Automated higher-order complexity analysis

Higher-Order Automated Theorem Provers

Higher-Order Automated Theorem Proving

The history of building automated theorem provers for higher-order logic is almost as old as the field of deduction systems itself. The first successful attempts to mechanize and implement higher-order logic were those of Huet [13] and Jensen and Pietrzykowski [17]. They combine the resolution principle for higher-order logic (first studied in [1]) with higher-order unification. The unification...

Automated Cost Analysis of a Higher-Order Language in Coq

The cost analysis of a program is a function from the size of its input to the number of steps the program takes to run. In this work we address two difficulties associated with constructing cost analyses. First, what is the cost of a higher-order program? If an expression takes a function as input, what is the “size” of that input? If an expression evaluates to a function, what is its “cost”? ...

Complexity Analysis for a Lazy Higher-Order Language

This paper is concerned with the time-analysis of functional programs. Techniques which enable us to reason formally about a program's execution costs have had relatively little attention in the study of functional programming. We concentrate here on the construction of equations which compute the time-complexity of expressions in a lazy higher-order language. The problem with higher-order func...

The Complexity of Flow Analysis in Higher-Order Languages

This dissertation proves lower bounds on the inherent difficulty of deciding flow analysis problems in higher-order programming languages. We give exact characterizations of the computational complexity of 0CFA, the kCFA hierarchy, and related analyses. In each case, we precisely capture both the expressiveness and feasibility of the analysis, identifying the elements responsible for the trade-...