(Part of the Coq FAQ)

An evaluable constant is a constant which is unfoldable.

A goal is a statement to be proved.

A meta variable in Coq represents a “hole”, i.e. a part of a proof that is still unknown.

Gallina is the specification language of Coq. Complete documentation of this language can be found in the Reference Manual.

It is the language of Gallina commands; i.e. definitions, lemmas, ...

A dependent type is a type which depends on some term. For instance "vector of size n" is a dependent type representing all the vectors of size n. Its type depends on n.

This is a proof generated by some computation which is done using the internal reduction of Coq (not using the tactic language of Coq (Ltac) nor the implementation language for Coq). An example of a tactic using the reflection mechanism is the ring tactic. The reflection method consist in reflecting a subset of Coq language (for example the arithmetical expressions) into an object of the Coq language itself (in this case an inductive type denoting arithmetical expressions). For more information see [1], [2], and [3] below and the last chapter of the Coq’Art book.

This is any logic which does not assume that "A or not A".

See this part of the FAQ.

Opaque definitions can not be unfolded but transparent ones can.

[1] Doug Howe. Computation meta theory in nuprl. In E. Lusk and R. Overbeek, editors, The Proceedings of the Ninth International Conference of Autom ated Deduction, volume 310, pages 238–257. Springer-Verlag, 1988.

[2] John Harrison. Meta theory and reflection in theorem proving:a survey and cri tique. Technical Report CRC-053, SRI International Cambridge Computer Science Research Center, 1995.

[3] Samuel Boutin. Using reflection to build efficient and certified decision pro cedures. In M. Abadi and T. Ito, editors, Proceedings of TACS'97, volume 1281 of LNCS. Springer-Verlag, 1997.