| LOGIC | Classical logic and dependent equality |
| ARITH | Basic Peano arithmetic |
| ZARITH | Basic integer arithmetic |
| BOOL | Booleans (basic functions and results) |
| LISTS | Monomorphic and polymorphic lists (basic functions and results), Streams (infinite sequences defined with co-inductive types) |
| SETS | Sets (classical, constructive, finite, infinite, power set, etc.) |
| RELATIONS | Relations (definitions and basic results). There is a subdirectory about well-founded relations (WELLFOUNDED) |
| SORTING | Various sorting algorithms |
| REALS | Axiomatization of Real Numbers (classical, basic functions and results, integer part and fractional part, requires the ZARITH library) |
Require (see
chapter 5). Library.dvi. They are also accessible on the WWW
through the Coq homepage
10.
form ::= ` zarith_formula ` term ::= ` zarith ` zarith_formula ::= zarith = zarith | zarith <= zarith | zarith < zarith | zarith >= zarith | zarith > zarith | zarith = zarith = zarith | zarith <= zarith <= zarith | zarith <= zarith < zarith | zarith < zarith <= zarith | zarith < zarith < zarith | zarith <> zarith | zarith ? = zarith zarith ::= zarith + zarith | zarith - zarith | zarith * zarith | | zarith | | - zarith | ident | [ term ] | ( zarith ... zarith ) | ( zarith , ... , zarith ) | integer
Figure 3.4: Syntax of expressions in integer arithmetics