001 - /————————-———-—-——Efi J...

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Unformatted text preview: /————————-———-—-——Efi / J 1 , Problem 1:- Is there any environment 8 and type T such that S t x x : T? If so, give the 8 and T and show a typing derivation for 8 t x x : T. If not, prove it. Solution:- Here xx is an application. Let x = 7tZ.T, which is of type 291". xx => (MZ:Z).T) (l(Z:z).T) J Here we cannot reduce this application because the argument of type 29T is different from type 2. So, there will not be any environment 8 and type T such that xx is of type T. Problem 2.:- Find an environment 8 under which the term f x y has type Boo]. Can you give a simple description of the set of all such environments? / An environmmt 8 in which x and y is of type B001 and f is a function of type Bool -) B001 9 Bool. Example functions set:- {AND, OR, NOR, NAND, XOR“ 41? SJ mpg-371 m}md€7 . ”2/ ...
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