1/* 2 * Part of plml: Prolog-Matlab interface 3 * Copyright Samer Abdallah (Queen Mary University of London; UCL) 2004-2015 4 * 5 * This program is free software; you can redistribute it and/or 6 * modify it under the terms of the GNU General Public License 7 * as published by the Free Software Foundation; either version 2 8 * of the License, or (at your option) any later version. 9 * 10 * This program is distributed in the hope that it will be useful, 11 * but WITHOUT ANY WARRANTY; without even the implied warranty of 12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 * GNU General Public License for more details. 14 * 15 * You should have received a copy of the GNU General Public 16 * License along with this library; if not, write to the Free Software 17 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA 18 */ 19 20:- module(plml_dcg, 21 [ term_mlstring/3 % (+Id, +Expr, -String) ~Prolog term to Matlab string 22 , term_texatom/2 % (+Expr, -Atom) ~Prolog term to TeX expression 23 24 , op(650,fy,'`') % quoting things 25 , op(160,xf,'``') % postfix transpose operator 26 , op(100,fy,@) % function handles 27 28 % note slightly reduced precedence of array operators - 29 % hope this doesn't break everything... 30 , op(210,xfy,.^) % array exponentiation 31 , op(410,yfx,.*) % array times 32 , op(410,yfx,./) % array division 33 , op(410,xfy,.\) % reverse array division 34 , op(400,xfy,\) % reverse matrix division 35 , op(100,yfx,#) % field indexing (note left-associativity) 36 , op(750,fy,\\) % thunk abdstraction 37 , op(750,xfy,\\) % lambda abdstraction 38 ]). 39 40 41:- multifile user:pl2ml_hook/2, pl2ml_hook/3.

Matlab DCG

Types

ml_stmt - A Matlab statement

X;Y     :: ml_stmt :-  X::ml_stmt, Y::ml_stmt.
X,Y     :: ml_stmt :-  X::ml_stmt, Y::ml_stmt.
X=Y     :: ml_stmt :-  X::ml_lval, Y::ml_expr.
hide(X) :: ml_stmt :-  X::ml_stmt.

ml_expr(A)       % A Matlab expression, possibly with multiple return values
ml_loc ---> mat(atom,atom).  % Matbase locator

Matlab expression syntax

The Matlab expression syntax adopted by this module allows Prolog terms to represent or denote Matlab expressions. Let T be the domain of recognised Prolog terms (corresponding to the type ml_expr), and M be the domain of Matlab expressions written in Matlab syntax. Then V : T->M is the valuation function which maps Prolog term X to Matlab expression V[X]. These are some of the constructs it recognises:

Constructs valid only in top level statements, not subexpressions:

X;Y             % |--> V[X]; V[Y]  (sequential evaluation hiding first result)
X,Y             % |--> V[X], V[Y]  (sequential evaluation displaying first result)
X=Y             % |--> V[X]=V[Y] (assignment, X must denote a valid left-value)
hide(X)         % |--> V[X]; (execute X but hide return value)
if(X,Y)         % |--> if V[X], V[Y], end
if(X,Y,Z)       % |--> if V[X], V[Y], else V[Z], end

Things that look and work like Matlab syntax (more or less):

+X              % |--> uplus(V[X])
-X              % |--> uminus(V[X])
X+Y             % |--> plus(V[X],V[Y])
X-Y             % |--> minus(V[X],V[Y])
X^Y             % |--> mpower(V[X],V[Y])
X*Y             % |--> mtimes(V[X],V[Y])
X/Y             % |--> mrdivide(V[X],V[Y])
X\Y             % |--> mldivide(V[X],V[Y])
X.^Y            % |--> power(V[X],V[Y])
X.*Y            % |--> times(V[X],V[Y])
X./Y            % |--> rdivide(V[X],V[Y])
X.\Y            % |--> ldivide(V[X],V[Y])
X:Y:Z           % |--> colon(V[X],V[Y],V[Z])
X:Z             % |--> colon(V[X],V[Z])
X>Z             % |--> gt(V[X],V[Y])
X>=Z            % |--> ge(V[X],V[Y])
X<Z             % |--> lt(V[X],V[Y])
X=<Z            % |--> le(V[X],V[Y])
X==Z            % |--> eq(V[X],V[Y])
[X1,X2,...]     % |--> [ V[X1], V[X2], ... ]
[X1;X2;...]     % |--> [ V[X1]; V[X2]; ... ]
{X1,X2,...}     % |--> { V[X1], V[X2], ... }
{X1;X2;...}     % |--> { V[X1]; V[X2]; ... }
@X              % |--> @V[X] (function handle)

Things that do not look like Matlab syntax but provide standard Matlab features:

'Infinity'      % |--> inf (positive infinity)
'Nan'           % |--> nan (not a number)
X``             % |--> ctranpose(V[X]) (conjugate transpose, V[X]')
X#Y             % |--> getfield(V[X],V[q(Y)])
X\\Y            % |--> @(V[X])V[Y] (same as lambda(X,Y))
\\Y             % |--> @()V[Y] (same as thunk(Y))
lambda(X,Y)     % |--> @(V[X])V[Y] (anonymous function with arguments X)
thunk(Y)        % |--> @()V[Y] (anonymous function with no arguments)
vector(X)       % |--> horzcat(V[X1],V[X2], ...)
atvector(X)     % as vector but assumes elements of X are assumed all atomic
cell(X)         % construct 1xN cell array from elements of X
`X              % same as q(X)
q(X)            % wrap V[X] in single quotes (escaping internal quotes)
qq(X)           % wrap V[X] in double quotes (escaping internal double quotes)
tq(X)           % wrap TeX expression in single quotes (escape internal quotes)

Referencing different value representations.

mat(X,Y)           % denotes a value in the Matbase using a dbload expression
mx(X:mx_blob)      % denotes an MX Matlab array in SWI memory
ws(X:ws_blob)      % denotes a variable in a Matlab workspace
wsseq(X:ws_blob)   % workspace variable containing list as cell array.

Tricky bits.

apply(X,AX)        % X must denote a function or array, applied to list of arguments AX.
cref(X,Y)          % cell dereference, |--> V[X]{ V[Y1], V[Y2], ... }
arr(Lists)         % multidimensional array from nested lists.
arr(Lists,Dims)    % multidimensional array from nested lists.

Things to bypass default formatting

noeval(_)          % triggers a failure when processed
atom(X)            % write atom X as write/1
term(X)            % write term X as write/1
\(P)               % escape and call phrase P directly to generate Matlab string
$(X)               % calls pl2ml_hook/2, denotes V[Y] where plml_hook(X,Y).
'$VAR'(N)          % gets formatted as p_N where N is assumed to be atomic.

All other Prolog atoms are written using write/1, while other Prolog terms are assumed to be calls to Matlab functions named according to the head functor. Thus V[ <head>( <arg1>, <arg2>, ...) ] = <head>(V[<arg1>, V[<arg2>], ...).

There are some incompatibilities between Matlab syntax and Prolog syntax, that is, syntactic structures that Prolog cannot parse correctly:

'Command line' syntax, ie where a function of string arguments: "save('x','Y')" can be written as "save x Y" in Matlab, but in Prolog, you must use function call syntax with quoted arguments: save(`x,`'Y').
Matlab's postfix transpose operator "x'" must be written using a different posfix operator "x``" or function call syntax "ctranspose(x)".
Matlab cell referencing using braces, as in x{1,2} must be written as "cref(x,1,2)".
Field referencing using dot (.), eg x.thing - currently resolved by using hash (#) operator, eg x#thing.
Using variables as arrays and indexing them. The problem is that Prolog doesn't let you write a term with a variable as the head functor.

To be done

- Use mat(I) and tmp(I) as types to include engine Id.

Clarify relationship between return values and valid Matlab denotation.

Reshape/2 array representation: reshape([ ... ],Size) Expression language: arr(Vals,Shape,InnerFunctor) - allows efficient representation of arrays of arbitrary things. Will require more strict nested list form.

Deprecate old array(Vals::Type) and cell(Vals::Type) left-value syntax.

Remove I from ml_expr//2 and add to mx type? */

195:- use_module(library(dcg_core)). 196:- use_module(library(dcg_codes)). 197 198:- set_prolog_flag(back_quotes,symbol_char). 199:- set_prolog_flag(double_quotes,codes). 200 201:- op(650,fy,`). % quoting things 202:- op(160,xf,``). % postfix transpose operator 203:- op(100,fy,@). % function handles 204:- op(200,xfy,.^). % array exponentiation 205:- op(410,yfx,.*). % array times 206:- op(410,yfx,./). % array division 207:- op(410,xfy,.\). % array reverse division 208:- op(400,xfy,\). % matrix reverse division 209:- op(100,yfx,#). % field indexing (note left-associativity) 210 211:- dynamic current_engine/1. 212 213 214%% pl2ml_hook(+I:engine,+X:term,-Y:ml_expr) is nondet. 215%% pl2ml_hook(+X:term,-Y:ml_expr) is nondet. 216% Clauses of pl2ml_hook/2 allow for extensions to the Matlab expression 217% language such that =|V[$X] = V[Y]|= if =|pl2ml_hook(X,Y)|=. 218pl2ml_hook(_,X,Y) :- pl2ml_hook(X,Y). 219 220/* 221 * DCG for term to matlab conversion 222 * the big problem with Matlab syntax is that you cannot always replace 223 * a name representing a value with an expression that reduces to that 224 * value. Eg 225 * X=magic(5), X(3,4) 226 * is ok, but 227 * (magic(5))(3,4) 228 * is not. Similarly x=@sin, x(0.5) but not (@sin)(0.5) 229 * This is really infuriating. 230 */ 231 232 233% top level statement rules 234stmt(I,hide(A)) --> !, stmt(I,(A;nop)). 235stmt(I,(A;B)) --> !, stmt(I,A), ";", stmt(I,B). 236stmt(I,(A,B)) --> !, stmt(I,A), ",", stmt(I,B). 237stmt(I,A=B) --> !, ml_expr(I,A), "=", ml_expr(I,B). 238stmt(I,if(A,B)) --> !, "if ",ml_expr(I,A), ", ", stmt(I,B), ", end". 239stmt(I,if(A,B,C)) --> !, "if ",ml_expr(I,A), ", ", stmt(I,B), ", else ", stmt(I,C), ", end". 240stmt(I,Expr) --> !, ml_expr(I,Expr). 241 242 243%% ml_expr(+Id:ml_eng,+X:ml_expr(A))// is nondet. 244% Convert Matlab expression as a Prolog term to string representation. 245ml_expr(_,\X) --> !, phrase(X). 246ml_expr(I,$X) --> !, {pl2ml_hook(I,X,Y)}, ml_expr(I,Y). 247ml_expr(I,q(X)) --> !, q(stmt(I,X)). 248ml_expr(I,qq(X)) --> !, qq(stmt(I,X)). 249ml_expr(_,tq(X)) --> !, q(pl2tex(X)). 250ml_expr(_,atom(X)) --> !, atm(X). 251ml_expr(_,term(X)) --> !, wr(X). % this could be dangerous 252ml_expr(_,mat(X,Y)) --> !, "dbload(", loc(X,Y), ")". 253ml_expr(_,loc(L)) --> !, { L=mat(X,Y) }, loc(X,Y). 254ml_expr(I,mx(X)) --> !, ml_expr(I,$mx(X)). % punt these out to the pl2ml_hook, to be picked up plml_core 255ml_expr(I,ws(A)) --> !, ml_expr(I,$ws(A)). % ditto 256ml_expr(I,wsseq(A)) --> !, ml_expr(I,$ws(A)). 257ml_expr(_,noeval(_)) --> !, {fail}. % causes evaluation to fail. 258 259ml_expr(_,'Infinity') --> !, "inf". 260ml_expr(_,'Nan') --> !, "nan". 261 262ml_expr(I,A+B) --> !, "plus", args(I,A,B). 263ml_expr(I,A-B) --> !, "minus", args(I,A,B). 264ml_expr(I, -B) --> !, "uminus", args(I,B). 265ml_expr(I, +B) --> !, "uplus", args(I,B). 266ml_expr(I,A^B) --> !, "mpower", args(I,A,B). 267ml_expr(I,A*B) --> !, "mtimes", args(I,A,B). 268ml_expr(I,A/B) --> !, "mrdivide", args(I,A,B). 269ml_expr(I,A\B) --> !, "mldivide", args(I,A,B). 270ml_expr(I,A.^B)--> !, "power", args(I,A,B). 271ml_expr(I,A.*B)--> !, "times", args(I,A,B). 272ml_expr(I,A./B)--> !, "rdivide", args(I,A,B). 273ml_expr(I,A.\B)--> !, "ldivide", args(I,A,B). 274ml_expr(I,A>B) --> !, "gt",args(I,A,B). 275ml_expr(I,A<B) --> !, "lt",args(I,A,B). 276ml_expr(I,A>=B)--> !, "ge",args(I,A,B). 277ml_expr(I,A=<B)--> !, "le",args(I,A,B). 278ml_expr(I,A==B)--> !, "eq",args(I,A,B). 279ml_expr(I,A:B) --> !, range(I,A,B). 280 281ml_expr(_,[]) --> !, "[]". 282ml_expr(_,{}) --> !, "{}". 283ml_expr(I,[X]) --> !, "[", matrix(v,I,X), "]". 284ml_expr(I,[X|XX]) --> !, "[", ml_expr(I,X), seqmap(do_then_call(",",ml_expr(I)),XX), "]". 285ml_expr(I,{X}) --> !, "{", matrix(_,I,X), "}". 286ml_expr(_,atom_list(L)) --> !, "[", seqmap_with_sep(",",atm,L), "]". 287 288ml_expr(I, `B) --> !, q(stmt(I,B)). 289ml_expr(I,A#B) --> !, "getfield", args(I,A,q(B)). 290ml_expr(I,B``) --> !, "ctranspose", args(I,B). 291ml_expr(_,@B) --> !, "@", atm(B). 292ml_expr(I, \\B) --> !, "@()", ml_expr(I,B). 293ml_expr(I, A\\B) --> !, { term_variables(A,V), varnames(V) }, 294 "@(", varlist(A), ")", ml_expr(I,B). 295ml_expr(I,lambda(A,B)) --> !, ml_expr(I,A\\B). 296ml_expr(I,thunk(B)) --> !, ml_expr(I, \\B). 297 298 299% !! This is problematic: we are using apply to represent both 300% function application and array dereferencing. For function 301% calls, A must be a function name atom or a function handle 302% If A is an array, it cannot be an expression, unless we 303% switch to using the paren Matlab function, which will be slower. 304ml_expr(I,apply(A,B)) --> !, ml_expr(I,A), arglist(I,B). 305ml_expr(I,cref(A,B)) --> !, ml_expr(I,A), "{", clist(I,B), "}". 306 307% array syntax 308ml_expr(I,arr($X)) --> !, { pl2ml_hook(I,X,L) }, ml_expr(I,arr(L)). 309ml_expr(I,arr(L)) --> !, { array_dims(L,D) }, array(D,I,L). 310ml_expr(I,arr(D,L)) --> !, array(D,I,L). 311ml_expr(I,arr(D,L,P)) --> !, array(D,I,P,L). 312ml_expr(I,atvector(L))--> !, "[", clist_at(I,L), "]". 313ml_expr(I,vector(L)) --> !, "[", clist(I,L), "]". 314ml_expr(I,cell(L)) --> !, "{", clist(I,L), "}". 315ml_expr(_,'$VAR'(N)) --> !, "p_", atm(N). 316 317% catch these and throw exception 318ml_expr(_,hide(A)) --> {throw(ml_illegal_expression(hide(A)))}. 319ml_expr(_,(A;B)) --> {throw(ml_illegal_expression((A;B)))}. 320ml_expr(_,(A,B)) --> {throw(ml_illegal_expression((A,B)))}. 321ml_expr(_,A=B) --> {throw(ml_illegal_expression(A=B))}. 322 323% these are the catch-all clauses which will deal with matlab names, and literals 324% should we filter on the head functor? 325ml_expr(_,A) --> {string(A)}, !, q(str(A)). 326ml_expr(_,A) --> {atomic(A)}, !, atm(A). 327ml_expr(I,F) --> {F=..[H|AX]}, atm(H), arglist(I,AX). 328 329ml_expr_with(I,Lambda,Y) --> {copy_term(Lambda,Y\\PY)}, ml_expr(I,PY). 330 331 332% dimensions implicit in nested list representation 333array_dims([X|_],M) :- !, array_dims(X,N), succ(N,M). 334array_dims(_,0).

343array(0,I,X) --> !, ml_expr(I,X). 344array(1,I,L) --> !, "[", seqmap_with_sep(";",ml_expr(I),L), "]". 345array(2,I,L) --> !, "[", seqmap_with_sep(",",array(1,I),L), "]". 346array(N,I,L) --> {succ(M,N)}, "cat(", atm(N), ",", seqmap_with_sep(",",array(M,I),L), ")". 347 348array(0,I,P,X) --> !, ml_expr_with(I,P,X). 349array(1,I,P,L) --> !, "[", seqmap_with_sep(";",ml_expr_with(I,P),L), "]". 350array(2,I,P,L) --> !, "[", seqmap_with_sep(",",array(1,I,P),L), "]". 351array(N,I,P,L) --> {succ(M,N)}, "cat(", atm(N), ",", seqmap_with_sep(",",array(M,I,P),L), ")". 352 353matrix(h,I,(A,B)) --> !, ml_expr(I,A), ",", matrix(h,I,B). 354matrix(v,I,(A;B)) --> !, ml_expr(I,A), ";", matrix(v,I,B). 355matrix(_,I,A) --> !, ml_expr(I,A). 356 357 358% colon syntax for ranges 359range(I,A,B:C) --> !, "colon", arglist(I,[A,B,C]). 360range(I,A,B) --> !, "colon", args(I,A,B).

398atm(A,C,T) :- format(codes(C,T),'~w',[A]). 399 400varnames(L) :- varnames(1,L). 401varnames(_,[]). 402varnames(N,[TN|Rest]) :- 403 atom_concat(p_,N,TN), succ(N,M), 404 varnames(M,Rest).

413term_texatom(Term,Atom) :- phrase(pl2tex(Term),String), !, atom_codes(Atom,String). 414 415 416 417/* __________________________________________________________________________________ 418 * Dealing with the Matbase 419 * 420 * The Matbase is a file system tree which contains lots of 421 * MAT files which have been created by using the dbsave 422 * Matlab function. 423 */

437pl2tex(A=B) --> !, pl2tex(A), "=", pl2tex(B). 438pl2tex(A+B) --> !, pl2tex(A), "+", pl2tex(B). 439pl2tex(A-B) --> !, pl2tex(A), "-", pl2tex(B). 440pl2tex(A*B) --> !, pl2tex(A), "*", pl2tex(B). 441pl2tex(A.*B) --> !, pl2tex(A), "*", pl2tex(B). 442pl2tex(A/B) --> !, pl2tex(A), "/", pl2tex(B). 443pl2tex(A./B) --> !, pl2tex(A), "/", pl2tex(B). 444pl2tex(A\B) --> !, pl2tex(A), "\\", pl2tex(B). 445pl2tex(A.\B) --> !, pl2tex(A), "\\", pl2tex(B). 446pl2tex(A^B) --> !, pl2tex(A), "^", brace(pl2tex(B)). 447pl2tex(A.^B) --> !, pl2tex(A), "^", brace(pl2tex(B)). 448pl2tex((A,B))--> !, pl2tex(A), ", ", pl2tex(B). 449pl2tex(A;B)--> !, pl2tex(A), "; ", pl2tex(B). 450pl2tex(A:B)--> !, pl2tex(A), ": ", pl2tex(B). 451pl2tex({A}) --> !, "\\{", pl2tex(A), "\\}". 452pl2tex([]) --> !, "[]". 453pl2tex([X|XS]) --> !, "[", seqmap_with_sep(", ",pl2tex,[X|XS]), "]". 454 455pl2tex(A\\B) --> !, "\\lambda ", pl2tex(A), ".", pl2tex(B). 456pl2tex(@A) --> !, "@", pl2tex(A). 457pl2tex(abs(A)) --> !, "|", pl2tex(A), "|". 458pl2tex(A) --> {atomic(A)}, escape_with(0'\\,0'_,at(A)). 459pl2tex(A) --> 460 {compound(A), A=..[H|T] }, 461 pl2tex(H), paren(seqmap_with_sep(", ",pl2tex,T))