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| magistraleinformatica:mpp:start [22/09/2025 alle 19:59 (12 giorni fa)] – [Lectures (1st part)] Roberto Bruni | magistraleinformatica:mpp:start [02/10/2025 alle 12:36 (3 giorni fa)] (versione attuale) – [Lectures (1st part)] Roberto Bruni |
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| ^ N ^ Date ^^ Time ^ Room ^ Lecture notes ^ Links ^ | ^ N ^ Date ^^ Time ^ Room ^ Lecture notes ^ Links ^ |
| | 1 | Tue | 16/09 | 16:00-18:00 | C1 | 01 - Introduction to the course | | | | 1 | Tue | 16/09 | 16:00-18:00 | C1 | {{ :magistraleinformatica:mpp:2025-09-16_-_01_-_intro.pdf |01 - Introduction to the course}} | | |
| | 2 | Thu | 18/09 | 09:00-11:00 | L1 | 02 - Preliminaries:\\ //from syntax to semantics, the role of formal semantics, SOS approach, small-step operational semantics, big-step operational semantics, denotational semantics, compositionality principle, normalisation, determinacy, consistency, equivalence, congruence// | | | | 2 | Thu | 18/09 | 09:00-11:00 | L1 | {{ :magistraleinformatica:mpp:2025-09-18_-_02_-_semantics.pdf |02 - Preliminaries}}:\\ //from syntax to semantics, the role of formal semantics, SOS approach, small-step operational semantics, big-step operational semantics, denotational semantics, compositionality principle, normalisation, determinacy, consistency, equivalence, congruence// | | |
| | 3 | Fri | 19/09 | 16:00-18:00 | L1 | Exercises\\ \\ 03 - Unification:\\ //inference process, signatures, substitutions, most general than relation, unification problem, most general unifiers, unification algorithm// | | | | 3 | Fri | 19/09 | 16:00-18:00 | L1 | Exercises\\ \\ {{ :magistraleinformatica:mpp:2025-09-19_-_03_-_unification.pdf |03 - Unification}}:\\ //inference process, signatures, substitutions, most general than relation, unification problem, most general unifiers, unification algorithm// | | |
| | 4 | | | | | Exercises:\\ //unification, goal-oriented derivations//\\ \\ 04 - Logical systems:\\ //logical systems, derivations, theorems, logic programs, goal-oriented derivations//\\ \\ 05 - Induction:\\ //precedence relation, infinite descending chains, well-founded relations, well-founded induction, mathematical induction, proof of induction principle, structural induction, termination of arithmetic expressions// | | | | 4 | Tue | 23/09 | 16:00-18:00 | C1 | Exercises:\\ //unification, goal-oriented derivations//\\ \\ {{ :magistraleinformatica:mpp:2025-09-23_-_04_-_logic.pdf |04 - Logical systems}}:\\ //logical systems, derivations, theorems, logic programs, goal-oriented derivations// | | |
| | 5 | | | | | Exercises:\\ //induction//\\ \\ 05 - Induction (ctd.):\\ //determinacy of arithmetic expressions, many-sorted signatures, arithmetic and boolean expressions, structural induction over many-sorted signatures, termination of boolean expressions, memories, update operation, operational semantics of commands// | | | | 5 | Thu | 25/09 | 09:00-11:00 | L1 | {{ :magistraleinformatica:mpp:2025-09-25_-_05a_-_induction.pdf |05 - Induction}}:\\ //precedence relation, infinite descending chains, well-founded relations, well-founded induction, mathematical induction, proof of induction principle, structural induction, termination of arithmetic expressions, determinacy of arithmetic expressions, many-sorted signatures, arithmetic and boolean expressions, structural induction over many-sorted signatures, termination of boolean expressions, memories, update operation, operational semantics of commands// | | |
| | 6 | | | | | 05 - Induction (ctd.):\\ //divergence, rule for divergence, limits of structural induction, induction on derivations, rule induction, determinacy of commands// | | | | 6 | Fri | 26/09 | 16:00-18:00 | L1 | Exercises:\\ //induction//\\ \\ {{ :magistraleinformatica:mpp:2025-09-26_-_05b_-_more_induction.pdf |05 - More induction}} (Structural Induction)://many-sorted signatures, arithmetic and boolean expressions, structural induction over many-sorted signatures, termination of boolean expressions, memories, update operation, operational semantics of commands// | | |
| | 7 | | | | | 06 - Equivalence:\\ //operational equivalence, concrete equivalences, parametric equivalences, equivalence and divergence//\\ \\ 07 - Induction and recursion:\\ //well-founded recursion, lexicographic precedence relation, Ackermann function, denotational semantics of arithmetic expressions, consistency of operational and denotational semantics for arithmetic expressions, fixpoint equations// | | | | 7 | Tue | 30/09 | 16:00-18:00 | C1 | Exercises:\\ //induction//\\ \\ {{ :magistraleinformatica:mpp:2025-09-30_-_05c_-_rule_induction.pdf |05 - More induction (Rule Induction)}}:\\ //divergence, rule for divergence, limits of structural induction, induction on derivations, rule induction, determinacy of commands// | | |
| | 8 | | | | | 08 - Partial orders and fixpoints:\\ //partial orders, Hasse diagrams, chains, least element, minimal element, bottom element, upper bounds, least upper bound, limits, complete partial orders, powerset completeness, prefix independence, CPO of partial functions, monotonicity// | | | | 8 | Thu | 02/10 | 09:00-11:00 | L1 | {{ :magistraleinformatica:mpp:2025-10-02_-_06_-_equivalence.pdf |06 - Equivalence}}:\\ //operational equivalence, concrete equivalences, parametric equivalences, equivalence and divergence//\\ \\ {{ :magistraleinformatica:mpp:2025-10-02_-_07_-_recursion.pdf |07 - Induction and recursion}}:\\ //well-founded recursion, lexicographic precedence relation, Ackermann function, denotational semantics of arithmetic expressions, towards denotational semantics of commands// | | |
| | 9 | | | | | Exercises:\\ //induction, termination, determinacy, divergence//\\ \\ 08 - Partial orders and fixpoints (ctd.):\\ //continuity, Kleene's fixpoint theorem, McCarthy's 91 function// | | | | 9 | Fri | 03/10 | 16:00-18:00 | L1 | 08 - Partial orders and fixpoints:\\ //consistency of operational and denotational semantics for arithmetic expressions, fixpoint equations, partial orders, Hasse diagrams, chains, least element, minimal element, bottom element, upper bounds, least upper bound, limits, complete partial orders, powerset completeness, prefix independence, CPO of partial functions, monotonicity//\\ \\ Exercises:\\ //induction, termination, determinacy, divergence// | | |
| | 10 | | | | | 08 - Partial orders and fixpoints (ctd.):\\ //recursive definitions of partial functions as logical systems, immediate consequences operator, set of theorems as fixpoint//\\ \\ 09 - Denotational semantics:\\ //lambda-notation, free variables, capture-avoiding substitutions, alpha-conversion, beta rule, conditionals, denotational semantics of commands, fixpoint computation// | | | | 10 | | | | | 08 - Partial orders and fixpoints (ctd.):\\ //continuity, Kleene's fixpoint theorem, McCarthy's 91 function, recursive definitions of partial functions as logical systems, immediate consequences operator, set of theorems as fixpoint//\\ \\ 09 - Denotational semantics:\\ //lambda-notation, free variables, capture-avoiding substitutions, alpha-conversion, beta rule, conditionals, denotational semantics of commands, fixpoint computation// | | |
| | 11 | | | | | Exercises:\\ //posets//\\ \\ 10 - Consistency:\\ //denotational equivalence, congruence, compositionality principle, consistency of commands, correctness, completeness// | | | | 11 | | | | | Exercises:\\ //posets//\\ \\ 10 - Consistency:\\ //denotational equivalence, congruence, compositionality principle, consistency of commands, correctness, completeness// | | |
| | 12 | | | | | Exercises:\\ //well-founded recursion, posets, semantics//\\ \\ 11 - Haskell:\\ //an overview//\\ \\ Haskell ghci:\\ //basics, tuples, lists, list comprehension, guards, pattern matching, lambda, partial application, zip, exercises// | | | | 12 | | | | | Exercises:\\ //well-founded recursion, posets, semantics//\\ \\ 11 - Haskell:\\ //an overview//\\ \\ Haskell ghci:\\ //basics, tuples, lists, list comprehension, guards, pattern matching, lambda, partial application, zip, exercises// | | |
