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Diffstat (limited to 'doc/sphinx/addendum/program.rst')
| -rw-r--r-- | doc/sphinx/addendum/program.rst | 12 |
1 files changed, 6 insertions, 6 deletions
diff --git a/doc/sphinx/addendum/program.rst b/doc/sphinx/addendum/program.rst index 28fe68d78d..d6895f5fe5 100644 --- a/doc/sphinx/addendum/program.rst +++ b/doc/sphinx/addendum/program.rst @@ -18,7 +18,7 @@ program as in a regular functional programming language whilst using as rich a specification as desired and proving that the code meets the specification using the whole |Coq| proof apparatus. This is done using a technique originating from the “Predicate subtyping” mechanism of -PVS :cite:`Rushby98`, which generates type-checking conditions while typing a +PVS :cite:`Rushby98`, which generates type checking conditions while typing a term constrained to a particular type. Here we insert existential variables in the term, which must be filled with proofs to get a complete |Coq| term. |Program| replaces the |Program| tactic by Catherine @@ -72,8 +72,8 @@ operation (see :ref:`extendedpatternmatching`). This permits to get the proper equalities in the context of proof obligations inside clauses, without which reasoning is very limited. -+ Generation of inequalities. If a pattern intersects with a previous - one, an inequality is added in the context of the second branch. See ++ Generation of disequalities. If a pattern intersects with a previous + one, a disequality is added in the context of the second branch. See for example the definition of div2 below, where the second branch is typed in a context where :g:`∀ p, _ <> S (S p)`. + Coercion. If the object being matched is coercible to an inductive @@ -87,7 +87,7 @@ coercions. .. opt:: Program Cases This controls the special treatment of pattern-matching generating equalities - and inequalities when using |Program| (it is on by default). All + and disequalities when using |Program| (it is on by default). All pattern-matches and let-patterns are handled using the standard algorithm of |Coq| (see :ref:`extendedpatternmatching`) when this option is deactivated. @@ -104,7 +104,7 @@ Syntactic control over equalities ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ To give more control over the generation of equalities, the -typechecker will fall back directly to |Coq|’s usual typing of dependent +type checker will fall back directly to |Coq|’s usual typing of dependent pattern-matching if a return or in clause is specified. Likewise, the if construct is not treated specially by |Program| so boolean tests in the code are not automatically reflected in the obligations. One can @@ -175,7 +175,7 @@ Program Definition .. TODO refer to production in alias -See also: Sections :ref:`vernac-controlling-the-reduction-strategies`, :tacn:`unfold` +.. seealso:: Sections :ref:`vernac-controlling-the-reduction-strategies`, :tacn:`unfold` .. _program_fixpoint: |