15-317 Constructive Logic
Lecture 17: Modes, Termination, and Coverage

Twelf is an implementation of LF as a logic programming language with a number of additional features. Besides the strong type system, it can also check mode, termination, and coverage properties of programs.

Modes specify the expected input/output behavior of predicates (represented in Twelf as type families) and mode checking will verify that the program satisfies a given input/output specification. Termination checking verifies that a given predicate will always terminate. If a predicate passes type, mode, and termination checking we know that every well-typed, well-moded query will terminate either with success (and a well-typed substitution for its free variables) or fail. Certain predicates such as append, are intended to compute total functions and should therefore never fail on any input. This can be verified through coverage. All these checks together can certify that programs are total in their inputs, always succeeding and producing ground outputs.

• Reading: ??-??.pdf
• Code: list.elf, nd.elf, code directory
• Key concepts:
  • Input and output modes
  • Mode checking
  • Termination
  • Termination checking
  • Coverage
  • Total predicates
• Previous lecture: The LF Logical Framework
• Next lecture: Certifying Theorem Proving

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