Functional Programming And Capture-Avoiding Substitution - Computer Science Assignment Help

Assignment Task

Variables 

Next, we will build a function that generates a fresh variable. First, we create an infinite supply of variables; then we remove those already in use. We will store used variables as an alphabetically sorted list, with each variable mentioned at most once: we only care if variables occur, and not how often. To help with this you are given the merge function from the merge sort algorithm in the tutorials

Assignment : 

a) Complete the infinite list variables, which contains the variables "a" through "z", then repeats these suffixed with 1, "a1",...,"z1", then 2, "a2",...,"z2", etc. 

*Main> [variables !! i | i <- [0,1,25,26,27,100,3039]] ["a","b","z","a1","b1","w3","x116"] 

b) Complete the function filterVariables which takes two lists of variables and re turns the first with all variables from the second list removed from it. 

*Main> filterVariables ["y","z","a1","a2"] ["y","a1","a3"] ["z","a2"] 

c) Complete the function fresh which given a list of variables, generates a fresh variable not occurring in the list. Use filterVariables to remove the given variables from variables, then take the first variable in the remaining list. 

*Main> fresh ["a","b","x"] 

"c" 

d) Complete the function used that collects all the variable names used in a Term, both as a Variable and in a Lambda abstraction. Return them in an ordered list (use merge to combine two ordered lists into one). 

*Main> used example 

["a","b","x","y"]

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