I suppose there will a limit to how many ‘forgotten semi-presidentialism’ postings there can be, but I still have a few more to share.
I have never seen Cuba classed as semi-presidential, but this was the case from 1940-1959.
In 1940, a new constitution was passed. The text is available in Spanish from the really excellent Database of the Americas website. There is also an English version available here (enjoy the musical accompaniment).
The 1940 constitution provided for a popularly elected president. The president was to be elected via a US-style or Finnish-style electoral college (Article 140). In addition, there was a Council of Ministers that included a prime minister (Article 151). The president could dismiss the prime minister. So, this was a president-parliamentary form of semi-presidentialism.
The Council of Ministers was collectively responsible to both the Chamber and the Senate (Article 164). Either Chamber could propose a motion of confidence. An absolute majority was required for the no-confidence motion to be passed (Article 165). If the motion was passed, the government had to resign (Article 168).
The Cuban legislature was highly fractionalised and there were 15 different prime ministers from 1940-1959.
Polity classes Cuba as, in effect, a partial democracy from 1940-52 when former president Batista staged a coup. I am slightly unclear as to the constitutional situation at that time. My understanding is that Batista suspended the constitution. Certainly, a new constitution was passed in February 1959 following the Cuban revolution led by Fidel Castro. This constitution was not semi-presidential.
I think Cuba is perhaps the second most surprising case of semi-presidentialism. There is one other that took me even more by surprise when I learned about it and I will do a post at a future date. In the meantime, if anyone would like to hazard a guess as to what is the most surprising example in the history of semi-presidentialism, then please leave a comment.