Implicit computational complexity

Implicit computational complexity (ICC) is a subfield of computational complexity theory that characterizes programs by constraints on the way in which they are constructed, without reference to a specific underlying machine model or to explicit bounds on computational resources unlike conventional complexity theory. ICC was developed in the 1990s and employs the techniques of proof theory, substructural logic, model theory and recursion theory to prove bounds on the expressive power of high-level formal languages. ICC is also concerned with the practical realization of functional programming languages, language tools and type theory that can control the resource usage of programs in a formally verifiable sense.

Two leading approaches to resource certification have been Static Analysis (SA) and Implicit Computational Complexity (ICC). SA is algorithmic in nature: it focuses on a broad programming language of choice, and seeks to determine by syntactic means whether given programs in that language are feasible. In contrast, ICC attempts to create from the outset specialized programming languages or methods that delineate a complexity class. Thus, SA's focus is on compile time, making no demand on the programmer; whereas ICC is a language-design discipline."