Add public headers

Declarations for the string core, stdio, stdlib, unistd, errno, sys/types, and the raw syscall interface; the FILE layout stays private in src/internal.h.

Ultraworked with [Sisyphus](https://github.com/code-yeongyu/oh-my-openagent)

Co-authored-by: Sisyphus <[email protected]>

include/string.h

@@ -0,0 +1,32 @@
+/*
+ * string.h — memory and string operations.
+ *
+ * All functions here are real, tiny, and freestanding: no libc, no
+ * compiler builtins. They are the foundation everything else builds on.
+ */
+
+#ifndef _NULSL_STRING_H
+#define _NULSL_STRING_H
+
+#include <stddef.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+size_t strlen(const char *s);
+int strcmp(const char *a, const char *b);
+int strncmp(const char *a, const char *b, size_t n);
+char *strcpy(char *dst, const char *src);
+char *strncpy(char *dst, const char *src, size_t n);
+
+void *memcpy(void *restrict dst, const void *restrict src, size_t n);
+void *memmove(void *dst, const void *src, size_t n);
+void *memset(void *dst, int c, size_t n);
+int memcmp(const void *a, const void *b, size_t n);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* _NULSL_STRING_H */