blob: caba76c826965cd48cf8af430c1ae9df68ad5ee2 (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
|
#+BEGIN_EXPORT html
<h1>A Series on Ltac</h1>
#+END_EXPORT
Ltac is the “tactic language” of Coq. It is commonly advertised as the common
approach to write proofs, which tends to bias how it is introduced to new Coq
users (/e.g./, in Master courses). In this series, we present Ltac as the
metaprogramming tool it is, since fundamentally it is an imperative language
which allows for constructing Coq terms interactively and incrementally.
- [[./LtacMetaprogramming.html][Ltac is an Imperative Metaprogramming Language]] ::
Ltac generates terms, therefore it is a metaprogramming language. It does it
incrementally, by using primitives to modifying an implicit state, therefore
it is an imperative language. Henceforth, it is an imperative metaprogramming
language.
- [[./LtacPatternMatching.html][Pattern Matching on Types and Contexts]] ::
Ltac allows for pattern matching on types and contexts. In this article, we
give a short introduction on this feature of key importance. Ltac programs
(“proof scripts”) generate terms, and the shape of said terms can be very
different regarding the initial context. For instance, ~induction x~ will
refine the current goal using an inductive principle dedicated to the type of
~x~.
- [[./MixingLtacAndGallina.html][Mixing Ltac and Gallina Together for Fun and Profit]] ::
One of the most misleading introduction to Coq is to say that “Gallina is for
programs, while tactics are for proofs.” Gallina is the preferred way to
construct programs, and tactics are the preferred way to construct proofs.
The key word here is “preferred.” Coq actually allows for /mixing/
Ltac and Gallina together.
|