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**11 - 16**of**16**### Analysing Resource Use in the λ-Calculus By Type Inference

, 1994

"... If we view functions as processes, then their resources are their arguments, supplied through application, and used by the function to produce a result. In this paper, we define resource use for functions, based on the syntactic notion of needed redexes from [BKKS86]. We introduce a variant of neede ..."

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If we view functions as processes, then their resources are their arguments, supplied through application, and used by the function to produce a result. In this paper, we define resource use for functions, based on the syntactic notion of needed redexes from [BKKS86]. We introduce a variant of neededhess, tail-neededness, and define packets of needed descendants of redexes in order to mea- sure the degree of neededhess. These results are generalised to produce a semantic characterisation of the resource use properties of functions, using a term-model. By means of the Curry-Howard isomorphism, we apply these ideas to proof trees of propositions in Intuitionistic Logic to demonstrate that propositions, i.e. types, can be used to express the usage properties of functions. A resource-aware type system capable of inferring such types for A-terms is presented.

### Type Logical Grammar: Categorial Logic of Signs

, 1994

"... tracting away from contingent aspects of the channel's physical realization and from the use of the information by the recipient. For instance, the finiteness of language processors demands that the meanings of sufficiently complex signs be a function of the meanings of their parts: thus compos ..."

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tracting away from contingent aspects of the channel's physical realization and from the use of the information by the recipient. For instance, the finiteness of language processors demands that the meanings of sufficiently complex signs be a function of the meanings of their parts: thus compositionality. Without additional constraints, compositionality could be trivially satisfied (Zadrozny 1994). But the fact that language users derive their implicit contract for sign meaning from finite evidence imposes strong uniformity requirements on signs. While this argument has not, to my knowledge, been made rigorous through an axiomatic treatment, type-logical grammar offers a promising notion of uniformity: to say, for instance, that a sign c meaning z has type B/A is to say that c + a (where + is a suitable sign combination operator) has type B and means z(x), given that a has type A and means x. But uniformity must also go backwards, if the use and meaning of a sign is to be induced from

### Under consideration for publication in J. Functional Programming 1 The Logic of Demand in Haskell

"... Haskell is a functional programming language whose evaluation is lazy by default. However, Haskell also provides pattern matching facilities which add a modicum of eagerness to its otherwise lazy default evaluation. This mixed or \non-strict" semantics can be quite dicult to reason with. This p ..."

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Haskell is a functional programming language whose evaluation is lazy by default. However, Haskell also provides pattern matching facilities which add a modicum of eagerness to its otherwise lazy default evaluation. This mixed or \non-strict" semantics can be quite dicult to reason with. This paper introduces a programming logic, P-logic, which neatly formalizes the mixed evaluation in Haskell pattern-matching as a logic, thereby simplifying the task of specifying and verifying Haskell programs. In P-logic, aspects of demand are reected or represented within both the predicate language and its model theory, allowing for expressive and comprehensible program veri cation.

### Consistency Preserving Updates: Extended Abstract

"... N. Bidoit, S. Cerrito, Ch. Froidevaux 1 1 Introduction The concern in this paper is to formalize update under transition constraints in an incomplete information setting. A wide variety of proposals for formalizing database (knowledge base) update semantics exists (e.g. [9] [11] [15] [4] [12] [13 ..."

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N. Bidoit, S. Cerrito, Ch. Froidevaux 1 1 Introduction The concern in this paper is to formalize update under transition constraints in an incomplete information setting. A wide variety of proposals for formalizing database (knowledge base) update semantics exists (e.g. [9] [11] [15] [4] [12] [13]). In this paper we investigate a substantially different proposal exploiting some features of linear logic [7]. Our aim is to provide a mechanism to perform updates such that if we start with a "consistent database" then the result of an update is a new database which is always "consistent". The database is specified by three kinds of information : ffl Atomic facts : intuitively, the database stores explicitly two kinds of facts, true ones and false ones. We deal with incomplete information in a very simple and naive way, that is, for an information (proposition) A, if neither A nor the negation of A is stored then A has the status unknown. ffl Deduction rules : we deal with two kinds o...