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package coffee.liz.lambda.bind;
import coffee.liz.lambda.ast.Expression;
import coffee.liz.lambda.ast.Expression.IdentifierExpression;
import coffee.liz.lambda.ast.Expression.AbstractionExpression;
import coffee.liz.lambda.ast.Expression.ApplicationExpression;
import coffee.liz.lambda.ast.SourceSpan;
import coffee.liz.lambda.eval.Environment;
import java.util.Optional;
import coffee.liz.lambda.eval.Value;
import coffee.liz.lambda.eval.Value.Free;
import coffee.liz.lambda.eval.Value.Closure;
import lombok.Getter;
/**
* Converts an integer to its Church numeral representation.
*
* <p>
* Church numerals encode n as {@code λf.λx.f(f(...f(x)...))} with n
* applications of f.
*/
@Getter
public class ToChurch implements ExternalBinding {
private final String name = "ToChurch";
/**
* Converts a free variable containing an integer string to a Church numeral.
*
* @param env
* the current environment
* @param val
* a Free value whose name is an integer string
* @return a Closure representing the Church numeral
*/
@Override
public Value apply(final Environment env, final Value val) {
final Free free = (Free) val;
final int n = Integer.parseInt(free.name());
Expression body = new IdentifierExpression(Optional.empty(), SourceSpan.UNKNOWN, "x");
for (int i = 0; i < n; i++) {
body = new ApplicationExpression(Optional.empty(), SourceSpan.UNKNOWN,
new IdentifierExpression(Optional.empty(), SourceSpan.UNKNOWN, "f"), body);
}
return new Closure(env, "f", new AbstractionExpression(Optional.empty(), SourceSpan.UNKNOWN, "x", body));
}
}
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