Twelf

Twelf is an implementation of the logical framework LF developed by Frank Pfenning and Carsten Schürmann at Carnegie Mellon University. It is used for logic programming and for the formalization of programming language theory. At its simplest, a Twelf program (called a "signature") is a collection of declarations of type families (relations) and constants that inhabit those type families. For example, the following is the standard definition of the natural numbers, with standing for zero and the successor operator. nat : type. z : nat. s : nat -> nat. Here is a type, and and are constant terms. As a dependently typed system, types can be indexed by terms, which allows the definition of more interesting type families. Here is a definition of addition: plus : nat -> nat -> nat -> type. plus_zero : {M:nat} plus M z M. plus_succ : {M:nat} {N:nat} {P:nat} plus M (s N) (s P)