Can a defendant appeal the validity of his guilty plea?

[66 Cal.2d 575] When a defendant pleads guilty to a crime not divided into degrees (or when he pleads guilty to a particular degree of the crime) no trial is held on the question of guilt and there are no controverted issues, since he admits every element of the crime, and the plea necessarily results in a judgment of conviction. Under these circumstances there is rationale for confining the right of appeal to a situation in which fundamental errors may have occurred. Even prior to the 1965 enactment of section 1237.5 a defendant could attack the validity of his guilty plea only upon limited appeal grounds, such as lack of jurisdiction of the trial court or the legality of the proceedings. (Stephens v. Toomey (1959) 51 Cal.2d 864, 870, 338 P.2d 182.) Section 1237.5, while codifying and perhaps somewhat broadening these grounds, added provisions, not previously set forth, that one of the specified grounds for appeal be stated by the defendant in a declaration under penalty of perjury and that a certificate of probable cause for the appeal be filed by the trial judge. The primary purpose of these new requirements is to prevent frivolous appeals challenging the validity of guilty pleas.