1. CSE 341 -- S. Tanimoto Introduction to ML
History
Special features
Interacting with ML
ML’s basic types
ML’s composite types
Math. background for type description.
CSE S. Tanimoto Introduction to ML

2. CSE 341 -- S. Tanimoto Introduction to ML
History
Early 1970s: Design and implementation of ML by Milner, Morris, and Wadsworth at the Univ. of Edinburgh, Scotland.
ML: Metalanguage of the Edinburgh LCF system.
LCF = Logic for Computable Functions
Gordon, Michael, Robin Milner, and Christopher Wadsworth. "Edinburgh LCF: A Mechanized Logic of Computation," Lecture Notes in Computer Science,
Vol.78, Springer-Verlag, NY, 1979.
Mid 1980s: Standardization of ML.
CSE S. Tanimoto Introduction to ML

3. CSE 341 -- S. Tanimoto Introduction to ML
Special Features
A higher-order functional language.
Statically type-checked, but polymorphic.
Incorporates automatic type inference.
Incorporates pattern matching.
Garbage-collected.
Has a formal semantics.
CSE S. Tanimoto Introduction to ML

4. CSE 341 -- S. Tanimoto Introduction to ML
Interaction with ML
ML, like Lisp, provides a READ-EVAL-PRINT loop.
Whenever ML prints the value of an expression, it also prints the TYPE of the value.
ML keeps track of the types of variables and functions by solving systems of constraints.
ML does not use assignment. On the other hand, it does use binding. Thus it uses the ‘=‘ sign in a mathematical sense.
val flavor = "strawberry" ;
binds a string to an identifier.
CSE S. Tanimoto Introduction to ML

5. CSE 341 -- S. Tanimoto Introduction to ML
Sample Interactions
3 * 5 ;
val it = 8 : int
real(8);
val it = 8.0 : real
8.0 + real(1);
val it = 9.0 : real
CSE S. Tanimoto Introduction to ML

6. CSE 341 -- S. Tanimoto Introduction to ML
ML’s Basic Types
3 * 5 ;
val it = 8 : int
3.0 * 5.0 ;
val it = 8.0 : real
true ;
val it = true : bool
"rock" ^ "candy" ;
val it = "rockcandy" : string
#"a" ;
val it = #"a" : char
CSE S. Tanimoto Introduction to ML

7. CSE 341 -- S. Tanimoto Introduction to ML
ML’s Composite Types
Tuples:
val mytuple = (26, "Oct." , 2001);
val mytuple = (26, "Oct." , 2001) : int * string * int
Each component can have a different type.
Lists:
[1, 2, 3] ;
val it = [1, 2, 3] : int list
["nice"];
val it = ["nice"] : string list
All components must have the same type.
CSE S. Tanimoto Introduction to ML

8. Math Background to Formal Representation of Types
Set: a collection of items.
Binary relation: a set of ordered pairs, whose elements come from a first set and a second set, which may be identical, partially overlapping, or disjoint.
Cartesian product S1  S2  ...  Sn of sets S1, S2, ..., Sn.
Function: A special kind of binary relation.
CSE S. Tanimoto Introduction to ML

9. CSE 341 -- S. Tanimoto Introduction to ML
Set
A collection of items.
Must be well-defined, so that there is, in principle, a criterion that can be used to decide the membership of any item in the set.
The set of all letters of the English alphabet.
The set of all positive integers.
NOT: The set of all sets that are not members of themselves. (SOASTANMOT). Is SOASTANMOT in SOASTANMOT? If so, then SOASTANMOT violates its own definition; if not,then it SHOULD be in SOASTANMOT. This is known as Russell’s paradox.
CSE S. Tanimoto Introduction to ML

10. CSE 341 -- S. Tanimoto Introduction to ML
Binary Relation
A set of ordered pairs.
First element comes from a set called the domain.
Second element comes from a set called the codomain.
D1 = {a, b, c}
C1 = {0, 1}
B1 = {(a, 0), (a, 1), (c, 0), (c, 1)}
B1 is a binary with domain D1 and codomain C1.
Often, however, the domain and codomain are identical.
D2 = C2 = {a, b, c}
B2 = { (a, a), (b, b), (c, c), (a, c), (c, a)}
B2 is a binary relation on D2.
CSE S. Tanimoto Introduction to ML

11. CSE 341 -- S. Tanimoto Introduction to ML
Cartesian Product
A way to combine sets to get new sets.
Let S1 = {a, b, c}
Let S2 = {1, 2}
S1  S2 = { (a,1), (a,2), (b,1), (b,2), (c,1), (c,2) }
A three-way cartesian product:
S2  S2  S2 = { (1,1,1), (1,1,2), (1,2,1), (1,2,2), (2,1,1), (2,1,2), (2,2,1), (2,2,2) }
This is not equivalent to (S2  S2 )  S2 or S2  (S2  S2 ).
CSE S. Tanimoto Introduction to ML

12. CSE 341 -- S. Tanimoto Introduction to ML
Function
Function: A binary relation whose first components are from a set called the domain, and whose second components are from a set called the range, and such that each domain element is paired with one and only one range element.
D = {a, b, c}; R = {0, 1}
F = { (a,0), (b,0), (c,1)} is a function from D to R.
F: D  R
B = { (a,0), (a,1), (b,0), (c,0) } is not a function.
CSE S. Tanimoto Introduction to ML