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...Coding in lambda calculus normanramsey spring introduction natural numbers thelambdacalculus is a universal model of computation what anatural number n coded using an idea alonzo church s this means the proper study course theory com nis as capability taking function f and argu putation but roughly speaking powerful mentx andapplyingf to x times examples any deterministic sequential computer that we can imagine equivalent other turing machine roughlyspeaking alsomeans canrunanyprogram toconvince yourself really t write down all there no better exercise than translate code into matter how large either zero or successor one benets translating someother m has relatively painless by contrast ability apply plus more time obeying for demands compiler law given high level languages have sorts syntactic forms succ anddatastructures whereaslambdacalculushasonlythreeforms therefore dene follows term it not obvious be trans lated handout sketches some standard translations ideas about syntax data...