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| magistraleinformatica:mpp:start [07/09/2025 alle 11:23 (5 settimane fa)] – [Models for Programming Paradigms] Roberto Bruni | magistraleinformatica:mpp:start [10/10/2025 alle 22:45 (4 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\\ \\ 02 - Preliminaries:\\ //from syntax to semantics, the role of formal semantics, SOS approach, small-step operational semantics, big-step operational semantics// | | | | 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 (ctd):\\ //denotational semantics, compositionality principle, normalisation, determinacy, consistency, equivalence, congruence//\\ \\ 03 - Unification:\\ //inference process, signatures, substitutions, most general than relation, unification problem// | | | | 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 | 03 - Unification (ctd):\\ //unification problem, most general unifiers, unification algorithm//\\ \\ 04 - Logical systems:\\ //logical systems, derivations, theorems, logic programs, goal-oriented derivations// | | | | 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//\\ \\ 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//\\ \\ Exercises:\\ //termination, determinacy, 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// | | | | - | Fri | 03/10 | 16:00-18:00 | L1 | **Canceled:**\\ //General strike// | | |
| | 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// | | | | 9 | Tue | 07/10 | 16:00-18:00 | C1 | Exercises:\\ //termination, determinacy, divergence//\\ \\ {{ :magistraleinformatica:mpp:2025-10-07_-_08a_-_cpo.pdf |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// | | |
| | 11 | | | | | Exercises:\\ //posets//\\ \\ 10 - Consistency:\\ //denotational equivalence, congruence, compositionality principle, consistency of commands, correctness, completeness// | | | | 10 | Tue | 14/10 | 16:00-18:00 | C1 | 08 - Partial orders and fixpoints (ctd.):\\ //monotonicity, 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//\\ \\ Exercises:\\ //well-founded recursion, posets, semantics// | | |
| | 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// | | | | 11 | Thu | 16/10 | 09:00-11:00 | L1 | 09 - Denotational semantics:\\ //lambda-notation, free variables, capture-avoiding substitutions, alpha-conversion, beta rule, conditionals, denotational semantics of commands, fixpoint computation// | | |
| | 13 | | | | | Haskell ghci (ctd):\\ //recursive definitions, tail recursion, let-in, where, map, filter, fixpoint operator// | | | | 12 | Fri | 03/10 | 16:00-18:00 | L1 | 10 - Consistency:\\ //denotational equivalence, congruence, compositionality principle, consistency of commands, correctness, completeness// | | |
| | | 13 | | | | | 11 - Haskell:\\ //an overview//\\ \\ Haskell ghci:\\ //basics, tuples, lists, list comprehension, guards, pattern matching, lambda, partial application, zip, exercises//\\ \\ Haskell ghci (ctd):\\ //recursive definitions, tail recursion, let-in, where, map, filter, fixpoint operator// | | |
| | 14 | | | | | Haskell ghci (ctd.):\\ //folds, application, function composition, exercises//\\ \\ 12 - HOFL:\\ //syntax, pre-terms, types, types judgements, type system, type checking, type inference, principal type// | | | | 14 | | | | | Haskell ghci (ctd.):\\ //folds, application, function composition, exercises//\\ \\ 12 - HOFL:\\ //syntax, pre-terms, types, types judgements, type system, type checking, type inference, principal type// | | |
| | 15 | | | | | 12 - HOFL (ctd.):\\ //canonical forms, operational semantics, lazy vs eager evaluation// | | | | 15 | | | | | 12 - HOFL (ctd.):\\ //canonical forms, operational semantics, lazy vs eager evaluation// | | |
