Explicit Substitutions for Constructive Necessity
نویسندگان
چکیده
This paper introduces a -calculus with explicit substitutions, corresponding to an S4 modal logic of constructive necessity. As well as being semantically well motivated, the calculus can be used (a) to develop abstract machines, and (b) as a framework for specifying and analysing computation stages in the context of functional languages. We prove several syntactic properties of this calculus, which we call xDIML, and then sketch its use as an interpretation of binding analysis and partial evaluation which respects execution of programs in stages.
منابع مشابه
Explicit Substitutitions for
This paper introduces a-calculus with explicit substitutions, corresponding to an S4 modal logic of constructive necessity. As well as being semantically well motivated, the calculus can be used (a) to develop abstract machines, and (b) as a framework for specifying and analysing computation stages in the context of functional languages. We prove several syntactic properties of this calculus, w...
متن کاملExplicit Substitutions Calculi with Explicit Eta Rules
It has been argued that the notion of substitution in the λ-calculus needs to be made explicit and many calculi have been developed in which the computational steps of the substitution operation involved in β-contractions have been atomised. In contrast to the great variety of developments for making explicit formalisations of the Beta rule, less work has been done for giving explicit definitio...
متن کاملExplicit substitutions calculi with one step Eta-reduction decided explicitly
It has long been argued that the notion of substitution in the λ-calculus needs to be made explicit. This resulted in many calculi have been developed in which the computational steps of the substitution operation involved in β-contractions have been atomised. In contrast to the great variety of developments for making explicit formalisations of the Beta rule, less work has been done for giving...
متن کاملSUBSEXPL: a tool for simulating and comparing explicit substitutions calculi1
We present the system SUBSEXPL used for simulating and comparing explicit substitutions calculi. The system allows the manipulation of expressions of the λ-calculus and of three different styles of explicit substitutions: the λσ, the λse and the suspension calculus. A variation of the suspension calculus, which allows for combination of steps of β-contraction is included too. Implementations of...
متن کاملPerpetuality for Full and Safe Composition (in a Constructive Setting)
We study perpetuality in calculi with explicit substitutions having full composition. A simple perpetual strategy is used to define strongly normalising terms inductively. This gives a simple argument to show preservation of β-strong normalisation as well as strong normalisation for typed terms. Particularly, the strong normalisation proof is based on implicit substitution rather than explicit ...
متن کامل