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functional-programmingsmlsmlnjcons

Interpreting []::[], []::[]::[] in sml

I would like to ask how []::[] and []::[]::[] are interpreted conceptually in SML/NJ.

My thought :

I thought that []::[] would generates error or generates a empty list but in fact it generates val it = [[]] : 'a list list.

After I know that []::[] generates [[]] : 'a list list, I thought that []::[]::[] would generate [[[]]] : 'a list list list but in fact it generates [[],[]] : 'a list list

Solution

  • :: is right-associative: In a::b::c::[] a,b,c must be elements of the same type and 

    a::b::c::[] = a::(b::(c::[]))
            = a::(b::[c])
            = a::[b,c]
            = [a,b,c]

    This remains true even if a,b,c are []: 

    []::[]::[]::[] = [[],[],[]]