1. While there have been a number of proposals to integrate dimensional analysis into existing compilers 1, 7, 8, 9], it appears that no one has made the easy observation that dimensional analysis ts neatly into the pattern of ML-style type inference 4, 5, 6]. In this paper we show how to add dimensions to the simply-typed lambda calculus, and we show that every typable dimension-preserving ter...

This project to extend the simply-typed Lambda calculus λ→ to have types dependent on constant value. In particular this language will be used to check the validity of matrix computation.

In the Böhm theorem workshop on Crete island, Zoran Petric called Statman’s “Typical Ambiguity theorem” typed Böhm theorem. Moreover, he gave a new proof of the theorem based on set-theoretical models of the simply typed lambda calculus. In this paper, we study the linear version of the typed Böhm theorem on a fragment of Intuitionistic Linear Logic. We show that in the multiplicative fragment ...

The paper presents a simple format for typed logics with states by adding a function for register update to standard typed lambda calculus. It is shown that universal validity of equality for this extended language is decidable (extending a well-known result of Friedman for typed lambda calculus). This system is next extended to a full fledged typed dynamic logic, and it is illustrated how the ...

EFSs are logic programs expressing various formal languages. Typed EFSs are EFSs augmented by introducing types for variables. In this paper, we define a subclass of the typed EFSs, called DS-typed regular EFSs, to model XML documents. We show that the class of languages defined by DS-typed regular EFSs properly includes the class of languages defined by balanced grammars, one formal model of s...

We introduce a notion of Grothendieck logical relation and use it to characterise the deenability of morphisms in stable bicartesian closed categories by terms of the simply-typed lambda calculus with nite products and nite sums. Our techniques are based on concepts from topos theory, however our exposition is elementary.

We show that the call-by-name monad translation of simply typed lambda calculus extended with sum and product types extends to special and general inductive and coinductive types so that its crucial property of preserving typings and βand commuting reductions is maintained. Specific similar-purpose translations such as CPS translations follow from the general monad translations by specializatio...

It is well known that connuence and strong normalization are preserved when combining left-linear algebraic rewriting systems with the simply typed lambda calculus. It is equally well known that connuence fails when adding either the usual extensional rule for , or recursion together with the usual contraction rule for surjective pairing. We show that connuence and normalization are modular pro...