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From: Michael Hanus <hanus_at_I2.Informatik.RWTH-Aachen.DE>

Date: Fri, 6 Jun 1997 18:32:41 +0200

Dear Colleague,

I have updated the report on Curry.

This update is based on the discussion which we had on this mailing

list and further discussions with individual people.

The new version is available via the Curry web pages or directly at

http://www-i2.informatik.rwth-aachen.de/~hanus/curry/papers/report.dvi.Z

In order to encourage the discussion on the proposed changes,

I summarize the most important changes w.r.t. the first version of

December 5, 1996:

- the syntax is made compatible with Haskell

- restriction to confluent programs are dropped, i.e., non-deterministic

functions are allowed, but sufficient criteria to ensure

"well-definedness" of functions in the traditional sense are given,

see Section 2.2

- equational constraints and concurrent conjunction introduced (Section 2.3)

- meaning of committed choice modified (now it is compatible

with concurrent constraint languages)

- Prelude added (Appendix B)

- Syntax added (Appendix C)

The main conceptual change is the introduction of equational

constraints, which are described in Section 2.3.

This is only a slight conceptual modification (on the level of

types), but it solves a lot of problems with the current definition

of equality. Here are the main ideas concerning the introduction of

equational constraints:

1. Distinguish between usual Boolean functions (as in Haskell)

and constraints. Boolean functions can deliver True and False

as result values, whereas constraints are either satisfiable

and the computation proceeds or unsatisfiable and the computation

is discarded. Since the type of Boolean values is different

from constraints, you cannot apply the function "not" to negate

constraints (this causes one of the problems in the old version).

If one wants to compute with negative constraints, the constraint

system (currently only equations on data terms) must be enriched.

Thus, we distinguish between the test equality t1==t2, which a Boolean

function like in Haskell (since it suspends if one argument is an unkown

value), and the equational constraint {t1=t2}, which must be

solved in order to proceed the computation and thus may bind

unknown arguments. In terms of Saraswat's framework for concurrent

constraint programming, t1==t2 corresponds to "ask" and {t1=t2} to

"tell".

2. Constraints are applied (i.e., solved) only in conditions of

function rules, i.e., the condition of a function

rule has not type Bool but type "constraint" (in contrast

to the condition in if-then-else which has type Bool since

the outcomes True and False are necessary). This view

is fully compatible with logic programming and CLP

where the constraint in the conditional part must be satisfied

in order to apply the rule. If the constraint is not satisfiable,

then this rule cannot be applied. In order to be compatible

with Haskell, a Haskell rule "l | b = r" can be viewed

as equivalent to "l | {b=True} = r". This clearly shows

that one is interested in only computing the value True for

the condition.

3. Constraints can be constructed using the (concurrent) conjunction

/\, i.e., the sequential conjunction && of Haskell is a Boolean

function whereas /\ works on constraints. An important difference

is that a constraint {c1 /\ c2} can be evaluated concurrently.

Thus, all potential parallelism is expressed by constraints,

while the functional kernel (without constraints) expresses

a sequential computation. This point of view is compatible

with recent parallel functional languages like Goffin or Eden:

They use Haskell as a kernel language plus a coordination

language (constraints in Goffin, process constructs in Eden)

to express parallelism. By this simple distinction between

Boolean functions and constraints, Curry does not only

cover CLP but also covers and generalizes concurrent constraint

languages and functional parallel languages.

4. Since constraints are first-class citizens, one can also

define functions to generate constraints (which corresponds

to "skeletons" of high-level parallel languages). Functions

could also have constraints as parameters, but the only way

to use a constraint parameter is to pass it to the output or

apply it in the condition of its rule.

5. The introduction of constraints makes it also clear how to

connect external constraints solvers or enrich Curry with

more sophisticated constraint structures (like disequality,

arithmetic, or finite domain constraints): constraints are

only applied or tested for satisfiability in conditions of rules.

6. The introduction of constraints solves also some problems

which we have in connection with encapsulated search, but this

will be the topic of a future version.

You may look into the report for examples, in particular

Appendix A.5, where I have added a simple example how to do

concurrent object-oriented programming in Curry.

I hope that you agree with this proposal, since, after working

with this, I become more and more convinced that this is a

reasonable way to go.

If you want to see some really running examples, you could also

use our prototype implementation of Curry. This implementation,

called TasteCurry, is implemented by a very simple interpreter

written in Prolog. It is slow, but it implements a substantial

subset of Curry (e.g., it has polymorphic type inference,

an automatic generator for definitional trees, higher-order

functions and lambda-abstraction, local "where"-declarations,

monadic I/O, comitted choice etc). Since we haven't written any

parser, we use a Prolog-like syntax instead of concrete Curry

syntax, but I hope this will be improved in the next time

with the help of Sergio Antoy. You can run this interpreter

via our web interface for running TasteCurry programs. Please look at

http://www-i2.informatik.rwth-aachen.de/~hanus/tastecurry/

Enjoy!

Any kinds of comments are welcome!

Best regards,

Michael

Received on Fri Jun 06 1997 - 19:36:00 CEST

Date: Fri, 6 Jun 1997 18:32:41 +0200

Dear Colleague,

I have updated the report on Curry.

This update is based on the discussion which we had on this mailing

list and further discussions with individual people.

The new version is available via the Curry web pages or directly at

http://www-i2.informatik.rwth-aachen.de/~hanus/curry/papers/report.dvi.Z

In order to encourage the discussion on the proposed changes,

I summarize the most important changes w.r.t. the first version of

December 5, 1996:

- the syntax is made compatible with Haskell

- restriction to confluent programs are dropped, i.e., non-deterministic

functions are allowed, but sufficient criteria to ensure

"well-definedness" of functions in the traditional sense are given,

see Section 2.2

- equational constraints and concurrent conjunction introduced (Section 2.3)

- meaning of committed choice modified (now it is compatible

with concurrent constraint languages)

- Prelude added (Appendix B)

- Syntax added (Appendix C)

The main conceptual change is the introduction of equational

constraints, which are described in Section 2.3.

This is only a slight conceptual modification (on the level of

types), but it solves a lot of problems with the current definition

of equality. Here are the main ideas concerning the introduction of

equational constraints:

1. Distinguish between usual Boolean functions (as in Haskell)

and constraints. Boolean functions can deliver True and False

as result values, whereas constraints are either satisfiable

and the computation proceeds or unsatisfiable and the computation

is discarded. Since the type of Boolean values is different

from constraints, you cannot apply the function "not" to negate

constraints (this causes one of the problems in the old version).

If one wants to compute with negative constraints, the constraint

system (currently only equations on data terms) must be enriched.

Thus, we distinguish between the test equality t1==t2, which a Boolean

function like in Haskell (since it suspends if one argument is an unkown

value), and the equational constraint {t1=t2}, which must be

solved in order to proceed the computation and thus may bind

unknown arguments. In terms of Saraswat's framework for concurrent

constraint programming, t1==t2 corresponds to "ask" and {t1=t2} to

"tell".

2. Constraints are applied (i.e., solved) only in conditions of

function rules, i.e., the condition of a function

rule has not type Bool but type "constraint" (in contrast

to the condition in if-then-else which has type Bool since

the outcomes True and False are necessary). This view

is fully compatible with logic programming and CLP

where the constraint in the conditional part must be satisfied

in order to apply the rule. If the constraint is not satisfiable,

then this rule cannot be applied. In order to be compatible

with Haskell, a Haskell rule "l | b = r" can be viewed

as equivalent to "l | {b=True} = r". This clearly shows

that one is interested in only computing the value True for

the condition.

3. Constraints can be constructed using the (concurrent) conjunction

/\, i.e., the sequential conjunction && of Haskell is a Boolean

function whereas /\ works on constraints. An important difference

is that a constraint {c1 /\ c2} can be evaluated concurrently.

Thus, all potential parallelism is expressed by constraints,

while the functional kernel (without constraints) expresses

a sequential computation. This point of view is compatible

with recent parallel functional languages like Goffin or Eden:

They use Haskell as a kernel language plus a coordination

language (constraints in Goffin, process constructs in Eden)

to express parallelism. By this simple distinction between

Boolean functions and constraints, Curry does not only

cover CLP but also covers and generalizes concurrent constraint

languages and functional parallel languages.

4. Since constraints are first-class citizens, one can also

define functions to generate constraints (which corresponds

to "skeletons" of high-level parallel languages). Functions

could also have constraints as parameters, but the only way

to use a constraint parameter is to pass it to the output or

apply it in the condition of its rule.

5. The introduction of constraints makes it also clear how to

connect external constraints solvers or enrich Curry with

more sophisticated constraint structures (like disequality,

arithmetic, or finite domain constraints): constraints are

only applied or tested for satisfiability in conditions of rules.

6. The introduction of constraints solves also some problems

which we have in connection with encapsulated search, but this

will be the topic of a future version.

You may look into the report for examples, in particular

Appendix A.5, where I have added a simple example how to do

concurrent object-oriented programming in Curry.

I hope that you agree with this proposal, since, after working

with this, I become more and more convinced that this is a

reasonable way to go.

If you want to see some really running examples, you could also

use our prototype implementation of Curry. This implementation,

called TasteCurry, is implemented by a very simple interpreter

written in Prolog. It is slow, but it implements a substantial

subset of Curry (e.g., it has polymorphic type inference,

an automatic generator for definitional trees, higher-order

functions and lambda-abstraction, local "where"-declarations,

monadic I/O, comitted choice etc). Since we haven't written any

parser, we use a Prolog-like syntax instead of concrete Curry

syntax, but I hope this will be improved in the next time

with the help of Sergio Antoy. You can run this interpreter

via our web interface for running TasteCurry programs. Please look at

http://www-i2.informatik.rwth-aachen.de/~hanus/tastecurry/

Enjoy!

Any kinds of comments are welcome!

Best regards,

Michael

Received on Fri Jun 06 1997 - 19:36:00 CEST

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