss diierent ways to represent the syntax of dependent types using Martin-LL of type theory as a metalanguage. In particular, we show how to give an intrinsic syntax in which meaningful contexts, types in a context, and terms of a certain type in a context, are generated directly without rst introducing raw terms, types, and contexts. In the rst representation we deene inductively the no...
متن کاملPure Type Systems, Cut and Explicit Substitutions
Pure type systems are a general formalism allowing to represent many type systems – in particular, Barendregt’s λ-cube, including Girard’s system F , dependent types, and the calculus of constructions. We built a variant of pure type systems by adding a cut rule associated to an explicit substitution in the syntax, according to the Curry-Howardde Bruijn correspondence. The addition of the cut r...
متن کاملProof-term synthesis on dependent-type systems via explicit substitutions
Typed A-terms are used as a compact and linear representation of proofs in intuitionistic logic. This is possible since the Curry-Howard isomorphism relates proof trees with typed A-terms. The proofs-as-terms principle can be used to check a proof by type checking the A-term extracted from the complete proof tree. However, proof trees and typed A-terms are built differently. Usually, an auxilia...
متن کاملExplicit Pure Type Systems for the λ-Cube
Pure type systems are a general formalism allowing to represent many type systems – in particular, Barendregt’s λ-cube, including Girard’s system F , dependent types, and the calculus of constructions. We built a variant of pure type systems by adding a cut rule associated to an explicit substitution in the syntax, according to the Curry-Howardde Bruijn correspondence. The addition of the cut r...
متن کاملPractical Programming with Higher-Order Encodings and Dependent Types
Higher-order abstract syntax (HOAS) refers to the technique of representing variables of an object-language using variables of a meta-language. The standard first-order alternatives force the programmer to deal with superficial concerns such as substitutions, whose implementation is often routine, tedious, and error-prone. In this paper, we describe the underlying calculus of Delphin. Delphin i...
متن کامل