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An Introduction to Logical Frameworks
Iliano Cervesato
Department of Computer Science
Stanford University
Dates:
14-15-16 October 1998
Time:
14:00-17:00
Place:
??
Language:
The course will be taught in English, but questions in French are welcome
Prerequisites:
Basic notions about logic and mainly programming languages
Formal systems such as logics, process calculi, programming languages,
and security protocols are growing in complexity while the concerns about
their correct behavior are becoming more stringent. Therefore, tools that
automate reasoning about these formalism are expected to play an important
role in their definition and analysis. Logical frameworks provide
a language to represent deductive systems as well as methods to assist
reasoning about them.
In this course, I will present a progression of logical frameworks of
increasing expressiveness. They will range from the language of Horn clauses,
the fragment of classical logic on which Prolog is founded, to the
linear logical framework LLF. I will also hint at further developments
currently under investigation. The course will be centered around a case-study
drawn from the area of programming languages. Other examples will be analysed
as (answers to) exercises.
- Representation of deductive systems I (October 14)
- Deductive systems:
judgments and derivations
- Logical frameworks:
adequacy, immediacy, computability
- Horn clauses:
classical and intuitionistic logic, representation of a fragment
of Mini-ML, judgment-as-proposition, abstract syntax,
handling derivations
- Multi-sorted Horn clauses:
syntactic limitations of Horn clauses, multi-sorted logic, syntactic
judgments-as-types
- Higher-order terms:
more syntactic limitations of Horn clauses, binders, higher-order
abstract syntax, higher-order terms
- Representation of deductive systems II (October 15)
- Hereditary Harrop formulas:
semantic limitations of Horn clauses, parametric and hypothetical
judgments
- LF type theory:
limitations of hereditary Harrop formulas in representing derivations,
Curry-Howard isomorphism, LF, judgments-as-types and
derivations-as-objects
- LLF type theory:
limitations of LF in representing state, linear logic, linear
type theories, LLF, Mini-ML with references
- Further issues:
extensional quantification, negation, ordered assumptions
- Reasoning about deductive systems (October 16)
- Reasoning about deductive system in LF and LLF
- Twelf
- Value soundness for Mini-ML with references
- Type preservation for Mini-ML with references
- Iliano Cervesato:
Logical
Framework Design: Why not just classical logic?,
under review for the Proceedings of the Seventh CSLI Workshop on
Logic, Language and Computation (M. Faller, S. Kaufmann, M. Pauly
editors), CSLI Publications, 1999.
- Iliano Cervesato and Frank Pfenning:
A
Linear Logical Framework,
submitted to Information & Computation.
- Frank Pfenning:
Linear Logic,
course notes for a graduate the course 15-816, "Linear Logic",
given at Carnegie Mellon University on the Spring 1998 (courtesy
Frank Pfenning).
- Frank Pfenning and Carsten Schümann:
Twelf User's guide, version 1.2
- Robert Harper, Furio Honsell, and Gordon Plotkin:
A Framework for Defining Logics.
Journal of the ACM, 40(1):143-184, 1993.
- Dale Miller, Gopalan Nadathur, Frank Pfenning, and Andre Scedrov:
Uniform Proofs as a Foundation for Logic Programming.
Annals of Pure and Applied Logic, 51:125-157, 1991.
- Frank Pfenning:
Computation and Deduction,
npublished lecture notes.
Iliano Cervesato
()