Should your specification language be typed

Abstract

Most specification languages have a type system. Type systems are hard to get right, and getting them wrong can lead to inconsistencies. Set theory can serve as the basis for a specification language without types. This possibility, which has been widely overlooked, offers many advantages. Untyped set theory is simple and is more flexible than any simple typed formalism. Polymorphism, overloading, and subtyping can make a type system more powerful, but at the cost of increased complexity, and such refinements can never attain the flexibility of having no types at all. Typed formalisms have advantages too, stemming from the power of mechanical type checking. While types serve little purpose in hand proofs, they do help with mechanized proofs. In the absence of verification, type checking can catch errors in specifications. It may be possible to have the best of both worlds by adding typing annotations to an untyped specification language.We consider only specification languages, not programming languages.

Why mathematics needs engineering

“…Such users would be justified in dismissing as impractical any definition that infringes on these "acquired rights". Similar considerations in the context of specification languages are found in [35]. In the specification language TLA + [36, p. 48], the notation [X → Y ] has the meaning of X → Y as defined by the ISO standard.…”

Impact of Using a Static-type System in Computer Programming*

“…However, large specifications are seldom verified, and type checking can catch errors that would otherwise go undetected [13]. Moreover, based on the data provided by Stefan Hanenberg in his empirical study [10], at least in his experiment settings, the total debugging time of the exceptions, which could have been handled by a type checker (in static-type systems), is less than the time that must be invested to handle the type checker itself.…”

A Mechanized Translation from Higher-Order Logic to Set Theory

“…This idea has been mentioned in the literature several times [5,9,20,6], and, in principle, Isabelle/ZF could be a starting point to explore these possibilities. This work intends to explore how HOL-style reasoning can be turned into settheoretic reasoning, mechanized in Isabelle/ZF.…”