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

40CHAPTER 4. COMPUTING WITH FUNCTIONS OVER INDUCTIVELY DEFINED SETS
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)
clean enough to learn important concepts (e.g. typing and recursion)
SML uses functions as a computational model (we already understand them)
SML has an interpreted runtime system (inspect program state)
Book: SML for the working programmer by Larry Paulson [Pau91]
Web resources: see the post on the course forum in PantaRhei.
Homework: install it, and play with it at home!
©: Michael Kohlhase 61
Disclaimer: We will not give a full introduction to SML in this course, only enough to make the
course self-contained. There are good books on ML and various web resources:
• A book by Bob Harper (CMU) http://www-2.cs.cmu.edu/~rwh/smlbook/
• The Moscow ML home page, one of the ML’s that you can try to install, it also has many
interesting links http://www.dina.dk/~sestoft/mosml.html
• The home page of SML-NJ (SML of New Jersey), the standard ML http://www.smlnj.org/
also has a ML interpreter and links Online Books, Tutorials, Links, FAQ, etc. And of course
you can download SML from there for Unix as well as for Windows.
• A tutorial from Cornell University. It starts with ”Hello world” and covers most of the
material we will need for the course. http://www.cs.cornell.edu/gries/CSCI4900/ML/
gimlFolder/manual.html
• and finally a page on ML by the people who originally invented ML: http://www.lfcs.
inf.ed.ac.uk/software/ML/
One thing that takes getting used to is that SML is an interpreted language. Instead of transforming
the program text into executable code via a process called “compilation” in one go, the SML
interpreter provides a run time environment that can execute well-formed program snippets in a
dialogue with the user. After each command, the state of the run-time systems can be inspected
to judge the effects and test the programs. In our examples we will usually exhibit the input to
the interpreter and the system response in a program block of the form
- input to the interpreter
system response