A Catalog of Design Patterns in FLP
February 2001
Index
Links
| Intent |
Prevent invoking a constructor that might create invalid data |
| Applicability |
A type is too general for a problem |
| Structure |
Replace a call to a constructor with a call
to a function with the same signature.
The function checks the validity of the arguments and
either invokes the constructor or fails |
| Consequences |
Invalid instances of a type are not created |
Motivation
The Missionaries and Cannibals puzzle deals with
3 missionaries and 3 cannibals that cross forth and back
a river on a boat. A state of the puzzle is likely defined by
the following type:
| data State = State Int Int Bool |
where the two integers define the number of missionaries and
cannibals, respectively, on the initial bank of the river and
the boolean tells whether the boat is on the initial bank.
Unfortunately, this representation allows the construction of
states, e.g., State 5 -2 True, that are inconsistent
with the logic of the problem.
Applications
mission.curry
queens.curry
waterjug.curry
knight.curry
| Concurrent Distinct Choices |
| Intent |
Ensure that a mapping from indices to values is injective |
| Applicability |
Index-value pairs are computed concurrently |
| Structure |
A value of the problem is used as an index
in the representation of the mapping (the roles are reversed).
Initially, the values in the representation of the mapping are
free variables. During the computation, the variable at a given
index of the representation is bound to a token which is unique
for that index
|
| Consequences |
The index-value relation is an injective mapping |
Motivation
A cryptarithmetic puzzle presents an arithmetic computation
in which the digits are replaced by letters.
The problem is to find a correspondence from letters to digits
that satisfies the computation. For example:
SEND + MORE = MONEY
9567 + 1085 = 10652 |
A solution is
an injective mapping representing the correspondence from letters to
digits. In an efficient implementation,
the equations for the units, tens, hundreds, etc.,
residuate in no predefined order and are computed concurrently.
Applications
send-more.curry
queens.curry
Further information
Variations of this pattern and more application can be
found here.
| Intent |
Compute the solutions of a problem incrementally |
| Applicability |
A solution consists of a sequence of steps |
| Structure |
Compute a solution of a problem from an
initial partial solution that contains no steps.
Non-deterministically extend the partial solution
step by step until the solution is complete |
| Consequences |
Avoid the explicit representation of the search space |
Motivation
The solutions of many popular puzzles and common problems can be
modeled as sequences of steps. For example, the solution of the
stagecoach problem, which consists in finding a route between
two cities in a network of connections, is a sequence of legs;
the solution of the N-queens puzzle is a sequence of queen placements
on the board;
the solution of the missionaries and cannibals puzzles is a sequence
of river crossing, etc.
Applications
inc_search.curry
mission.curry
queens.curry
stagecoach.curry
waterjug.curry
knight.curry
| Locally Defined Global Identifier |
| Intent |
Ensure that a locally defined identifier is globally distinct |
| Applicability |
A global identifier is declared in a local scope |
| Structure |
Globally distinct identifiers are declared
as local unbound variables possibly to be bound later |
| Consequences |
Local identifiers are globally distinct |
Motivation
A graphical user interface is assembled from components.
Some component, e.g., a slidebar, must refer to some other
component, e.g., a textfield, which is not defined in the same scope.
This and other similar problems, e.g., dynamically generated
HTML pages, are abstracted by the composition
of graphs independently defined. A graph may need to refer to a
node of another graph which is defined by a local identifier, but
must be unique among all the graphs of a composition.
Applications
Graph.curry (library)
examples.curry
(examples of use of the library)
thompson.curry
(NFA construction for accepting regular expressions)
Further information
Variations of this pattern and more application can be
found here.
| Intent |
Ensure that the values of a public type are private |
| Applicability |
The values of a type must be internally/automatically
computed by an application |
| Structure |
Use only unbound variables to define instances of a type.
Enforce this policy by wrapping the values with a private constructor |
| Consequences |
Literal values of a type are not accessible to the programmer |
Motivation
Some data structures express the relations between elements that
are not expressive or interesting by themselves.
For example, in a graphical user interface the name of a textfield
is interesting only because a slidebar must refer to it.
A similar situation occurs in HTML documents.
A generalization of this situation is a graph where the nodes
must be defined only to define the edges.
In these situations it is more general and flexible to avoid
a specific representation of nodes as, e.g., integers or
strings.
Applications
Graph.curry (library)
examples.curry
(examples of use of the library)
thompson.curry
(NFA construction for accepting regular expressions)
| Composite-Visitor-Interpreter |
These patterns are popular and important in Object Oriented programming
languages. Declarative languages trivialize these patterns.
For example, a hierarchy of classes in
an OO language is replaced by a single type declaration in a
functional language, and a visitor is replaced by a single function
that uses pattern matching.
Below are the links to some simple programs that show how the features
of a declarative language simplify the use of these patterns.
Applications
Expr.curry
Statement.curry
Store.curry
Tests.curry
| Intent |
Merge together the generator and tester of a search problem |
| Applicability |
Search problems implemented with a generate-and-test architecture |
| Structure |
Generate the elements of a search space
with a function that simultaneously tests, as much as possible
for the problem at hand, the generated elements. |
| Consequences |
Elements of the search space are not passed from
generator to tester. Sometimes, the code is simpler,
clearer and more efficient. Partially constructed elements
can be eliminated before completion. |
Motivation
Many search problems are solved by generating each element
of a search space an testing whether the element is a goal.
Lazy evaluation is a useful or essential for the efficiency
of execution. However, using strict equality may decrease the
effectiveness of lazy evaluation. Merging together generator
and tester may improve the efficiency. In particular it
reduces the control needed to pass elements from the generator
to the tester and it may allow earlier testing and consequently
pruning of the search space.
Applications
24.curry
queens.curry