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Introduction
Raymond Smullyan was born in 1919, after the Great War and before the Great Depression. I have known him since I was a graduate student and he was my...
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Dance of the Starlings
In this birdwatching paper our binoculars are focused upon a particular bird from Smullyan’s enchanted forest of combinatory birds (Smullyan in To...
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On the Dynamic Increase of Multiplicities in Matrix Proof Methods for Classical Higher-Order Logic
A major source of the undecidability of a logic is the number of instances—the so-called multiplicities—of existentially quantified formulas that are...
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Logical Frameworks
One way to define a logic is to specify a language and a deductive system. For example, the language of first-order logic consists of the syntactic...
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Theory of Judgments and Derivations
We propose a computational and logical framework NF (Natural Framework) which is suitable for presenting mathematics formally. Our framework is an...
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Normalization of S-terms is decidable
The combinator S has the reduction rule S x y z → x z (y z). We investigate properties of ground terms built from S alone. We...
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Introduction au λ-calcul pur
These course notes introduce pure λ-calculus, the basic formal system underlying functional programming languages. Section 1 discusses notations for...