A Type System Theory for Higher-Order Intensional Logic Support for Variable Bindings in Hybrid Intensional-Imperative Programs in GIPSY

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We describe a type system for a platform called the General Intensional Programming System (GIPSY), designed to support intensional programming languages built upon intensional logic and their imperative counter-parts for the intensional execution model. In GIPSY, the type system glues the static and dynamic typing between intensional and imperative languages in its compiler and run-time environments to support the intensional evaluation of expressions written in various dialects of the intensional programming language Lucid. The intensionality makes expressions to explicitly take into the account a multidimensional context of evaluation with the context being a first-class value that serves a number of applications that need the notion of context to proceed. We describe and discuss the properties of such a type system and the related type theory as well as particularities of the semantics, design and implementation of the GIPSY type system.