Document non-standard string operators (#8679)

This adds documentation for `str.indexof_re`, `str.update`, `str.rev`,
`str.to_lower`, and `str.to_upper`. Note that it moves the documentation
of strings to the "non-standard or extended theories".

diff --git a/docs/theories/strings.rst b/docs/theories/strings.rst
new file mode 100644 (file)
index 0000000..8a5cad2
--- /dev/null
+++ b/docs/theories/strings.rst
@@ -0,0 +1,68 @@
+Theory Reference: Strings
+=========================
+
+cvc5 supports all operators of the `SMT-LIB standard for strings
+<https://smtlib.cs.uiowa.edu/theories-UnicodeStrings.shtml>`_. It additionally
+supports some non-standard operators that are described below.
+
+Semantics
+^^^^^^^^^
+
+.. code-block::
+
+   * (str.indexof_re String RegLan Int Int)
+
+     Let w₂ = ⟦str.substr⟧(w, i, |w| - i)
+
+     - ⟦str.indexof_re⟧(w, L, i) = -1     if no substring of w₂ is in L or i < 0
+
+     - ⟦str.indexof_re⟧(w, L, i) = |u₁|
+       where u₁, w₁ are the shortest words such that 
+         - w₂ = u₁w₁u₂
+         - w₁ ∈ L
+                                          if some substring of w₂ is in L and i > 0
+
+   * (str.update String Int String)
+
+     - ⟦str.update⟧(w, i, w₂) = w         if i < 0 or i >= |w|
+
+     - ⟦str.update⟧(w, i, w₂) = u₁u₂u₃
+       where
+         - w = u₁w₃u₃
+         - |w₃| = |u₂|
+         - |u₁| = i
+         - u₂u₄ = w₂
+         - |u₂| = min(|w₂|, |w| - i)      otherwise
+
+   * (str.rev String String)
+
+     ⟦str.rev⟧(w) is the string obtained by reversing w, e.g.,
+     ⟦str.rev⟧("abc") = "cba".
+
+   * (str.to_lower String String)
+
+     ⟦str.to_lower⟧(w) = w₂
+     where
+       - |w| = |w₂|
+       - the i-th character ri in w₂ is:
+
+         code(ri) = code(si) + ite(65 <= code(si) <= 90, 32, 0)
+
+         where si is the i-th character in w
+
+     Note: This operator performs the case conversion for the ASCII portion of
+     Unicode only.
+
+   * (str.to_upper String String)
+
+     ⟦str.to_upper⟧(w) = w₂
+     where
+       - |w| = |w₂|
+       - the i-th character ri in w₂ is:
+
+         code(ri) = code(si) - ite(97 <= code(si) <= 122, 32, 0)
+
+         where si is the i-th character in w
+
+     Note: This operator performs the case conversion for the ASCII portion of
+     Unicode only.

diff --git a/docs/theories/theories.rst b/docs/theories/theories.rst
index fd00cc658ef58cbc9de7a65b49edcbacae4c8e61..1eb165b9e6173e09dd45e41484ce10f95d645b0a 100644 (file)
--- a/docs/theories/theories.rst
+++ b/docs/theories/theories.rst
@@ -34,4 +34,5 @@ Non-standard or extended theories
    separation-logic
    sequences
    sets-and-relations
+   strings
    transcendentals