[FileCheck] Remove implementation types from API

Summary:
Remove use of FileCheckPatternContext and FileCheckString concrete types
from FileCheck API to allow moving it and the other implementation only
only declarations into a private header file.

Reviewers: jhenderson, chandlerc, jdenny, probinson, grimar, arichardson, rnk

Subscribers: hiraditya, llvm-commits

Tags: #llvm

Differential Revision: https://reviews.llvm.org/D68186

llvm-svn: 373211