An Introduction to Functional Programming Through Lambda Calculus

- 101 -LIST_EQUAL [] [] = TRUELIST_EQUAL [] (H::T) = FALSELIST_EQUAL (H::T) [] = FALSEOtherwise they are the same if the heads are equal and the tails are the same:LIST_EQUAL (H1::T1) (H2::T2) = LIST_EQUAL T1 T2if H1 H2LIST_EQUAL (H1::T1) (H2::T2) = FALSEif NOT ( H1 H2)Notice again that the comparison operation depends on the type of the list elements.Here, we will compare lists of numbers, for example:LIST_EQUAL [1,2,3] [1,2,3] -> ... ->LIST_EQUAL [2,3] [2,3] -> ... ->LIST_EQUAL [3] [3] -> ... ->LIST_EQUAL [] [] -> ... ->TRUEIn our notation this algortithm is:rec LIST_EQUAL L1 L2 =IF AND (ISNIL L1) (ISNIL L2)THEN TRUEELSEIF OR (ISNIL L1) (ISNIL L2)THEN FALSEELSEIF EQUAL (HEAD L1) (HEAD L2)THEN LIST_EQUAL (TAIL L1) (TAIL L2)ELSE FALSEFor example consider:LIST_EQUAL [1,2,3] [1,2,4] -> ... ->{ EQUAL (HEAD [1,2,3]) (HEAD [1,2,4])) -> ... ->EQUAL 1 1 -> ... ->TRUE}LIST_EQUAL (TAIL [1,2,3]) (TAIL [1,2,4]) -> ... ->LIST_EQUAL [2,3] [2,4] -> ... ->{ EQUAL (HEAD [2,3]) (HEAD [2,4])) -> ... ->EQUAL 2 2 -> ... ->TRUE}