source: src/ResolvExpr/CandidateFinder.cpp @ 87e0b015

//
// Cforall Version 1.0.0 Copyright (C) 2015 University of Waterloo
//
// The contents of this file are covered under the licence agreement in the
// file "LICENCE" distributed with Cforall.
//
// CandidateFinder.cpp --
//
// Author           : Aaron B. Moss
// Created On       : Wed Jun 5 14:30:00 2019
// Last Modified By : Aaron B. Moss
// Last Modified On : Wed Jun 5 14:30:00 2019
// Update Count     : 1
//

#include "CandidateFinder.hpp"

#include <deque>
#include <iterator>               // for back_inserter
#include <sstream>
#include <string>
#include <unordered_map>
#include <vector>

#include "Candidate.hpp"
#include "CompilationState.h"
#include "Cost.h"
#include "ExplodedArg.hpp"
#include "RenameVars.h"           // for renameTyVars
#include "Resolver.h"
#include "ResolveTypeof.h"
#include "SatisfyAssertions.hpp"
#include "typeops.h"              // for adjustExprType, conversionCost, polyCost, specCost
#include "Unify.h"
#include "AST/Expr.hpp"
#include "AST/Node.hpp"
#include "AST/Pass.hpp"
#include "AST/Print.hpp"
#include "AST/SymbolTable.hpp"
#include "AST/Type.hpp"
#include "Common/utility.h"       // for move, copy
#include "SymTab/Mangler.h"
#include "SymTab/Validate.h"      // for validateType
#include "Tuples/Tuples.h"        // for handleTupleAssignment

#define PRINT( text ) if ( resolvep ) { text }

namespace ResolvExpr {

const ast::Expr * referenceToRvalueConversion( const ast::Expr * expr, Cost & cost ) {
        if ( expr->result.as< ast::ReferenceType >() ) {
                // cast away reference from expr
                cost.incReference();
                return new ast::CastExpr{ expr, expr->result->stripReferences() };
        }
        
        return expr;
}

/// Unique identifier for matching expression resolutions to their requesting expression
UniqueId globalResnSlot = 0;

Cost computeConversionCost( 
        const ast::Type * argType, const ast::Type * paramType, const ast::SymbolTable & symtab, 
        const ast::TypeEnvironment & env 
) {
        PRINT(
                std::cerr << std::endl << "converting ";
                ast::print( std::cerr, argType, 2 );
                std::cerr << std::endl << " to ";
                ast::print( std::cerr, paramType, 2 );
                std::cerr << std::endl << "environment is: ";
                ast::print( std::cerr, env, 2 );
                std::cerr << std::endl;
        )
        Cost convCost = conversionCost( argType, paramType, symtab, env );
        PRINT(
                std::cerr << std::endl << "cost is " << convCost << std::endl;
        )
        if ( convCost == Cost::infinity ) return convCost;
        convCost.incPoly( polyCost( paramType, symtab, env ) + polyCost( argType, symtab, env ) );
        PRINT(
                std::cerr << "cost with polycost is " << convCost << std::endl;
        )
        return convCost;
}

namespace {
        /// First index is which argument, second is which alternative, third is which exploded element
        using ExplodedArgs_new = std::deque< std::vector< ExplodedArg > >;

        /// Returns a list of alternatives with the minimum cost in the given list
        CandidateList findMinCost( const CandidateList & candidates ) {
                CandidateList out;
                Cost minCost = Cost::infinity;
                for ( const CandidateRef & r : candidates ) {
                        if ( r->cost < minCost ) {
                                minCost = r->cost;
                                out.clear();
                                out.emplace_back( r );
                        } else if ( r->cost == minCost ) {
                                out.emplace_back( r );
                        }
                }
                return out;
        }

        /// Computes conversion cost for a given expression to a given type
        const ast::Expr * computeExpressionConversionCost( 
                const ast::Expr * arg, const ast::Type * paramType, const ast::SymbolTable & symtab, const ast::TypeEnvironment & env, Cost & outCost 
        ) {
                Cost convCost = computeConversionCost( arg->result, paramType, symtab, env );
                outCost += convCost;

                // If there is a non-zero conversion cost, ignoring poly cost, then the expression requires 
                // conversion. Ignore poly cost for now, since this requires resolution of the cast to 
                // infer parameters and this does not currently work for the reason stated below
                Cost tmpCost = convCost;
                tmpCost.incPoly( -tmpCost.get_polyCost() );
                if ( tmpCost != Cost::zero ) {
                        ast::ptr< ast::Type > newType = paramType;
                        env.apply( newType );
                        return new ast::CastExpr{ arg, newType };

                        // xxx - *should* be able to resolve this cast, but at the moment pointers are not 
                        // castable to zero_t, but are implicitly convertible. This is clearly inconsistent, 
                        // once this is fixed it should be possible to resolve the cast.
                        // xxx - this isn't working, it appears because type1 (parameter) is seen as widenable, 
                        // but it shouldn't be because this makes the conversion from DT* to DT* since 
                        // commontype(zero_t, DT*) is DT*, rather than nothing

                        // CandidateFinder finder{ symtab, env };
                        // finder.find( arg, ResolvMode::withAdjustment() );
                        // assertf( finder.candidates.size() > 0, 
                        //      "Somehow castable expression failed to find alternatives." );
                        // assertf( finder.candidates.size() == 1, 
                        //      "Somehow got multiple alternatives for known cast expression." );
                        // return finder.candidates.front()->expr;
                }

                return arg;
        }

        /// Computes conversion cost for a given candidate
        Cost computeApplicationConversionCost( 
                CandidateRef cand, const ast::SymbolTable & symtab 
        ) {
                auto appExpr = cand->expr.strict_as< ast::ApplicationExpr >();
                auto pointer = appExpr->func->result.strict_as< ast::PointerType >();
                auto function = pointer->base.strict_as< ast::FunctionType >();

                Cost convCost = Cost::zero;
                const auto & params = function->params;
                auto param = params.begin();
                auto & args = appExpr->args;

                for ( unsigned i = 0; i < args.size(); ++i ) {
                        const ast::Type * argType = args[i]->result;
                        PRINT(
                                std::cerr << "arg expression:" << std::endl;
                                ast::print( std::cerr, args[i], 2 );
                                std::cerr << "--- results are" << std::endl;
                                ast::print( std::cerr, argType, 2 );
                        )

                        if ( param == params.end() ) {
                                if ( function->isVarArgs ) {
                                        convCost.incUnsafe();
                                        PRINT( std::cerr << "end of params with varargs function: inc unsafe: " 
                                                << convCost << std::endl; ; )
                                        // convert reference-typed expressions into value-typed expressions
                                        cand->expr = ast::mutate_field_index( 
                                                appExpr, &ast::ApplicationExpr::args, i, 
                                                referenceToRvalueConversion( args[i], convCost ) );
                                        continue;
                                } else return Cost::infinity;
                        }

                        if ( auto def = args[i].as< ast::DefaultArgExpr >() ) {
                                // Default arguments should be free - don't include conversion cost.
                                // Unwrap them here because they are not relevant to the rest of the system
                                cand->expr = ast::mutate_field_index( 
                                        appExpr, &ast::ApplicationExpr::args, i, def->expr );
                                ++param;
                                continue;
                        }

                        // mark conversion cost and also specialization cost of param type
                        const ast::Type * paramType = (*param)->get_type();
                        cand->expr = ast::mutate_field_index( 
                                appExpr, &ast::ApplicationExpr::args, i, 
                                computeExpressionConversionCost( 
                                        args[i], paramType, symtab, cand->env, convCost ) );
                        convCost.decSpec( specCost( paramType ) );
                        ++param;  // can't be in for-loop update because of the continue
                }

                if ( param != params.end() ) return Cost::infinity;

                // specialization cost of return types can't be accounted for directly, it disables 
                // otherwise-identical calls, like this example based on auto-newline in the I/O lib:
                //
                //   forall(otype OS) {
                //     void ?|?(OS&, int);  // with newline
                //     OS&  ?|?(OS&, int);  // no newline, always chosen due to more specialization
                //   }

                // mark type variable and specialization cost of forall clause
                convCost.incVar( function->forall.size() );
                for ( const ast::TypeDecl * td : function->forall ) {
                        convCost.decSpec( td->assertions.size() );
                }

                return convCost;
        }

        void makeUnifiableVars( 
                const ast::ParameterizedType * type, ast::OpenVarSet & unifiableVars, 
                ast::AssertionSet & need 
        ) {
                for ( const ast::TypeDecl * tyvar : type->forall ) {
                        unifiableVars[ tyvar->name ] = ast::TypeDecl::Data{ tyvar };
                        for ( const ast::DeclWithType * assn : tyvar->assertions ) {
                                need[ assn ].isUsed = true;
                        }
                }
        }

        /// Gets a default value from an initializer, nullptr if not present
        const ast::ConstantExpr * getDefaultValue( const ast::Init * init ) {
                if ( auto si = dynamic_cast< const ast::SingleInit * >( init ) ) {
                        if ( auto ce = si->value.as< ast::CastExpr >() ) {
                                return ce->arg.as< ast::ConstantExpr >();
                        } else {
                                return si->value.as< ast::ConstantExpr >();
                        }
                }
                return nullptr;
        }

        /// State to iteratively build a match of parameter expressions to arguments
        struct ArgPack {
                std::size_t parent;          ///< Index of parent pack
                ast::ptr< ast::Expr > expr;  ///< The argument stored here
                Cost cost;                   ///< The cost of this argument
                ast::TypeEnvironment env;    ///< Environment for this pack
                ast::AssertionSet need;      ///< Assertions outstanding for this pack
                ast::AssertionSet have;      ///< Assertions found for this pack
                ast::OpenVarSet open;        ///< Open variables for this pack
                unsigned nextArg;            ///< Index of next argument in arguments list
                unsigned tupleStart;         ///< Number of tuples that start at this index
                unsigned nextExpl;           ///< Index of next exploded element
                unsigned explAlt;            ///< Index of alternative for nextExpl > 0

                ArgPack()
                : parent( 0 ), expr(), cost( Cost::zero ), env(), need(), have(), open(), nextArg( 0 ), 
                  tupleStart( 0 ), nextExpl( 0 ), explAlt( 0 ) {}
                
                ArgPack( 
                        const ast::TypeEnvironment & env, const ast::AssertionSet & need, 
                        const ast::AssertionSet & have, const ast::OpenVarSet & open )
                : parent( 0 ), expr(), cost( Cost::zero ), env( env ), need( need ), have( have ), 
                  open( open ), nextArg( 0 ), tupleStart( 0 ), nextExpl( 0 ), explAlt( 0 ) {}
                
                ArgPack(
                        std::size_t parent, const ast::Expr * expr, ast::TypeEnvironment && env, 
                        ast::AssertionSet && need, ast::AssertionSet && have, ast::OpenVarSet && open, 
                        unsigned nextArg, unsigned tupleStart = 0, Cost cost = Cost::zero, 
                        unsigned nextExpl = 0, unsigned explAlt = 0 )
                : parent(parent), expr( expr ), cost( cost ), env( move( env ) ), need( move( need ) ),
                  have( move( have ) ), open( move( open ) ), nextArg( nextArg ), tupleStart( tupleStart ),
                  nextExpl( nextExpl ), explAlt( explAlt ) {}
                
                ArgPack(
                        const ArgPack & o, ast::TypeEnvironment && env, ast::AssertionSet && need, 
                        ast::AssertionSet && have, ast::OpenVarSet && open, unsigned nextArg, Cost added )
                : parent( o.parent ), expr( o.expr ), cost( o.cost + added ), env( move( env ) ), 
                  need( move( need ) ), have( move( have ) ), open( move( open ) ), nextArg( nextArg ), 
                  tupleStart( o.tupleStart ), nextExpl( 0 ), explAlt( 0 ) {}
                
                /// true if this pack is in the middle of an exploded argument
                bool hasExpl() const { return nextExpl > 0; }

                /// Gets the list of exploded candidates for this pack
                const ExplodedArg & getExpl( const ExplodedArgs_new & args ) const {
                        return args[ nextArg-1 ][ explAlt ];
                }
                
                /// Ends a tuple expression, consolidating the appropriate args
                void endTuple( const std::vector< ArgPack > & packs ) {
                        // add all expressions in tuple to list, summing cost
                        std::deque< const ast::Expr * > exprs;
                        const ArgPack * pack = this;
                        if ( expr ) { exprs.emplace_front( expr ); }
                        while ( pack->tupleStart == 0 ) {
                                pack = &packs[pack->parent];
                                exprs.emplace_front( pack->expr );
                                cost += pack->cost;
                        }
                        // reset pack to appropriate tuple
                        std::vector< ast::ptr< ast::Expr > > exprv( exprs.begin(), exprs.end() );
                        expr = new ast::TupleExpr{ expr->location, move( exprv ) };
                        tupleStart = pack->tupleStart - 1;
                        parent = pack->parent;
                }
        };

        /// Instantiates an argument to match a parameter, returns false if no matching results left
        bool instantiateArgument( 
                const ast::Type * paramType, const ast::Init * init, const ExplodedArgs_new & args, 
                std::vector< ArgPack > & results, std::size_t & genStart, const ast::SymbolTable & symtab, 
                unsigned nTuples = 0 
        ) {
                if ( auto tupleType = dynamic_cast< const ast::TupleType * >( paramType ) ) {
                        // paramType is a TupleType -- group args into a TupleExpr
                        ++nTuples;
                        for ( const ast::Type * type : *tupleType ) {
                                // xxx - dropping initializer changes behaviour from previous, but seems correct
                                // ^^^ need to handle the case where a tuple has a default argument
                                if ( ! instantiateArgument( 
                                        type, nullptr, args, results, genStart, symtab, nTuples ) ) return false;
                                nTuples = 0;
                        }
                        // re-constitute tuples for final generation
                        for ( auto i = genStart; i < results.size(); ++i ) {
                                results[i].endTuple( results );
                        }
                        return true;
                } else if ( const ast::TypeInstType * ttype = Tuples::isTtype( paramType ) ) {
                        // paramType is a ttype, consumes all remaining arguments
                        
                        // completed tuples; will be spliced to end of results to finish
                        std::vector< ArgPack > finalResults{};

                        // iterate until all results completed
                        std::size_t genEnd;
                        ++nTuples;
                        do {
                                genEnd = results.size();

                                // add another argument to results
                                for ( std::size_t i = genStart; i < genEnd; ++i ) {
                                        unsigned nextArg = results[i].nextArg;
                                        
                                        // use next element of exploded tuple if present
                                        if ( results[i].hasExpl() ) {
                                                const ExplodedArg & expl = results[i].getExpl( args );

                                                unsigned nextExpl = results[i].nextExpl + 1;
                                                if ( nextExpl == expl.exprs.size() ) { nextExpl = 0; }

                                                results.emplace_back(
                                                        i, expl.exprs[ results[i].nextExpl ], copy( results[i].env ),
                                                        copy( results[i].need ), copy( results[i].have ), 
                                                        copy( results[i].open ), nextArg, nTuples, Cost::zero, nextExpl,
                                                        results[i].explAlt );

                                                continue;
                                        }

                                        // finish result when out of arguments
                                        if ( nextArg >= args.size() ) {
                                                ArgPack newResult{
                                                        results[i].env, results[i].need, results[i].have, results[i].open };
                                                newResult.nextArg = nextArg;
                                                const ast::Type * argType = nullptr;

                                                if ( nTuples > 0 || ! results[i].expr ) {
                                                        // first iteration or no expression to clone,
                                                        // push empty tuple expression
                                                        newResult.parent = i;
                                                        std::vector< ast::ptr< ast::Expr > > emptyList;
                                                        newResult.expr = 
                                                                new ast::TupleExpr{ CodeLocation{}, move( emptyList ) };
                                                        argType = newResult.expr->result;
                                                } else {
                                                        // clone result to collect tuple
                                                        newResult.parent = results[i].parent;
                                                        newResult.cost = results[i].cost;
                                                        newResult.tupleStart = results[i].tupleStart;
                                                        newResult.expr = results[i].expr;
                                                        argType = newResult.expr->result;

                                                        if ( results[i].tupleStart > 0 && Tuples::isTtype( argType ) ) {
                                                                // the case where a ttype value is passed directly is special,
                                                                // e.g. for argument forwarding purposes
                                                                // xxx - what if passing multiple arguments, last of which is
                                                                //       ttype?
                                                                // xxx - what would happen if unify was changed so that unifying
                                                                //       tuple
                                                                // types flattened both before unifying lists? then pass in
                                                                // TupleType (ttype) below.
                                                                --newResult.tupleStart;
                                                        } else {
                                                                // collapse leftover arguments into tuple
                                                                newResult.endTuple( results );
                                                                argType = newResult.expr->result;
                                                        }
                                                }

                                                // check unification for ttype before adding to final
                                                if ( 
                                                        unify( 
                                                                ttype, argType, newResult.env, newResult.need, newResult.have,
                                                                newResult.open, symtab ) 
                                                ) {
                                                        finalResults.emplace_back( move( newResult ) );
                                                }

                                                continue;
                                        }

                                        // add each possible next argument
                                        for ( std::size_t j = 0; j < args[nextArg].size(); ++j ) {
                                                const ExplodedArg & expl = args[nextArg][j];

                                                // fresh copies of parent parameters for this iteration
                                                ast::TypeEnvironment env = results[i].env;
                                                ast::OpenVarSet open = results[i].open;

                                                env.addActual( expl.env, open );

                                                // skip empty tuple arguments by (nearly) cloning parent into next gen
                                                if ( expl.exprs.empty() ) {
                                                        results.emplace_back(
                                                                results[i], move( env ), copy( results[i].need ), 
                                                                copy( results[i].have ), move( open ), nextArg + 1, expl.cost );
                                                        
                                                        continue;
                                                }

                                                // add new result
                                                results.emplace_back(
                                                        i, expl.exprs.front(), move( env ), copy( results[i].need ), 
                                                        copy( results[i].have ), move( open ), nextArg + 1, nTuples, 
                                                        expl.cost, expl.exprs.size() == 1 ? 0 : 1, j );
                                        }
                                }

                                // reset for next round
                                genStart = genEnd;
                                nTuples = 0;
                        } while ( genEnd != results.size() );

                        // splice final results onto results
                        for ( std::size_t i = 0; i < finalResults.size(); ++i ) {
                                results.emplace_back( move( finalResults[i] ) );
                        }
                        return ! finalResults.empty();
                }

                // iterate each current subresult
                std::size_t genEnd = results.size();
                for ( std::size_t i = genStart; i < genEnd; ++i ) {
                        unsigned nextArg = results[i].nextArg;

                        // use remainder of exploded tuple if present
                        if ( results[i].hasExpl() ) {
                                const ExplodedArg & expl = results[i].getExpl( args );
                                const ast::Expr * expr = expl.exprs[ results[i].nextExpl ];

                                ast::TypeEnvironment env = results[i].env;
                                ast::AssertionSet need = results[i].need, have = results[i].have;
                                ast::OpenVarSet open = results[i].open;

                                const ast::Type * argType = expr->result;

                                PRINT(
                                        std::cerr << "param type is ";
                                        ast::print( std::cerr, paramType );
                                        std::cerr << std::endl << "arg type is ";
                                        ast::print( std::cerr, argType );
                                        std::cerr << std::endl;
                                )

                                if ( unify( paramType, argType, env, need, have, open, symtab ) ) {
                                        unsigned nextExpl = results[i].nextExpl + 1;
                                        if ( nextExpl == expl.exprs.size() ) { nextExpl = 0; }

                                        results.emplace_back(
                                                i, expr, move( env ), move( need ), move( have ), move( open ), nextArg, 
                                                nTuples, Cost::zero, nextExpl, results[i].explAlt );
                                }

                                continue;
                        }

                        // use default initializers if out of arguments
                        if ( nextArg >= args.size() ) {
                                if ( const ast::ConstantExpr * cnst = getDefaultValue( init ) ) {
                                        ast::TypeEnvironment env = results[i].env;
                                        ast::AssertionSet need = results[i].need, have = results[i].have;
                                        ast::OpenVarSet open = results[i].open;

                                        if ( unify( paramType, cnst->result, env, need, have, open, symtab ) ) {
                                                results.emplace_back(
                                                        i, new ast::DefaultArgExpr{ cnst->location, cnst }, move( env ), 
                                                        move( need ), move( have ), move( open ), nextArg, nTuples );
                                        }
                                }

                                continue;
                        }

                        // Check each possible next argument
                        for ( std::size_t j = 0; j < args[nextArg].size(); ++j ) {
                                const ExplodedArg & expl = args[nextArg][j];

                                // fresh copies of parent parameters for this iteration
                                ast::TypeEnvironment env = results[i].env;
                                ast::AssertionSet need = results[i].need, have = results[i].have;
                                ast::OpenVarSet open = results[i].open;

                                env.addActual( expl.env, open );

                                // skip empty tuple arguments by (nearly) cloning parent into next gen
                                if ( expl.exprs.empty() ) {
                                        results.emplace_back(
                                                results[i], move( env ), move( need ), move( have ), move( open ), 
                                                nextArg + 1, expl.cost );
                                        
                                        continue;
                                }

                                // consider only first exploded arg
                                const ast::Expr * expr = expl.exprs.front();
                                const ast::Type * argType = expr->result;

                                PRINT(
                                        std::cerr << "param type is ";
                                        ast::print( std::cerr, paramType );
                                        std::cerr << std::endl << "arg type is ";
                                        ast::print( std::cerr, argType );
                                        std::cerr << std::endl;
                                )

                                // attempt to unify types
                                if ( unify( paramType, argType, env, need, have, open, symtab ) ) {
                                        // add new result
                                        results.emplace_back(
                                                i, expr, move( env ), move( need ), move( have ), move( open ), 
                                                nextArg + 1, nTuples, expl.cost, expl.exprs.size() == 1 ? 0 : 1, j );
                                }
                        }
                }

                // reset for next parameter
                genStart = genEnd;

                return genEnd != results.size();
        }

        /// Generate a cast expression from `arg` to `toType`
        const ast::Expr * restructureCast( 
                ast::ptr< ast::Expr > & arg, const ast::Type * toType, ast::GeneratedFlag isGenerated = ast::GeneratedCast
        ) {
                if ( 
                        arg->result->size() > 1 
                        && ! toType->isVoid() 
                        && ! dynamic_cast< const ast::ReferenceType * >( toType ) 
                ) {
                        // Argument is a tuple and the target type is neither void nor a reference. Cast each 
                        // member of the tuple to its corresponding target type, producing the tuple of those 
                        // cast expressions. If there are more components of the tuple than components in the 
                        // target type, then excess components do not come out in the result expression (but 
                        // UniqueExpr ensures that the side effects will still be produced)
                        if ( Tuples::maybeImpureIgnoreUnique( arg ) ) {
                                // expressions which may contain side effects require a single unique instance of 
                                // the expression
                                arg = new ast::UniqueExpr{ arg->location, arg };
                        }
                        std::vector< ast::ptr< ast::Expr > > components;
                        for ( unsigned i = 0; i < toType->size(); ++i ) {
                                // cast each component
                                ast::ptr< ast::Expr > idx = new ast::TupleIndexExpr{ arg->location, arg, i };
                                components.emplace_back( 
                                        restructureCast( idx, toType->getComponent( i ), isGenerated ) );
                        }
                        return new ast::TupleExpr{ arg->location, move( components ) };
                } else {
                        // handle normally
                        return new ast::CastExpr{ arg->location, arg, toType, isGenerated };
                }
        }

        /// Gets the name from an untyped member expression (must be NameExpr)
        const std::string & getMemberName( const ast::UntypedMemberExpr * memberExpr ) {
                if ( memberExpr->member.as< ast::ConstantExpr >() ) {
                        SemanticError( memberExpr, "Indexed access to struct fields unsupported: " );
                }

                return memberExpr->member.strict_as< ast::NameExpr >()->name;
        }

        /// Actually visits expressions to find their candidate interpretations
        struct Finder final : public ast::WithShortCircuiting {
                CandidateFinder & selfFinder;
                const ast::SymbolTable & symtab;
                CandidateList & candidates;
                const ast::TypeEnvironment & tenv;
                ast::ptr< ast::Type > & targetType;

                Finder( CandidateFinder & f )
                : selfFinder( f ), symtab( f.symtab ), candidates( f.candidates ), tenv( f.env ), 
                  targetType( f.targetType ) {}
                
                void previsit( const ast::Node * ) { visit_children = false; }

                /// Convenience to add candidate to list
                template<typename... Args>
                void addCandidate( Args &&... args ) {
                        candidates.emplace_back( new Candidate{ std::forward<Args>( args )... } );
                }

                void postvisit( const ast::ApplicationExpr * applicationExpr ) {
                        addCandidate( applicationExpr, tenv );
                }

                /// Set up candidate assertions for inference
                void inferParameters( CandidateRef & newCand, CandidateList & out ) {
                        // Set need bindings for any unbound assertions
                        UniqueId crntResnSlot = 0; // matching ID for this expression's assertions
                        for ( auto & assn : newCand->need ) {
                                // skip already-matched assertions
                                if ( assn.second.resnSlot != 0 ) continue;
                                // assign slot for expression if needed
                                if ( crntResnSlot == 0 ) { crntResnSlot = ++globalResnSlot; }
                                // fix slot to assertion
                                assn.second.resnSlot = crntResnSlot;
                        }
                        // pair slot to expression
                        if ( crntResnSlot != 0 ) {
                                newCand->expr.get_and_mutate()->inferred.resnSlots().emplace_back( crntResnSlot );
                        }

                        // add to output list; assertion satisfaction will occur later
                        out.emplace_back( newCand );
                }

                /// Completes a function candidate with arguments located
                void validateFunctionCandidate( 
                        const CandidateRef & func, ArgPack & result, const std::vector< ArgPack > & results, 
                        CandidateList & out 
                ) {
                        ast::ApplicationExpr * appExpr = 
                                new ast::ApplicationExpr{ func->expr->location, func->expr };
                        // sum cost and accumulate arguments
                        std::deque< const ast::Expr * > args;
                        Cost cost = func->cost;
                        const ArgPack * pack = &result;
                        while ( pack->expr ) {
                                args.emplace_front( pack->expr );
                                cost += pack->cost;
                                pack = &results[pack->parent];
                        }
                        std::vector< ast::ptr< ast::Expr > > vargs( args.begin(), args.end() );
                        appExpr->args = move( vargs );
                        // build and validate new candidate
                        auto newCand = 
                                std::make_shared<Candidate>( appExpr, result.env, result.open, result.need, cost );
                        PRINT(
                                std::cerr << "instantiate function success: " << appExpr << std::endl;
                                std::cerr << "need assertions:" << std::endl;
                                ast::print( std::cerr, result.need, 2 );
                        )
                        inferParameters( newCand, out );
                }

                /// Builds a list of candidates for a function, storing them in out
                void makeFunctionCandidates(
                        const CandidateRef & func, const ast::FunctionType * funcType, 
                        const ExplodedArgs_new & args, CandidateList & out
                ) {
                        ast::OpenVarSet funcOpen;
                        ast::AssertionSet funcNeed, funcHave;
                        ast::TypeEnvironment funcEnv{ func->env };
                        makeUnifiableVars( funcType, funcOpen, funcNeed );
                        // add all type variables as open variables now so that those not used in the parameter 
                        // list are still considered open
                        funcEnv.add( funcType->forall );

                        if ( targetType && ! targetType->isVoid() && ! funcType->returns.empty() ) {
                                // attempt to narrow based on expected target type
                                const ast::Type * returnType = funcType->returns.front()->get_type();
                                if ( ! unify( 
                                        returnType, targetType, funcEnv, funcNeed, funcHave, funcOpen, symtab ) 
                                ) {
                                        // unification failed, do not pursue this candidate
                                        return;
                                }
                        }

                        // iteratively build matches, one parameter at a time
                        std::vector< ArgPack > results;
                        results.emplace_back( funcEnv, funcNeed, funcHave, funcOpen );
                        std::size_t genStart = 0;

                        for ( const ast::DeclWithType * param : funcType->params ) {
                                auto obj = strict_dynamic_cast< const ast::ObjectDecl * >( param );
                                // Try adding the arguments corresponding to the current parameter to the existing 
                                // matches
                                if ( ! instantiateArgument( 
                                        obj->type, obj->init, args, results, genStart, symtab ) ) return;
                        }

                        if ( funcType->isVarArgs ) {
                                // append any unused arguments to vararg pack
                                std::size_t genEnd;
                                do {
                                        genEnd = results.size();

                                        // iterate results
                                        for ( std::size_t i = genStart; i < genEnd; ++i ) {
                                                unsigned nextArg = results[i].nextArg;

                                                // use remainder of exploded tuple if present
                                                if ( results[i].hasExpl() ) {
                                                        const ExplodedArg & expl = results[i].getExpl( args );

                                                        unsigned nextExpl = results[i].nextExpl + 1;
                                                        if ( nextExpl == expl.exprs.size() ) { nextExpl = 0; }

                                                        results.emplace_back(
                                                                i, expl.exprs[ results[i].nextExpl ], copy( results[i].env ),
                                                                copy( results[i].need ), copy( results[i].have ),
                                                                copy( results[i].open ), nextArg, 0, Cost::zero, nextExpl,
                                                                results[i].explAlt );

                                                        continue;
                                                }

                                                // finish result when out of arguments
                                                if ( nextArg >= args.size() ) {
                                                        validateFunctionCandidate( func, results[i], results, out );

                                                        continue;
                                                }

                                                // add each possible next argument
                                                for ( std::size_t j = 0; j < args[nextArg].size(); ++j ) {
                                                        const ExplodedArg & expl = args[nextArg][j];

                                                        // fresh copies of parent parameters for this iteration
                                                        ast::TypeEnvironment env = results[i].env;
                                                        ast::OpenVarSet open = results[i].open;

                                                        env.addActual( expl.env, open );

                                                        // skip empty tuple arguments by (nearly) cloning parent into next gen
                                                        if ( expl.exprs.empty() ) {
                                                                results.emplace_back(
                                                                        results[i], move( env ), copy( results[i].need ), 
                                                                        copy( results[i].have ), move( open ), nextArg + 1, 
                                                                        expl.cost );

                                                                continue;
                                                        }

                                                        // add new result
                                                        results.emplace_back(
                                                                i, expl.exprs.front(), move( env ), copy( results[i].need ),
                                                                copy( results[i].have ), move( open ), nextArg + 1, 0, expl.cost, 
                                                                expl.exprs.size() == 1 ? 0 : 1, j );
                                                }
                                        }

                                        genStart = genEnd;
                                } while( genEnd != results.size() );
                        } else {
                                // filter out the results that don't use all the arguments
                                for ( std::size_t i = genStart; i < results.size(); ++i ) {
                                        ArgPack & result = results[i];
                                        if ( ! result.hasExpl() && result.nextArg >= args.size() ) {
                                                validateFunctionCandidate( func, result, results, out );
                                        }
                                }
                        }
                }

                /// Adds implicit struct-conversions to the alternative list
                void addAnonConversions( const CandidateRef & cand ) {
                        // adds anonymous member interpretations whenever an aggregate value type is seen. 
                        // it's okay for the aggregate expression to have reference type -- cast it to the 
                        // base type to treat the aggregate as the referenced value
                        ast::ptr< ast::Expr > aggrExpr( cand->expr );
                        ast::ptr< ast::Type > & aggrType = aggrExpr.get_and_mutate()->result;
                        cand->env.apply( aggrType );
                        
                        if ( aggrType.as< ast::ReferenceType >() ) {
                                aggrExpr = new ast::CastExpr{ aggrExpr, aggrType->stripReferences() };
                        }

                        if ( auto structInst = aggrExpr->result.as< ast::StructInstType >() ) {
                                addAggMembers( structInst, aggrExpr, *cand, Cost::safe, "" );
                        } else if ( auto unionInst = aggrExpr->result.as< ast::UnionInstType >() ) {
                                addAggMembers( unionInst, aggrExpr, *cand, Cost::safe, "" );
                        }
                }

                /// Adds aggregate member interpretations
                void addAggMembers( 
                        const ast::ReferenceToType * aggrInst, const ast::Expr * expr, 
                        const Candidate & cand, const Cost & addedCost, const std::string & name 
                ) {
                        for ( const ast::Decl * decl : aggrInst->lookup( name ) ) {
                                auto dwt = strict_dynamic_cast< const ast::DeclWithType * >( decl );
                                CandidateRef newCand = std::make_shared<Candidate>( 
                                        cand, new ast::MemberExpr{ expr->location, dwt, expr }, addedCost );
                                // add anonymous member interpretations whenever an aggregate value type is seen 
                                // as a member expression
                                addAnonConversions( newCand );
                                candidates.emplace_back( move( newCand ) );
                        }
                }

                /// Adds tuple member interpretations
                void addTupleMembers( 
                        const ast::TupleType * tupleType, const ast::Expr * expr, const Candidate & cand, 
                        const Cost & addedCost, const ast::Expr * member 
                ) {
                        if ( auto constantExpr = dynamic_cast< const ast::ConstantExpr * >( member ) ) {
                                // get the value of the constant expression as an int, must be between 0 and the 
                                // length of the tuple to have meaning
                                long long val = constantExpr->intValue();
                                if ( val >= 0 && (unsigned long long)val < tupleType->size() ) {
                                        addCandidate(
                                                cand, new ast::TupleIndexExpr{ expr->location, expr, (unsigned)val }, 
                                                addedCost );
                                }
                        }
                }

                void postvisit( const ast::UntypedExpr * untypedExpr ) {
                        CandidateFinder funcFinder{ symtab, tenv };
                        funcFinder.find( untypedExpr->func, ResolvMode::withAdjustment() );
                        // short-circuit if no candidates
                        if ( funcFinder.candidates.empty() ) return;

                        std::vector< CandidateFinder > argCandidates = 
                                selfFinder.findSubExprs( untypedExpr->args );
                        
                        // take care of possible tuple assignments
                        // if not tuple assignment, handled as normal function call
                        Tuples::handleTupleAssignment( selfFinder, untypedExpr, argCandidates );

                        // find function operators
                        ast::ptr< ast::Expr > opExpr = new ast::NameExpr{ untypedExpr->location, "?()" };
                        CandidateFinder opFinder{ symtab, tenv };
                        // okay if there aren't any function operations
                        opFinder.find( opExpr, ResolvMode::withoutFailFast() );
                        PRINT(
                                std::cerr << "known function ops:" << std::endl;
                                print( std::cerr, opFinder.candidates, 1 );
                        )

                        // pre-explode arguments
                        ExplodedArgs_new argExpansions;
                        for ( const CandidateFinder & args : argCandidates ) {
                                argExpansions.emplace_back();
                                auto & argE = argExpansions.back();
                                for ( const CandidateRef & arg : args ) { argE.emplace_back( *arg, symtab ); }
                        }

                        // Find function matches
                        CandidateList found;
                        SemanticErrorException errors;
                        for ( CandidateRef & func : funcFinder ) {
                                try {
                                        PRINT(
                                                std::cerr << "working on alternative:" << std::endl;
                                                print( std::cerr, *func, 2 );
                                        )

                                        // check if the type is a pointer to function
                                        const ast::Type * funcResult = func->expr->result->stripReferences();
                                        if ( auto pointer = dynamic_cast< const ast::PointerType * >( funcResult ) ) {
                                                if ( auto function = pointer->base.as< ast::FunctionType >() ) {
                                                        CandidateRef newFunc{ new Candidate{ *func } };
                                                        newFunc->expr = 
                                                                referenceToRvalueConversion( newFunc->expr, newFunc->cost );
                                                        makeFunctionCandidates( newFunc, function, argExpansions, found );
                                                }
                                        } else if ( 
                                                auto inst = dynamic_cast< const ast::TypeInstType * >( funcResult ) 
                                        ) {
                                                if ( const ast::EqvClass * clz = func->env.lookup( inst->name ) ) {
                                                        if ( auto function = clz->bound.as< ast::FunctionType >() ) {
                                                                CandidateRef newFunc{ new Candidate{ *func } };
                                                                newFunc->expr = 
                                                                        referenceToRvalueConversion( newFunc->expr, newFunc->cost );
                                                                makeFunctionCandidates( newFunc, function, argExpansions, found );
                                                        }
                                                }
                                        }
                                } catch ( SemanticErrorException & e ) { errors.append( e ); }
                        }

                        // Find matches on function operators `?()`
                        if ( ! opFinder.candidates.empty() ) {
                                // add exploded function alternatives to front of argument list
                                std::vector< ExplodedArg > funcE;
                                funcE.reserve( funcFinder.candidates.size() );
                                for ( const CandidateRef & func : funcFinder ) { 
                                        funcE.emplace_back( *func, symtab );
                                }
                                argExpansions.emplace_front( move( funcE ) );

                                for ( const CandidateRef & op : opFinder ) {
                                        try {
                                                // check if type is pointer-to-function
                                                const ast::Type * opResult = op->expr->result->stripReferences();
                                                if ( auto pointer = dynamic_cast< const ast::PointerType * >( opResult ) ) {
                                                        if ( auto function = pointer->base.as< ast::FunctionType >() ) {
                                                                CandidateRef newOp{ new Candidate{ *op} };
                                                                newOp->expr = 
                                                                        referenceToRvalueConversion( newOp->expr, newOp->cost );
                                                                makeFunctionCandidates( newOp, function, argExpansions, found );
                                                        }
                                                }
                                        } catch ( SemanticErrorException & e ) { errors.append( e ); }
                                }
                        }

                        // Implement SFINAE; resolution errors are only errors if there aren't any non-error 
                        // candidates
                        if ( found.empty() && ! errors.isEmpty() ) { throw errors; }

                        // Compute conversion costs
                        for ( CandidateRef & withFunc : found ) {
                                Cost cvtCost = computeApplicationConversionCost( withFunc, symtab );

                                PRINT(
                                        auto appExpr = withFunc->expr.strict_as< ast::ApplicationExpr >();
                                        auto pointer = appExpr->func->result.strict_as< ast::PointerType >();
                                        auto function = pointer->base.strict_as< ast::FunctionType >();
                                        
                                        std::cerr << "Case +++++++++++++ " << appExpr->func << std::endl;
                                        std::cerr << "parameters are:" << std::endl;
                                        ast::printAll( std::cerr, function->params, 2 );
                                        std::cerr << "arguments are:" << std::endl;
                                        ast::printAll( std::cerr, appExpr->args, 2 );
                                        std::cerr << "bindings are:" << std::endl;
                                        ast::print( std::cerr, withFunc->env, 2 );
                                        std::cerr << "cost is: " << withFunc->cost << std::endl;
                                        std::cerr << "cost of conversion is:" << cvtCost << std::endl;
                                )

                                if ( cvtCost != Cost::infinity ) {
                                        withFunc->cvtCost = cvtCost;
                                        candidates.emplace_back( move( withFunc ) );
                                }
                        }
                        found = move( candidates );

                        // use a new list so that candidates are not examined by addAnonConversions twice
                        CandidateList winners = findMinCost( found );
                        promoteCvtCost( winners );

                        // function may return a struct/union value, in which case we need to add candidates 
                        // for implicit conversions to each of the anonymous members, which must happen after 
                        // `findMinCost`, since anon conversions are never the cheapest
                        for ( const CandidateRef & c : winners ) {
                                addAnonConversions( c );
                        }
                        spliceBegin( candidates, winners );

                        if ( candidates.empty() && targetType && ! targetType->isVoid() ) {
                                // If resolution is unsuccessful with a target type, try again without, since it 
                                // will sometimes succeed when it wouldn't with a target type binding.
                                // For example:
                                //   forall( otype T ) T & ?[]( T *, ptrdiff_t );
                                //   const char * x = "hello world";
                                //   unsigned char ch = x[0];
                                // Fails with simple return type binding (xxx -- check this!) as follows:
                                // * T is bound to unsigned char
                                // * (x: const char *) is unified with unsigned char *, which fails
                                // xxx -- fix this better
                                targetType = nullptr;
                                postvisit( untypedExpr );
                        }
                }

                /// true if expression is an lvalue
                static bool isLvalue( const ast::Expr * x ) {
                        return x->result && ( x->result->is_lvalue() || x->result.as< ast::ReferenceType >() );
                }

                void postvisit( const ast::AddressExpr * addressExpr ) {
                        CandidateFinder finder{ symtab, tenv };
                        finder.find( addressExpr->arg );
                        for ( CandidateRef & r : finder.candidates ) {
                                if ( ! isLvalue( r->expr ) ) continue;
                                addCandidate( *r, new ast::AddressExpr{ addressExpr->location, r->expr } );
                        }
                }

                void postvisit( const ast::LabelAddressExpr * labelExpr ) {
                        addCandidate( labelExpr, tenv );
                }

                void postvisit( const ast::CastExpr * castExpr ) {
                        ast::ptr< ast::Type > toType = castExpr->result;
                        assert( toType );
                        toType = resolveTypeof( toType, symtab );
                        toType = SymTab::validateType( castExpr->location, toType, symtab );
                        toType = adjustExprType( toType, tenv, symtab );

                        CandidateFinder finder{ symtab, tenv, toType };
                        finder.find( castExpr->arg, ResolvMode::withAdjustment() );

                        CandidateList matches;
                        for ( CandidateRef & cand : finder.candidates ) {
                                ast::AssertionSet need( cand->need.begin(), cand->need.end() ), have;
                                ast::OpenVarSet open( cand->open );

                                cand->env.extractOpenVars( open );

                                // It is possible that a cast can throw away some values in a multiply-valued 
                                // expression, e.g. cast-to-void, one value to zero. Figure out the prefix of the 
                                // subexpression results that are cast directly. The candidate is invalid if it 
                                // has fewer results than there are types to cast to.
                                int discardedValues = cand->expr->result->size() - toType->size();
                                if ( discardedValues < 0 ) continue;

                                // unification run for side-effects
                                unify( toType, cand->expr->result, cand->env, need, have, open, symtab );
                                Cost thisCost = castCost( cand->expr->result, toType, symtab, cand->env );
                                PRINT(
                                        std::cerr << "working on cast with result: " << toType << std::endl;
                                        std::cerr << "and expr type: " << cand->expr->result << std::endl;
                                        std::cerr << "env: " << cand->env << std::endl;
                                )
                                if ( thisCost != Cost::infinity ) {
                                        PRINT(
                                                std::cerr << "has finite cost." << std::endl;
                                        )
                                        // count one safe conversion for each value that is thrown away
                                        thisCost.incSafe( discardedValues );
                                        CandidateRef newCand = std::make_shared<Candidate>( 
                                                restructureCast( cand->expr, toType, castExpr->isGenerated ), 
                                                copy( cand->env ), move( open ), move( need ), cand->cost, 
                                                cand->cost + thisCost );
                                        inferParameters( newCand, matches );
                                }
                        }

                        // select first on argument cost, then conversion cost
                        CandidateList minArgCost = findMinCost( matches );
                        promoteCvtCost( minArgCost );
                        candidates = findMinCost( minArgCost );
                }

                void postvisit( const ast::VirtualCastExpr * castExpr ) {
                        assertf( castExpr->result, "Implicit virtual cast targets not yet supported." );
                        CandidateFinder finder{ symtab, tenv };
                        // don't prune here, all alternatives guaranteed to have same type
                        finder.find( castExpr->arg, ResolvMode::withoutPrune() );
                        for ( CandidateRef & r : finder.candidates ) {
                                addCandidate( 
                                        *r, 
                                        new ast::VirtualCastExpr{ castExpr->location, r->expr, castExpr->result } );
                        }
                }

                void postvisit( const ast::UntypedMemberExpr * memberExpr ) {
                        CandidateFinder aggFinder{ symtab, tenv };
                        aggFinder.find( memberExpr->aggregate, ResolvMode::withAdjustment() );
                        for ( CandidateRef & agg : aggFinder.candidates ) {
                                // it's okay for the aggregate expression to have reference type -- cast it to the 
                                // base type to treat the aggregate as the referenced value
                                Cost addedCost = Cost::zero;
                                agg->expr = referenceToRvalueConversion( agg->expr, addedCost );

                                // find member of the given type
                                if ( auto structInst = agg->expr->result.as< ast::StructInstType >() ) {
                                        addAggMembers( 
                                                structInst, agg->expr, *agg, addedCost, getMemberName( memberExpr ) );
                                } else if ( auto unionInst = agg->expr->result.as< ast::UnionInstType >() ) {
                                        addAggMembers( 
                                                unionInst, agg->expr, *agg, addedCost, getMemberName( memberExpr ) );
                                } else if ( auto tupleType = agg->expr->result.as< ast::TupleType >() ) {
                                        addTupleMembers( tupleType, agg->expr, *agg, addedCost, memberExpr->member );
                                }
                        }
                }

                void postvisit( const ast::MemberExpr * memberExpr ) {
                        addCandidate( memberExpr, tenv );
                }

                void postvisit( const ast::NameExpr * nameExpr ) {
                        std::vector< ast::SymbolTable::IdData > declList = symtab.lookupId( nameExpr->name );
                        PRINT( std::cerr << "nameExpr is " << nameExpr->name << std::endl; )
                        for ( auto & data : declList ) {
                                Cost cost = Cost::zero;
                                ast::Expr * newExpr = data.combine( nameExpr->location, cost );

                                CandidateRef newCand = std::make_shared<Candidate>(
                                        newExpr, copy( tenv ), ast::OpenVarSet{}, ast::AssertionSet{}, Cost::zero, 
                                        cost );
                                PRINT(
                                        std::cerr << "decl is ";
                                        ast::print( std::cerr, data.id );
                                        std::cerr << std::endl;
                                        std::cerr << "newExpr is ";
                                        ast::print( std::cerr, newExpr );
                                        std::cerr << std::endl;
                                )
                                newCand->expr = ast::mutate_field( 
                                        newCand->expr.get(), &ast::Expr::result, 
                                        renameTyVars( newCand->expr->result ) );
                                // add anonymous member interpretations whenever an aggregate value type is seen 
                                // as a name expression
                                addAnonConversions( newCand );
                                candidates.emplace_back( move( newCand ) );
                        }
                }

                void postvisit( const ast::VariableExpr * variableExpr ) {
                        // not sufficient to just pass `variableExpr` here, type might have changed since
                        // creation
                        addCandidate( 
                                new ast::VariableExpr{ variableExpr->location, variableExpr->var }, tenv );
                }

                void postvisit( const ast::ConstantExpr * constantExpr ) {
                        addCandidate( constantExpr, tenv );
                }

                void postvisit( const ast::SizeofExpr * sizeofExpr ) {
                        if ( sizeofExpr->type ) {
                                addCandidate( 
                                        new ast::SizeofExpr{ 
                                                sizeofExpr->location, resolveTypeof( sizeofExpr->type, symtab ) }, 
                                        tenv );
                        } else {
                                // find all candidates for the argument to sizeof
                                CandidateFinder finder{ symtab, tenv };
                                finder.find( sizeofExpr->expr );
                                // find the lowest-cost candidate, otherwise ambiguous
                                CandidateList winners = findMinCost( finder.candidates );
                                if ( winners.size() != 1 ) {
                                        SemanticError( 
                                                sizeofExpr->expr.get(), "Ambiguous expression in sizeof operand: " );
                                }
                                // return the lowest-cost candidate
                                CandidateRef & choice = winners.front();
                                choice->expr = referenceToRvalueConversion( choice->expr, choice->cost );
                                choice->cost = Cost::zero;
                                addCandidate( *choice, new ast::SizeofExpr{ sizeofExpr->location, choice->expr } );
                        }
                }

                void postvisit( const ast::AlignofExpr * alignofExpr ) {
                        if ( alignofExpr->type ) {
                                addCandidate( 
                                        new ast::AlignofExpr{ 
                                                alignofExpr->location, resolveTypeof( alignofExpr->type, symtab ) }, 
                                        tenv );
                        } else {
                                // find all candidates for the argument to alignof
                                CandidateFinder finder{ symtab, tenv };
                                finder.find( alignofExpr->expr );
                                // find the lowest-cost candidate, otherwise ambiguous
                                CandidateList winners = findMinCost( finder.candidates );
                                if ( winners.size() != 1 ) {
                                        SemanticError( 
                                                alignofExpr->expr.get(), "Ambiguous expression in alignof operand: " );
                                }
                                // return the lowest-cost candidate
                                CandidateRef & choice = winners.front();
                                choice->expr = referenceToRvalueConversion( choice->expr, choice->cost );
                                choice->cost = Cost::zero;
                                addCandidate( 
                                        *choice, new ast::AlignofExpr{ alignofExpr->location, choice->expr } );
                        }
                }

                void postvisit( const ast::UntypedOffsetofExpr * offsetofExpr ) {
                        const ast::ReferenceToType * aggInst;
                        if (( aggInst = offsetofExpr->type.as< ast::StructInstType >() )) ;
                        else if (( aggInst = offsetofExpr->type.as< ast::UnionInstType >() )) ;
                        else return;

                        for ( const ast::Decl * member : aggInst->lookup( offsetofExpr->member ) ) {
                                auto dwt = strict_dynamic_cast< const ast::DeclWithType * >( member );
                                addCandidate( 
                                        new ast::OffsetofExpr{ offsetofExpr->location, aggInst, dwt }, tenv );
                        }
                }

                void postvisit( const ast::OffsetofExpr * offsetofExpr ) {
                        addCandidate( offsetofExpr, tenv );
                }

                void postvisit( const ast::OffsetPackExpr * offsetPackExpr ) {
                        addCandidate( offsetPackExpr, tenv );
                }

                void postvisit( const ast::LogicalExpr * logicalExpr ) {
                        CandidateFinder finder1{ symtab, tenv };
                        finder1.find( logicalExpr->arg1, ResolvMode::withAdjustment() );
                        if ( finder1.candidates.empty() ) return;

                        CandidateFinder finder2{ symtab, tenv };
                        finder2.find( logicalExpr->arg2, ResolvMode::withAdjustment() );
                        if ( finder2.candidates.empty() ) return;

                        for ( const CandidateRef & r1 : finder1.candidates ) {
                                for ( const CandidateRef & r2 : finder2.candidates ) {
                                        ast::TypeEnvironment env{ r1->env };
                                        env.simpleCombine( r2->env );
                                        ast::OpenVarSet open{ r1->open };
                                        mergeOpenVars( open, r2->open );
                                        ast::AssertionSet need;
                                        mergeAssertionSet( need, r1->need );
                                        mergeAssertionSet( need, r2->need );

                                        addCandidate(
                                                new ast::LogicalExpr{ 
                                                        logicalExpr->location, r1->expr, r2->expr, logicalExpr->isAnd },
                                                move( env ), move( open ), move( need ), r1->cost + r2->cost );
                                }
                        }
                }

                void postvisit( const ast::ConditionalExpr * conditionalExpr ) {
                        // candidates for condition
                        CandidateFinder finder1{ symtab, tenv };
                        finder1.find( conditionalExpr->arg1, ResolvMode::withAdjustment() );
                        if ( finder1.candidates.empty() ) return;

                        // candidates for true result
                        CandidateFinder finder2{ symtab, tenv };
                        finder2.find( conditionalExpr->arg2, ResolvMode::withAdjustment() );
                        if ( finder2.candidates.empty() ) return;

                        // candidates for false result
                        CandidateFinder finder3{ symtab, tenv };
                        finder3.find( conditionalExpr->arg3, ResolvMode::withAdjustment() );
                        if ( finder3.candidates.empty() ) return;

                        for ( const CandidateRef & r1 : finder1.candidates ) {
                                for ( const CandidateRef & r2 : finder2.candidates ) {
                                        for ( const CandidateRef & r3 : finder3.candidates ) {
                                                ast::TypeEnvironment env{ r1->env };
                                                env.simpleCombine( r2->env );
                                                env.simpleCombine( r3->env );
                                                ast::OpenVarSet open{ r1->open };
                                                mergeOpenVars( open, r2->open );
                                                mergeOpenVars( open, r3->open );
                                                ast::AssertionSet need;
                                                mergeAssertionSet( need, r1->need );
                                                mergeAssertionSet( need, r2->need );
                                                mergeAssertionSet( need, r3->need );
                                                ast::AssertionSet have;

                                                // unify true and false results, then infer parameters to produce new 
                                                // candidates
                                                ast::ptr< ast::Type > common;
                                                if ( 
                                                        unify( 
                                                                r2->expr->result, r3->expr->result, env, need, have, open, symtab, 
                                                                common ) 
                                                ) {
                                                        // generate typed expression
                                                        ast::ConditionalExpr * newExpr = new ast::ConditionalExpr{ 
                                                                conditionalExpr->location, r1->expr, r2->expr, r3->expr };
                                                        newExpr->result = common ? common : r2->expr->result;
                                                        // convert both options to result type
                                                        Cost cost = r1->cost + r2->cost + r3->cost;
                                                        newExpr->arg2 = computeExpressionConversionCost( 
                                                                newExpr->arg2, newExpr->result, symtab, env, cost );
                                                        newExpr->arg3 = computeExpressionConversionCost(
                                                                newExpr->arg3, newExpr->result, symtab, env, cost );
                                                        // output candidate
                                                        CandidateRef newCand = std::make_shared<Candidate>(
                                                                newExpr, move( env ), move( open ), move( need ), cost );
                                                        inferParameters( newCand, candidates );
                                                }
                                        }
                                }
                        }
                }

                void postvisit( const ast::CommaExpr * commaExpr ) {
                        ast::TypeEnvironment env{ tenv };
                        ast::ptr< ast::Expr > arg1 = resolveInVoidContext( commaExpr->arg1, symtab, env );
                        
                        CandidateFinder finder2{ symtab, env };
                        finder2.find( commaExpr->arg2, ResolvMode::withAdjustment() );

                        for ( const CandidateRef & r2 : finder2.candidates ) {
                                addCandidate( *r2, new ast::CommaExpr{ commaExpr->location, arg1, r2->expr } );
                        }
                }

                void postvisit( const ast::ImplicitCopyCtorExpr * ctorExpr ) {
                        addCandidate( ctorExpr, tenv );
                }

                void postvisit( const ast::ConstructorExpr * ctorExpr ) {
                        CandidateFinder finder{ symtab, tenv };
                        finder.find( ctorExpr->callExpr, ResolvMode::withoutPrune() );
                        for ( CandidateRef & r : finder.candidates ) {
                                addCandidate( *r, new ast::ConstructorExpr{ ctorExpr->location, r->expr } );
                        }
                }

                void postvisit( const ast::RangeExpr * rangeExpr ) {
                        // resolve low and high, accept candidates where low and high types unify
                        CandidateFinder finder1{ symtab, tenv };
                        finder1.find( rangeExpr->low, ResolvMode::withAdjustment() );
                        if ( finder1.candidates.empty() ) return;

                        CandidateFinder finder2{ symtab, tenv };
                        finder2.find( rangeExpr->high, ResolvMode::withAdjustment() );
                        if ( finder2.candidates.empty() ) return;

                        for ( const CandidateRef & r1 : finder1.candidates ) {
                                for ( const CandidateRef & r2 : finder2.candidates ) {
                                        ast::TypeEnvironment env{ r1->env };
                                        env.simpleCombine( r2->env );
                                        ast::OpenVarSet open{ r1->open };
                                        mergeOpenVars( open, r2->open );
                                        ast::AssertionSet need;
                                        mergeAssertionSet( need, r1->need );
                                        mergeAssertionSet( need, r2->need );
                                        ast::AssertionSet have;

                                        ast::ptr< ast::Type > common;
                                        if ( 
                                                unify( 
                                                        r1->expr->result, r2->expr->result, env, need, have, open, symtab, 
                                                        common ) 
                                        ) {
                                                // generate new expression
                                                ast::RangeExpr * newExpr = 
                                                        new ast::RangeExpr{ rangeExpr->location, r1->expr, r2->expr };
                                                newExpr->result = common ? common : r1->expr->result;
                                                // add candidate
                                                CandidateRef newCand = std::make_shared<Candidate>(
                                                        newExpr, move( env ), move( open ), move( need ), 
                                                        r1->cost + r2->cost );
                                                inferParameters( newCand, candidates );
                                        }
                                }
                        }
                }

                void postvisit( const ast::UntypedTupleExpr * tupleExpr ) {
                        std::vector< CandidateFinder > subCandidates = 
                                selfFinder.findSubExprs( tupleExpr->exprs );
                        std::vector< CandidateList > possibilities;
                        combos( subCandidates.begin(), subCandidates.end(), back_inserter( possibilities ) );

                        for ( const CandidateList & subs : possibilities ) {
                                std::vector< ast::ptr< ast::Expr > > exprs;
                                exprs.reserve( subs.size() );
                                for ( const CandidateRef & sub : subs ) { exprs.emplace_back( sub->expr ); }

                                ast::TypeEnvironment env;
                                ast::OpenVarSet open;
                                ast::AssertionSet need;
                                for ( const CandidateRef & sub : subs ) {
                                        env.simpleCombine( sub->env );
                                        mergeOpenVars( open, sub->open );
                                        mergeAssertionSet( need, sub->need );
                                }

                                addCandidate(
                                        new ast::TupleExpr{ tupleExpr->location, move( exprs ) }, 
                                        move( env ), move( open ), move( need ), sumCost( subs ) );
                        }
                }

                void postvisit( const ast::TupleExpr * tupleExpr ) {
                        addCandidate( tupleExpr, tenv );
                }

                void postvisit( const ast::TupleIndexExpr * tupleExpr ) {
                        addCandidate( tupleExpr, tenv );
                }

                void postvisit( const ast::TupleAssignExpr * tupleExpr ) {
                        addCandidate( tupleExpr, tenv );
                }

                void postvisit( const ast::UniqueExpr * unqExpr ) {
                        CandidateFinder finder{ symtab, tenv };
                        finder.find( unqExpr->expr, ResolvMode::withAdjustment() );
                        for ( CandidateRef & r : finder.candidates ) {
                                // ensure that the the id is passed on so that the expressions are "linked"
                                addCandidate( *r, new ast::UniqueExpr{ unqExpr->location, r->expr, unqExpr->id } );
                        }
                }

                void postvisit( const ast::StmtExpr * stmtExpr ) {
                        addCandidate( resolveStmtExpr( stmtExpr, symtab ), tenv );
                }

                void postvisit( const ast::UntypedInitExpr * initExpr ) {
                        // handle each option like a cast
                        CandidateList matches;
                        PRINT(
                                std::cerr << "untyped init expr: " << initExpr << std::endl;
                        )
                        // O(n^2) checks of d-types with e-types
                        for ( const ast::InitAlternative & initAlt : initExpr->initAlts ) {
                                // calculate target type
                                const ast::Type * toType = resolveTypeof( initAlt.type, symtab );
                                toType = SymTab::validateType( initExpr->location, toType, symtab );
                                toType = adjustExprType( toType, tenv, symtab );
                                // The call to find must occur inside this loop, otherwise polymorphic return 
                                // types are not bound to the initialization type, since return type variables are 
                                // only open for the duration of resolving the UntypedExpr. 
                                CandidateFinder finder{ symtab, tenv, toType };
                                finder.find( initExpr->expr, ResolvMode::withAdjustment() );
                                for ( CandidateRef & cand : finder.candidates ) {
                                        ast::TypeEnvironment env{ cand->env };
                                        ast::AssertionSet need( cand->need.begin(), cand->need.end() ), have;
                                        ast::OpenVarSet open{ cand->open };

                                        PRINT(
                                                std::cerr << "  @ " << toType << " " << initAlt.designation << std::endl;
                                        )

                                        // It is possible that a cast can throw away some values in a multiply-valued 
                                        // expression, e.g. cast-to-void, one value to zero. Figure out the prefix of 
                                        // the subexpression results that are cast directly. The candidate is invalid 
                                        // if it has fewer results than there are types to cast to.
                                        int discardedValues = cand->expr->result->size() - toType->size();
                                        if ( discardedValues < 0 ) continue;

                                        // unification run for side-effects
                                        unify( toType, cand->expr->result, env, need, have, open, symtab );
                                        Cost thisCost = castCost( cand->expr->result, toType, symtab, env );
                                        
                                        if ( thisCost != Cost::infinity ) {
                                                // count one safe conversion for each value that is thrown away
                                                thisCost.incSafe( discardedValues );
                                                CandidateRef newCand = std::make_shared<Candidate>( 
                                                        new ast::InitExpr{ 
                                                                initExpr->location, restructureCast( cand->expr, toType ), 
                                                                initAlt.designation }, 
                                                        copy( cand->env ), move( open ), move( need ), cand->cost, thisCost );
                                                inferParameters( newCand, matches );
                                        }
                                }
                        }

                        // select first on argument cost, then conversion cost
                        CandidateList minArgCost = findMinCost( matches );
                        promoteCvtCost( minArgCost );
                        candidates = findMinCost( minArgCost );
                }

                void postvisit( const ast::InitExpr * ) {
                        assertf( false, "CandidateFinder should never see a resolved InitExpr." );
                }

                void postvisit( const ast::DeletedExpr * ) {
                        assertf( false, "CandidateFinder should never see a DeletedExpr." );
                }

                void postvisit( const ast::GenericExpr * ) {
                        assertf( false, "_Generic is not yet supported." );
                }
        };

        /// Prunes a list of candidates down to those that have the minimum conversion cost for a given 
        /// return type. Skips ambiguous candidates.
        CandidateList pruneCandidates( CandidateList & candidates ) {
                struct PruneStruct {
                        CandidateRef candidate;
                        bool ambiguous;

                        PruneStruct() = default;
                        PruneStruct( const CandidateRef & c ) : candidate( c ), ambiguous( false ) {}
                };

                // find lowest-cost candidate for each type
                std::unordered_map< std::string, PruneStruct > selected;
                for ( CandidateRef & candidate : candidates ) {
                        std::string mangleName;
                        {
                                ast::ptr< ast::Type > newType = candidate->expr->result;
                                candidate->env.apply( newType );
                                mangleName = Mangle::mangle( newType );
                        }

                        auto found = selected.find( mangleName );
                        if ( found != selected.end() ) {
                                if ( candidate->cost < found->second.candidate->cost ) {
                                        PRINT(
                                                std::cerr << "cost " << candidate->cost << " beats " 
                                                        << found->second.candidate->cost << std::endl;
                                        )

                                        found->second = PruneStruct{ candidate };
                                } else if ( candidate->cost == found->second.candidate->cost ) {
                                        // if one of the candidates contains a deleted identifier, can pick the other, 
                                        // since deleted expressions should not be ambiguous if there is another option 
                                        // that is at least as good
                                        if ( findDeletedExpr( candidate->expr ) ) {
                                                // do nothing
                                                PRINT( std::cerr << "candidate is deleted" << std::endl; )
                                        } else if ( findDeletedExpr( found->second.candidate->expr ) ) {
                                                PRINT( std::cerr << "current is deleted" << std::endl; )
                                                found->second = PruneStruct{ candidate };
                                        } else {
                                                PRINT( std::cerr << "marking ambiguous" << std::endl; )
                                                found->second.ambiguous = true;
                                        }
                                } else {
                                        PRINT(
                                                std::cerr << "cost " << candidate->cost << " loses to " 
                                                        << found->second.candidate->cost << std::endl;
                                        )
                                }
                        } else {
                                selected.emplace_hint( found, mangleName, candidate );
                        }
                }

                // report unambiguous min-cost candidates
                CandidateList out;
                for ( auto & target : selected ) {
                        if ( target.second.ambiguous ) continue;

                        CandidateRef cand = target.second.candidate;
                        
                        ast::ptr< ast::Type > newResult = cand->expr->result;
                        cand->env.applyFree( newResult );
                        cand->expr = ast::mutate_field(
                                cand->expr.get(), &ast::Expr::result, move( newResult ) );
                        
                        out.emplace_back( cand );
                }
                return out;
        }

} // anonymous namespace

void CandidateFinder::find( const ast::Expr * expr, ResolvMode mode ) {
        // Find alternatives for expression
        ast::Pass<Finder> finder{ *this };
        expr->accept( finder );

        if ( mode.failFast && candidates.empty() ) {
                SemanticError( expr, "No reasonable alternatives for expression " );
        }

        if ( mode.satisfyAssns || mode.prune ) {
                // trim candidates to just those where the assertions are satisfiable
                // - necessary pre-requisite to pruning
                CandidateList satisfied;
                std::vector< std::string > errors;
                for ( CandidateRef & candidate : candidates ) {
                        satisfyAssertions( candidate, symtab, satisfied, errors );
                }

                // fail early if none such
                if ( mode.failFast && satisfied.empty() ) {
                        std::ostringstream stream;
                        stream << "No alternatives with satisfiable assertions for " << expr << "\n";
                        for ( const auto& err : errors ) {
                                stream << err;
                        }
                        SemanticError( expr->location, stream.str() );
                }

                // reset candidates
                candidates = move( satisfied );
        }

        if ( mode.prune ) {
                // trim candidates to single best one
                PRINT(
                        std::cerr << "alternatives before prune:" << std::endl;
                        print( std::cerr, candidates );
                )

                CandidateList pruned = pruneCandidates( candidates );
                
                if ( mode.failFast && pruned.empty() ) {
                        std::ostringstream stream;
                        CandidateList winners = findMinCost( candidates );
                        stream << "Cannot choose between " << winners.size() << " alternatives for "
                                "expression\n";
                        ast::print( stream, expr );
                        stream << " Alternatives are:\n";
                        print( stream, winners, 1 );
                        SemanticError( expr->location, stream.str() );
                }

                auto oldsize = candidates.size();
                candidates = move( pruned );

                PRINT(
                        std::cerr << "there are " << oldsize << " alternatives before elimination" << std::endl;
                )
                PRINT(
                        std::cerr << "there are " << candidates.size() << " alternatives after elimination" 
                                << std::endl;
                )
        }

        // adjust types after pruning so that types substituted by pruneAlternatives are correctly 
        // adjusted
        if ( mode.adjust ) {
                for ( CandidateRef & r : candidates ) {
                        r->expr = ast::mutate_field( 
                                r->expr.get(), &ast::Expr::result, 
                                adjustExprType( r->expr->result, r->env, symtab ) );
                }
        }

        // Central location to handle gcc extension keyword, etc. for all expressions
        for ( CandidateRef & r : candidates ) {
                if ( r->expr->extension != expr->extension ) {
                        r->expr.get_and_mutate()->extension = expr->extension;
                }
        }
}

std::vector< CandidateFinder > CandidateFinder::findSubExprs( 
        const std::vector< ast::ptr< ast::Expr > > & xs 
) {
        std::vector< CandidateFinder > out;

        for ( const auto & x : xs ) {
                out.emplace_back( symtab, env );
                out.back().find( x, ResolvMode::withAdjustment() );
                
                PRINT(
                        std::cerr << "findSubExprs" << std::endl;
                        print( std::cerr, out.back().candidates );
                )
        }

        return out;
}

} // namespace ResolvExpr

// Local Variables: //
// tab-width: 4 //
// mode: c++ //
// compile-command: "make install" //
// End: //