gamma_ref.pl : Gamma-to-CHR examples references (hand-translated version) GAMMA is an acronym for General Abstract Model for Multiset Manipulation. It is a programming paradigm relying solely on multiset transformation. [For more please consider DETAILS in the comment.]
How to use: These four small programs can be used: - prime(N): prime numbers Returns all prime numbers Pi up to N by prime_M(Pi). - fact(N): factorial Returns the factorial N! by fact_M(N!). - sp(L1,L2): partition into sets Partitions the elements of L1 and L2 into sets S and T (with size(S)=size(L1)) so that all elements from S are smaller than those from T. E belongs to S is represented: sp_M((E,inS)). E belongs to T is represented: sp_M((E,inT)). - so(L): sort List L (n elements) is sorted to [S1,S2,..Sn]: so_M((i-1,Si)).
See also: File "Gamma_gen.pl" for the directly translated versions. [1] JP Banatre, D Le Metayer. Programming by Multiset Transformation. Communications of the ACM, 1993.
Program: Change the code, then submit! /* gamma_ref.pl: Gamma-to-CHR examples references (hand-translated version) (C) Hariolf.Betz at uni-ulm.de, 2006/02/01 This program is distributed under the terms of the GNU General Public License: http://www.gnu.org/licenses/gpl.html %% DESCRIPTION GAMMA is an acronym for General Abstract Model for Multiset Manipulation. It is a programming paradigm relying solely on multiset transformation. [For more please consider DETAILS in the comment.] %% DETAILS A GAMMA program necessarily contains a multiset S, a predicate R(x1,...,xn) and a function A(x1,...,xn). S gives the data on which to operate. R is a condition that may or may not be fulfilled by x1,...,xn, which is a sequence of elements of S. A is a function that will be applied on x1,...,xn, in case R(x1,...,xn) is true. The result of A(x1,...,xn) will replace the x1,...,xn in S. A GAMMA program is of the form: identifier(args) = G((R,A)) (S) where R(x,y) = ... A(x,y) = ... As for an example, the following GAMMA program calculates the faculty of a natural number N: fact(N) = G((R,A)) ({1, ..., N}) where R(x,y) = true A(x,y) = {x*y} This file is for your reference. It contains more conservative CHR versions of the GAMMA programs from [1] than "Gamma_gen.pl". They are closer to the usual CHR style of programming and probably much better readable. %% HOW TO USE These four small programs can be used:# - *prime(N)*: prime numbers# Returns all prime numbers Pi up to N by prime_M(Pi).# - *fact(N)*: factorial# Returns the factorial N! by fact_M(N!).# - *sp(L1,L2)*: partition into sets# Partitions the elements of L1 and L2 into sets S and T (with size(S)=size(L1)) so that all elements from S are smaller than those from T. E belongs to S is represented: sp_M((E,inS)). E belongs to T is represented: sp_M((E,inT)).# - *so(L)*: sort# List L (n elements) is sorted to [S1,S2,..Sn]: so_M((i-1,Si)).# %% SEE ALSO File "Gamma_gen.pl" for the directly translated versions. [1] JP Banatre, D Le Metayer. Programming by Multiset Transformation. Communications of the ACM, 1993. %% SAMPLE QUERIES Q: prime(7). A: prime_M(2), prime_M(3), prime_M(5), prime_M(7). Q: fact(5). A: fact_M(120). Q: sp([1,7,8],[4,5]). A: sp_M((1,inS)), sp_M((4,inS)), sp_M((5,inS)), sp_M((7,inT)), sp_M((8,inT)). Q: so([1,7,5,44,2]). A: so_M((0,1)), so_M((1,2)), so_M((2,5)), so_M((3,7)), so_M((4,44)). */ :- module(gamma_ref, [prime/1, prime_M/1, fact/1, fact_M/1, sp/2, sp_M/1, so/1, so_M/1]). :- use_module(library(chr)). %% Deprecated syntax used for SICStus 3.x %handler gamma_ref. %constraints %% Syntax for SWI / SICStus 4.x :- chr_constraint prime/1, prime_M/1, fact/1, fact_M/1, sp/2, sp_M/1, so/1, so/2, so_M/1. %---prime--- multiple(X,Y):- X mod Y=:=0. prime(2) <=> prime_M(2). prime(N) <=> N>2 | prime_M(N), N1 is N-1, prime(N1). prime_M(X), prime_M(Y) <=> multiple(X,Y) | prime_M(Y). % Original GAMMA program: % (G replaces the '\Gamma' character) % % prime_numbers(N) = G((R,A)) ({2, ..., N}) where % R(x,y) = multiple(x,y) % A(x,y) = {y} %---fact--- fact(1) <=> fact_M(1). fact(N) <=> N>1 | fact_M(N), N1 is N-1, fact(N1). fact_M(X), fact_M(Y) <=> A is X*Y, fact_M(A). % Original GAMMA program: % % fact(N) = G((R,A)) ({1, ..., N}) where % R(x,y) = true % A(x,y) = {x*y} %---sp--- sp([],[]) <=> true. sp([S1|S],T) <=> sp_M((S1,inS)), sp(S,T). sp(S,[T1|T]) <=> sp_M((T1,inT)), sp(S,T). sp_M((X,inS)),sp_M((Y,inT)) <=> X>Y | sp_M((X,inT)),sp_M((Y,inS)). % Original GAMMA program: % % sp(S,T) = G((R,A)) (S x {inS} + T x {inT}) where % R((x,inS), (y,inT)) = x>y % A((x,inS), (y,inT)) = {(x,inT),(y,inS)} %---sort--- so(A) <=> so(0,A). so(_,[]) <=> true. so(N,[H|T]) <=> so_M((N,H)), N1 is N+1, so(N1,T). so_M((I,V)), so_M((J,W)) <=> I>J, V<W | so_M((I,W)), so_M((J,V)). % Original GAMMA program: % (G replaces the '\Gamma' character) % % sort(Array) = G((R,A)) (Array) where % R((i,v), (j,w)) = (i>j) and (v<w) % A((i,v), (j,w)) = {(i,w),(j,v)}
Console: Enter query or select example from below, then submit and wait for answer! % loading generated/gamma_ref.pl | ?- consult(...). yes [0.590 seconds] | ?-