What does (true opl (false op2 true)) evaluate to? ○ true ○ false Recall that Operational Semantics gives meaning to expressions by the operations performed. Consider the two operational semantic rules for two languages A and B. OCaml will be the meta- language for both. Language A A; true true A; false false A; e1 ⇒v1 A; e2 ⇒ V2 A; (e1 opl e2) V3 = if v₁ then V2 else V1 v3 A; e1⇒v1 A; e2 ⇒ V2 v3 if v₁ then v₁ else v₂ A; (e1 op2 e2) v3 Language B A; true true A; false => false A; e1 ⇒v1 A; e2 ⇒ V2 V3 = v₁ && v₂ A; op3 e₁ e2 V3 A; e1 ⇒v1 A; e2 ⇒ V2 v3 = v1 || v2 A; op4 e₁ e2 ⇒ V3

Part A. Review the concepts by yourself: (1) Describe the difference between a regular grammar and a context-free grammar from their definitions focusing on the forms of productions. (2) Explain the definitions and relations among the language, grammar, and automata for context- free language. (3) Given a context-free grammar, why we need to remove the productions in form of A -> B or A - >1. to get an equivalent one? (4) Given a context-free grammar G, what is the relation L(G) and derivation tree? (5) What is the relation between Turing machine and our current computer? (6) What are the output of DFA/NFA, Pushdown Machine, and Turing Machine?

(b) Consider the following context-free grammar, partially augmented with semantic rules: {NP.sem(VP.sem)} + Det Nominal {Det.sem(Nominal.sem)} Nominal → Adj Nominal {Adj.sem(Nominal.sem)} {..} { ...} { ...} S → NP VP NP Det + every Det a → small Nominal → dog → barks Adj VP {...} Now consider the following two sentences, with their desired meaning represen- tations: A1 every dog barks A2 Vd Dog (d) =→ Je Barking (e) A Barker(e, d) B1 a small dog barks B2 3d Dog(d) A Small(d) ^ Je Barking(e) A Barker(e, d) Complete the above augmented grammar, by giving the semantics of 'every', 'a', 'small', 'dog', and barks', so that the desired meaning representations are obtained for A1 and B1. Show that your solution is correct, by first giving the lambda expressions obtained from A1 and B1 before any beta reductions, and then showing step-by-step that the beta reductions lead to A2 and B2.

1. Consider the following grammar and try to find out Operator Precedence and Associativity. Is the grammar Ambiguous? If so, find a string for which it is ambiguous and finally, convert to Unambiguous grammar without changing the original Language. S → S % A/ A A → B * A/ B В — В & C/С C → S/ id