GIML: Tutorial Two

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Tutorial two : Types

1. Predict the type of each of these objects. Check your answer by entering each followed by the semicolon. ("two", true, 2); ["two", true, 2]; ((1,2),(3,4,5)); [[1,2],[3,4,5]]; [[],[],[]]; ("andrew",size "andrew"); (["andrew"="andrew","andrew"="ben"],size "andrew", size);
2. Consider the following bindings. Try to predict the result before executing them. val (a,b) = (5,6); val (c,d) = (2,("xx","yy")); val (e,(f,g)) = (1,(2,3)); val (l,m,n) = ("xx",(1,2)); That last binding will fail as the left and right hand sides are incompatible. val (p, _ ) = (12, 10); val (q, 10) = (12, 10); val (r, 11) = (12, 10); Note the failed binding again. val u = 1::[2,3]; val v::w = 1::[2,3]; val h::t = [4,5,6]; Be sure that you understand how the final example works.
3. Consider the type of each of the following functions fun fone(x:int) = [x,x,x]; fun ftwo(x) = (x,x,x); fun fthree(x,y) = [x ^ "b", y]; fun ffour(x,y,z) = (x+(size y),z);
4. Find out the type of each of the in-built functions explode, rev, hd and tl. Try each function on a list or a string as appropriate. Make a note of each of the following: The type of explode and the name of its inverse. The type of rev and its inverse. The type of hd and what it is an abbreviation for The type of tl and what it is an abbreviation for. Evaluate each of the following; try to predict the result. hd(explode "south"); hd(tl(explode "north")); hd(rev(explode "east")); hd(tl(rev(explode "west"))); Optional Questions:
5. The function composition operator is o (say of). We can use it to create functions from functions. val first = hd o explode; val second = hd o tl o explode; Create the functions third, fourth and last in a similar manner. You should find that these functions extract a single character from a string. Notice that in a chain of composed functions the last is applied first.

   Note for Moscow ML users

6. Use the functions first, second ... to create the following: fun roll s = fourth s ^ first s ^ second s ^ third s; fun exch s = second s ^ first s ^ third s ^ fourth s; Test these functions on some four character string such as "ache" and "vile". To save typing you may use the function map - however as this is a higher order function which we have not yet covered you must not attempt to understand how it works. val words = ["ache", "vile", "amid", "evil", "ogre"]; map roll words; map exch words; The two permutations roll and exch can be used to generate any permutation of four characters. For example val what = roll o roll o roll o exch o roll; What's what "what"? Using only function composition on roll and exch define the functions which perform the following. fb "seat" -> "eats" fc "silt" -> "slit" fd "more" -> "rome" Warning : do not apply fb to "ears"