recursive-tree.cpp

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/************************************************************************
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    FAUST compiler
    Copyright (C) 2003-2004 GRAME, Centre National de Creation Musicale
    ---------------------------------------------------------------------
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    This program is distributed in the hope that it will be useful,
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    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
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#include <assert.h>
#include <stdio.h>
#include <stdlib.h>
#include <limits.h>
#include "tlib.hh"

// Declaration of implementation
static Tree calcDeBruijn2Sym (Tree t);
static Tree substitute(Tree t, int n, Tree id);
static Tree calcsubstitute(Tree t, int level, Tree id);
static Tree liftn(Tree t, int threshold);
static Tree calcliftn(Tree t, int threshold);

// recursive trees

Sym     DEBRUIJN    = symbol ("DEBRUIJN");
Sym     DEBRUIJNREF = symbol ("DEBRUIJNREF");
Sym     SUBSTITUTE  = symbol ("SUBSTITUTE");

Sym     SYMREC      = symbol ("SYMREC");
Sym     SYMRECREF   = symbol ("SYMRECREF");
Sym     SYMLIFTN    = symbol ("LIFTN");

//Tree  NOVAR       = tree("NOVAR");

//-----------------------------------------------------------------------------------------
// rec, isRec : declare recursive trees
//-----------------------------------------------------------------------------------------

// de Bruijn declaration of a recursive tree
Tree rec(Tree body)
{
    return tree(DEBRUIJN, body);
}

bool isRec(Tree t, Tree& body)
{
    return isTree(t, DEBRUIJN, body);
}

Tree ref(int level)
{
    assert(level > 0);
    return tree(DEBRUIJNREF, tree(level));  // reference to enclosing recursive tree starting from 1
}

bool isRef(Tree t, int& level)
{
    Tree    u;

    if (isTree(t, DEBRUIJNREF, u)) {
        return isInt(u->node(), &level);
    } else {
        return false;
    }
}


//-----------------------------------------------------------------------------------------
// Recursive tree in symbolic notation (using a recursive definition property)
//-----------------------------------------------------------------------------------------
Tree RECDEF = tree(symbol("RECDEF"));

// declaration of a recursive tree using a symbolic variable
Tree rec(Tree var, Tree body)
{
    Tree t = tree(SYMREC, var);
    t->setProperty(RECDEF, body);
    return t;
}

bool isRec(Tree t, Tree& var, Tree& body)
{
    if (isTree(t, SYMREC, var)) {
        body = t->getProperty(RECDEF);
        return true;
    } else {
        return false;
    }
}


Tree ref(Tree id)
{
    return tree(SYMREC, id);            // reference to a symbolic id
}

bool isRef(Tree t, Tree& v)
{
    return isTree(t, SYMREC, v);
}

//-----------------------------------------------------------------------------------------
// L'aperture d'un arbre est la plus profonde reference de Bruijn qu'il contienne.
// Les references symboliques compte pour zero ce qui veut dire qu'un arbre d'aperture
// 0 ne compte aucun reference de bruijn libres.

int CTree::calcTreeAperture( const Node& n, const tvec& br  )
{
    int x;
    if (n == DEBRUIJNREF) {

        if (isInt(br[0]->node(), &x)) {
            return x;
        } else {
            return 0;
        }

    } else if (n == DEBRUIJN) {

        return br[0]->fAperture - 1;

    } else {
        // return max aperture of branches
        int rc = 0;
        tvec::const_iterator    b = br.begin();
        tvec::const_iterator    z = br.end();
        while (b != z) {
            if ((*b)->aperture() > rc) rc = (*b)->aperture();
            ++b;
        }
        return rc;
    }
}

Tree lift(Tree t) { return liftn(t, 1); }

void printSignal(Tree sig, FILE* out, int prec=0);

// lift (t) : increase free references by 1

#if 0
static Tree _liftn(Tree t, int threshold);

static Tree liftn(Tree t, int threshold)
{
    fprintf(stderr, "call of liftn("); printSignal(t, stderr); fprintf(stderr, ", %d)\n", threshold);
    Tree r = _liftn(t, threshold);
    fprintf(stderr, "return of liftn("); printSignal(t, stderr); fprintf(stderr, ", %d) -> ", threshold);
    printSignal(r, stderr); fprintf(stderr, "\n");
    return r;
}
#endif


static Tree liftn(Tree t, int threshold)
{
    Tree L  = tree( Node(SYMLIFTN), tree(Node(threshold)) );
    Tree t2 = t->getProperty(L);

    if (!t2) {
        t2 = calcliftn(t, threshold);
        t->setProperty(L, t2);
    }
    return t2;
    
}

static Tree calcliftn(Tree t, int threshold)
{
    int     n;
    Tree    u;

    if (isClosed(t)) {

        return t;

    } else if (isRef(t,n)) {

        if (n < threshold) {
            // it is a bounded reference
            return t;
        } else {
            // it is a free reference
            return ref(n+1);
        }

    } else if (isRec(t,u)) {

        return rec(liftn(u, threshold+1));

    } else {
        int n = t->arity();
        //Tree  br[4];
        tvec    br(n);
        for (int i = 0; i < n; i++) {
            br[i] = liftn(t->branch(i), threshold);
        }
        //return CTree::make(t->node(), n, br);
        return CTree::make(t->node(), br);
    }

}

//-----------------------------------------------------------
// Transform a tree from deBruijn to symbolic representation
//-----------------------------------------------------------
Tree DEBRUIJN2SYM = tree(symbol("deBruijn2Sym"));

Tree deBruijn2Sym (Tree t)
{
    assert(isClosed(t));
    Tree t2 = t->getProperty(DEBRUIJN2SYM);

    if (!t2) {
        t2 = calcDeBruijn2Sym(t);
        t->setProperty(DEBRUIJN2SYM, t2);
    }
    return t2;
}

static Tree calcDeBruijn2Sym (Tree t)
{
    Tree    body, var;
    int     i;

    if (isRec(t,body)) {

        var = tree(unique("W"));
        return rec(var, deBruijn2Sym(substitute(body,1,ref(var))));

    } else if (isRef(t,var)) {

        return t;

    } else if (isRef(t,i)) {

        fprintf(stderr, "ERREUR, une reference de Bruijn touvee ! : ");
        printSignal(t, stderr);
        fprintf(stderr, ")\n");
        exit(1);
        return t;

    } else {

        //Tree  br[4];
        int     a = t->arity();
        tvec    br(a);

        for (int i = 0; i < a; i++) {
            br[i] = deBruijn2Sym(t->branch(i));
        }
        //return CTree::make(t->node(), a, br);
        return CTree::make(t->node(), br);
    }
}

static Tree substitute(Tree t, int level, Tree id)
{
    Tree S  = tree( Node(SUBSTITUTE), tree(Node(level)), id );
    Tree t2 = t->getProperty(S);

    if (!t2) {
        t2 = calcsubstitute(t, level, id);
        t->setProperty(S, t2);
    }
    return t2;
    
}

static Tree calcsubstitute(Tree t, int level, Tree id)
{
    int     l;
    Tree    body;

    if (t->aperture()<level) {
//      fprintf(stderr, "aperture %d < level %d !!\n", t->aperture(), level);
        return t;
    }
    if (isRef(t,l))          return (l == level) ? id : t;
    if (isRec(t,body))       return rec(substitute(body, level+1, id));

    int     ar = t->arity();
    //Tree  br[4];
    tvec    br(ar);
    for (int i = 0; i < ar; i++) {
        br[i] = substitute(t->branch(i), level, id);
    }
    //return CTree::make(t->node(), ar, br);
    return CTree::make(t->node(), br);
}


//--------------------------------------------------------------------------
// UpdateAperture (t) : recursively mark open and closed terms.
// closed term : fAperture == 0,  open term fAperture == -1

struct Env {
    Tree fTree; Env* fNext;
    Env(Tree t, Env* nxt) : fTree(t), fNext(nxt) {}
};

static void markOpen(Tree t);
static int recomputeAperture(Tree t, Env* p);
static int orderof (Tree t, Env* p);

void updateAperture(Tree t)
{
    markOpen(t);
    recomputeAperture(t, NULL);
}

//----------------------implementation--------------------------------

static void markOpen(Tree t)
{
    if (t->aperture() == INT_MAX) return;
    t->setAperture(INT_MAX);
    int ar = t->arity();
    for (int i = 0; i < ar; i++) {
        markOpen(t->branch(i));
    }
}

static int recomputeAperture(Tree t, Env* env)
{
    Tree    var, body;

    if (t->aperture() == 0) return 0;

    if (isRef(t, var)) {

        return orderof(var, env);

    } else if (isRec(t, var, body)) {

        Env e(var,env);
        int a = recomputeAperture(body, &e) - 1;
        if (a<=0) { /*print(t, stderr);*/ t->setAperture(0); }
        return a;

    } else {
        // return max aperture of branches
        int ma = 0;
        int ar = t->arity();
        for (int i = 0; i<ar; i++) {
            int a = recomputeAperture(t->branch(i), env);
            if (ma < a) ma = a;
        }
        if (ma <= 0)  { /*print(t, stderr);*/ t->setAperture(0); }
        return ma;
    }
}


static int orderof (Tree t, Env* p)
{
    if (p == NULL) return 0;
    if (t == p->fTree) return 1;

    int pos = 1;
    while (p != NULL) {
        if (t == p->fTree) return pos;
        p = p->fNext;
        pos++;
    }
    return 0;
}