Semantics of lambda-I and of other substructure lambda calculi

  • Bart Jacobs
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 664)


The ordinary untyped λ-calculus (the main object of study in [3]) will be denoted here by λK. Church originally introduced the λI-calculus, which can be understood as the λK-calculus without weakening: one cannot throw away variables. Similarly there is a affine calculus λA without contraction: there, one cannot duplicate variables. There is also a linear calculus λL in which one has neither weakening nor contraction. In λL variables occur precisely once.

We give a systematic description of the semantics of these four calculi. It starts with two sorts of domain theoretic models: graph models and filter models (of intersection types) are constructed for each of these calculi. Later on, we describe an appropriate categorical way to capture such structures in terms of monoidal categories (with diagonals or projections).


Natural Transformation Complete Lattice Monoidal Category Neutral Element Filter Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Bart Jacobs
    • 1
  1. 1.Mathematical Institute RUUTA UtrechtNL

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