doc-src/IsarRef/Thy/HOL_Specific.thy
changeset 40171 1fa547166a1d
parent 40170 751121d5ca35
child 40245 59f011c1877a
     1.1 --- a/doc-src/IsarRef/Thy/HOL_Specific.thy	Tue Oct 26 12:19:01 2010 +0200
     1.2 +++ b/doc-src/IsarRef/Thy/HOL_Specific.thy	Tue Oct 26 12:19:01 2010 +0200
     1.3 @@ -548,6 +548,71 @@
     1.4    \end{description}
     1.5  *}
     1.6  
     1.7 +subsection {* Functions with explicit partiality *}
     1.8 +
     1.9 +text {*
    1.10 +  \begin{matharray}{rcl}
    1.11 +    @{command_def (HOL) "partial_function"} & : & @{text "local_theory \<rightarrow> local_theory"} \\
    1.12 +    @{attribute_def (HOL) "partial_function_mono"} & : & @{text attribute} \\
    1.13 +  \end{matharray}
    1.14 +
    1.15 +  \begin{rail}
    1.16 +    'partial_function' target? '(' mode ')' fixes \\ 'where' thmdecl? prop
    1.17 +  \end{rail}
    1.18 +
    1.19 +  \begin{description}
    1.20 +
    1.21 +  \item @{command (HOL) "partial_function"} defines recursive
    1.22 +  functions based on fixpoints in complete partial orders. No
    1.23 +  termination proof is required from the user or constructed
    1.24 +  internally. Instead, the possibility of non-termination is modelled
    1.25 +  explicitly in the result type, which contains an explicit bottom
    1.26 +  element.
    1.27 +
    1.28 +  Pattern matching and mutual recursion are currently not supported.
    1.29 +  Thus, the specification consists of a single function described by a
    1.30 +  single recursive equation.
    1.31 +
    1.32 +  There are no fixed syntactic restrictions on the body of the
    1.33 +  function, but the induced functional must be provably monotonic
    1.34 +  wrt.\ the underlying order.  The monotonicitity proof is performed
    1.35 +  internally, and the definition is rejected when it fails. The proof
    1.36 +  can be influenced by declaring hints using the
    1.37 +  @{attribute (HOL) partial_function_mono} attribute.
    1.38 +
    1.39 +  The mandatory @{text mode} argument specifies the mode of operation
    1.40 +  of the command, which directly corresponds to a complete partial
    1.41 +  order on the result type. By default, the following modes are
    1.42 +  defined: 
    1.43 +
    1.44 +  \begin{description}
    1.45 +  \item @{text option} defines functions that map into the @{type
    1.46 +  option} type. Here, the value @{term None} is used to model a
    1.47 +  non-terminating computation. Monotonicity requires that if @{term
    1.48 +  None} is returned by a recursive call, then the overall result
    1.49 +  must also be @{term None}. This is best achieved through the use of
    1.50 +  the monadic operator @{const "Option.bind"}.
    1.51 +  
    1.52 +  \item @{text tailrec} defines functions with an arbitrary result
    1.53 +  type and uses the slightly degenerated partial order where @{term
    1.54 +  "undefined"} is the bottom element.  Now, monotonicity requires that
    1.55 +  if @{term undefined} is returned by a recursive call, then the
    1.56 +  overall result must also be @{term undefined}. In practice, this is
    1.57 +  only satisfied when each recursive call is a tail call, whose result
    1.58 +  is directly returned. Thus, this mode of operation allows the
    1.59 +  definition of arbitrary tail-recursive functions.
    1.60 +  \end{description}
    1.61 +
    1.62 +  Experienced users may define new modes by instantiating the locale
    1.63 +  @{const "partial_function_definitions"} appropriately.
    1.64 +
    1.65 +  \item @{attribute (HOL) partial_function_mono} declares rules for
    1.66 +  use in the internal monononicity proofs of partial function
    1.67 +  definitions.
    1.68 +
    1.69 +  \end{description}
    1.70 +
    1.71 +*}
    1.72  
    1.73  subsection {* Old-style recursive function definitions (TFL) *}
    1.74