Strictness Logic and Polymorphic Invariance
نویسنده
چکیده
We describe a logic for reasoning about higher-order strictness properties of typed lambda terms. The logic arises from axiomatising the inclusion order on certain closed subsets of domains. The axiomatisation of the lattice of strictness properties is shown to be sound and complete, and we then give a program logic for assigning properties to terms. This places work on strictness analysis via type inference on a firm theoretical foundation. We then use proof theoretic techniques to show how the derivable strictness properties of different instances of polymorphically typed terms are related.
منابع مشابه
Inference of polymorphic and conditional strictness propertiesThomas
We deene an inference system for modular strictness analysis of functional programs by extending a conjunctive strictness logic with polymorphic and conditional properties. This extended set of properties is used to deene a syntax-directed, polymorphic strictness analysis based on polymorphic recur-sion whose soundness is established via a translation from the polymorphic system into the conjun...
متن کاملProjections for Polymorphic First-Order Strictness Analysis
We apply the categorical properties of polymorphic functions to compile-time analysis, speciically projection-based strictness analysis. First we interpret parameterised types as functors in a suitable category, and show that they preserve monics and epics. Then we deene \strong" and \weak" polymorphism, the latter admitting certain projections that are not polymorphic in the usual sense. We pr...
متن کاملThe concept of logic entropy on D-posets
In this paper, a new invariant called {it logic entropy} for dynamical systems on a D-poset is introduced. Also, the {it conditional logical entropy} is defined and then some of its properties are studied. The invariance of the {it logic entropy} of a system under isomorphism is proved. At the end, the notion of an $ m $-generator of a dynamical system is introduced and a version of the Kolm...
متن کاملLogic Group
In this paper we define the functional language POLYREC with polymorphic and recursive types, and develop concrete and abstract interpretations for this language. These semantics, based on complete partial orderings and complete lattices, are subsequently used for definition and analysis of strictness. 1980 Mathematical Subject Classification (1985): 03B40, 68N15 1986 CR Classification System.:...
متن کاملStrictness Analysis in Logical Form
y Abstract This paper presents a framework for comparing two strictness analysis techniques: Abstract interpretation and non{standard type inference. The comparison is based on the representation of a lattice by its ideals. A formal system for deducing inclusions between ideals of a lattice is presented and proved sound and complete. Viewing the ideals as strictness properties we use the formal...
متن کامل