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Dependent Types and Explicit Substitutions
, 1999
"... We present a dependenttype system for a #calculus with explicit substitutions. In this system, metavariables, as well as substitutions, are firstclass objects. We show that the system enjoys properties like type uniqueness, subject reduction, soundness, confluence and weak normalization. ..."
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We present a dependenttype system for a #calculus with explicit substitutions. In this system, metavariables, as well as substitutions, are firstclass objects. We show that the system enjoys properties like type uniqueness, subject reduction, soundness, confluence and weak normalization.
Interpreting ChurchStyle Typed λCalculus in CurryStyle Type Assignment
, 1997
"... It is well known that there are problems with the labelled syntax in Churchstyle type assignment to lambdaterms, the syntax in which the types of bound variables are indicated, as in λx : # . M , since if #reduction is added then the ChurchRosser Theorem fails in general (although it has been p ..."
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It is well known that there are problems with the labelled syntax in Churchstyle type assignment to lambdaterms, the syntax in which the types of bound variables are indicated, as in λx : # . M , since if #reduction is added then the ChurchRosser Theorem fails in general (although it has been proved for some common systems of type assignment) . In this paper, the labelled syntax is interpreted in the standard syntax of Currystyle type assignment by means of a constant Label, so that λx : # . M is taken as an abbreviation for Label#(λx . M ). The constant Label can be defined as a closed term, so that the labelled syntax is ultimately interpreted in a syntax for which the ChurchRosser Theorem is known to hold for both #reduction and #reduction. This interpretation is carried through for three well known systems of type assignment: ordinary type assignment, the secondorder polymorphic typed lambdacalculus, and the calculus of constructions. These cases illustrate the general ...
Variants of the Basic Calculus of Constructions
, 2004
"... In this paper, a number of different versions of the basic calculus of constructions that have appeared in the literature are compared and the exact relationships between them are determined. The biggest differences between versions are those between the original version of Coquand and the version i ..."
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In this paper, a number of different versions of the basic calculus of constructions that have appeared in the literature are compared and the exact relationships between them are determined. The biggest differences between versions are those between the original version of Coquand and the version in early papers on the subject by Seldin. None of these results is very deep, but it seems useful to collect them in one place.
ThirdOrder Matching in the Polymorphic Lambda Calculus
"... We show that it is decidable whether a thirdorder matching problem in the polymorphic lambda calculus has a solution. The proof is constructive in the sense that an algorithm can be extracted from it that, given such a problem, returns a substitution if it has a solution and fail otherwise. 1 ..."
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We show that it is decidable whether a thirdorder matching problem in the polymorphic lambda calculus has a solution. The proof is constructive in the sense that an algorithm can be extracted from it that, given such a problem, returns a substitution if it has a solution and fail otherwise. 1
ThirdOrder Matching in the Presence of Type Constructors
"... We showthat it is decidable whether a thirdorder matching problem in! (an extension of the simply typed lambda calculus with type constructors) has a solution or not. We present an algorithm which, given such a problem, returns a solution for this problem if the problem has a solution and returns f ..."
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We showthat it is decidable whether a thirdorder matching problem in! (an extension of the simply typed lambda calculus with type constructors) has a solution or not. We present an algorithm which, given such a problem, returns a solution for this problem if the problem has a solution and returns fail otherwise. We also show that it is undecidable whether a thirdorder matching problem in! has a closed solution or not. 1