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5
votes
0answers
155 views

Proper full submodels of full models of type theory

Let $N$ be the standard full model of the simply typed lambda calculus with infinite base type $o$ and let $X$ be an infinite and coinfinite subset of $N(o)$. I want to know if there's a full ...
1
vote
1answer
138 views

combinator SSS(SS)SS is not strongly normalizing. Why?

I highly speculate that combinator SSS(SS)SS is not strongly normalizing. What is the argument for the non strong normalization?
13
votes
6answers
29k views

Difference between a 'calculus' and an 'algebra'

What is really the conceptual difference between a calculus and an algebra. Eg. Is SKI combinator calculus really a calculus? A friend claims that free variables are fundamental for a calculus, and ...