![]() But this extra baggage has the advantage of making it clearer what's going on: it makes it easier to see where a reduction is happening in a context and where actual computation is happening. If you're only ever going to use a single notion of reduction, introducing contexts requires some extra syntactic baggage. Lambda calculus is a formal model of computation. Lambda Calculus as a basis for functional programming languages More Lambda notes. Church numerals ML code: Church numerals. If you're going to manipulate several different notions of reduction, the presentation in terms of contexts is more compact: there's a single context rule, and its formulation is usually obvious so it can be omitted, all that needs to be stated is the permitted contexts if some syntactically valid contexts disallow reduction. Boolean values and operators ML code: booleans. If there isn’t one, look for a redex in N and reduce that.Reading Chris Hankin's book, "An Introduction to Lambda Calculus for Computer Scientists", I learnt that the rules for reductions in the pure $\lambda$-Calculus are the $\beta$-reduction rule, look on the left) and reduce it if you find it. The only reduction rule of interest in this course is called beta-reduction, and is dened by: (x. ![]() x x) x A term is closed if it has no free variables otherwise it is open. Technically, beta reduction can only be used when no free variables occurring in B are bound within A (so that ( x.
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