General Computer Science 320201 GenCS I & II Lecture ... - Kwarc

2.3 Computing with Functions over Inductively Defined Sets
2.3.1 Standard ML: Functions as First-Class Objects
Enough theory, let us start computing with functions
We will use Standard ML for now
c○: Michael Kohlhase 58
We will use the language SML for the course. This has three reasons
• The mathematical foundations of the computational model of SML is very simple: it consists
of functions, which we have already studied. You will be exposed to an imperative
programming language (C) in the lab and later in the course.
• We call programming languages where procedures can be fully described in terms of their
input/output behavior functional.
• As a functional programming language, SML introduces two very important concepts in a
very clean way: typing and recursion.
• Finally, SML has a very useful secondary virtue for a course at Jacobs University, where students
come from very different backgrounds: it provides a (relatively) level playing ground,
since it is unfamiliar to all students.
Generally, when choosing a programming language for a computer science course, there is the
choice between languages that are used in industrial practice (C, C++, Java, FORTRAN, COBOL,. . . )
and languages that introduce the underlying concepts in a clean way. While the first category have
the advantage of conveying important practical skills to the students, we will follow the motto
“No, let’s think” for this course and choose ML for its clarity and rigor. In our experience, if the
concepts are clear, adapting the particular syntax of a industrial programming language is not
that difficult.
Historical Remark: The name ML comes from the phrase “Meta Language”: ML was developed as
the scripting language for a tactical theorem prover 3 — a program that can construct mathematical
proofs automatically via “tactics” (little proof-constructing programs). The idea behind this is the
following: ML has a very powerful type system, which is expressive enough to fully describe proof
data structures. Furthermore, the ML compiler type-checks all ML programs and thus guarantees
that if an ML expression has the type A → B, then it implements a function from objects of
type A to objects of type B. In particular, the theorem prover only admitted tactics, if they were
type-checked with type P → P, where P is the type of proof data structures. Thus, using ML as
a meta-language guaranteed that theorem prover could only construct valid proofs.
The type system of ML turned out to be so convenient (it catches many programming errors
before you even run the program) that ML has long transcended its beginnings as a scripting
language for theorem provers, and has developed into a paradigmatic example for functional
programming languages.
Standard ML (SML)
Why this programming language?
Important programming paradigm (Functional Programming (with static typing))
because all of you are unfamiliar with it (level playing ground)
3 The “Edinburgh LCF” system
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