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...Free and bound variables equivalence substitution lecture notes on the lambda calculus introduction to reduction formaldenitionsof reductionand peter selinger programmingintheuntypedlambdacalculus booleans department of mathematics statistics natural numbers dalhousie university halifax canada fixed points recursive functions other data types pairs tuples lists trees etc abstract this is a set that developed out courses thechurch rossertheorem i taught at ottawa in extensionality topics covered these include un typed church rosser theorem combinatory algebras statement some consequences simply curry howard isomorphism weak preliminary remarks proof strong normalization polymorphism type inference denotational se mantics complete partial orders language pcf exercises contents combinatoryalgebras applicative structures combinatorycompleteness extensional vs intensional view thelambdacalculus thefailure soundness for untypedvs calculi lambdaalgebras lambdacalculusandcomputability connecti...