• Ring Solver, Coinductive predicates, Transfer tactic, • Superposition prover, Linters, • Fourier-Motzkin & Omega, • Many more • Access Lean internals using Lean • Type inference, Unifier, Simplifier

Ring Solver • Coinductive predicates • Transfer tactic • Superposition prover • Linters • Fourier-Motzkin & Omega • Many more Lean 3.x limitations • Lean programs are compiled into byte code and

82 5.4 Linear Arithmetic Tactic . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.5 Elimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.6 Further Examples . the two elimination rules associated with conjunction. An introduction rule for a logical symbol (e.g., ∧) is a lemma whose conclusion has that symbol as the outermost symbol. Dually, an elimination rule provide in order to justify a proposition with that symbol as the outermost position, whereas the elimination rules tell us what we may infer from such a proposition. In the above proof, we apply the introduction

setting, it shows how to “introduce” or establish an implication. Application can be viewed as an “elimination rule,” showing how to “eliminate” or use an implication in a proof. The other propositional connectives information on the library hierarchy), and each connective comes with its canonical introduction and elimination rules. 3.3.1 Conjunction The expression and.intro h1 h2 builds a proof of p ∧ q using proofs Similarly, and.elim_right h is a proof of q. They are commonly known as the right and left and-elimination rules. example (h : p ∧ q) : p := and.elim_left h example (h : p ∧ q) : q := and.elim_right h

Prop) (h1 h2 : p) : h1 = h2 := rfl Note: the combination of proof irrelevance and singleton Prop elimination in ι-reduction renders the ideal version of definitional equality, as described above, undecidable the terms it recognizes as well typed, and this does not cause problems in practice. Singleton elimination will be discussed in greater detail in Section 4.4. def R (x y : unit) := false def accrec := which takes arguments – (a : α) (the parameters) – {C : foo a → Type u} (the motive of the elimination) – for each i, the minor premise corresponding to constructori – (x : foo) (the major premise)

uch that all builds make use of bundling, limited tree-shaking, and also limited dead code elimination. --progress Log progress to the console while building. --proxy-config such that all builds make use of bundling, limited tree-shaking, and also limited dead code elimination. 28 --progress=true|false Log progress to the console while building. Default: true. 27 such that all builds make use of bundling, limited tree-shaking, and also limited dead code elimination. 19 --progress=true|false Log progress to the console while building. 20 --proxyConfig=proxyConfig

even a simple counter might differ on a combined stream vs. on separate streams Redundancy elimination Eliminate redundant operations, aka subgraph sharing B A B C D A B C D ??? Vasiliki Kalavri on a single core, one with operators B and C, the other with operators B and D. Redundancy elimination B A B C D A B C D ??? Vasiliki Kalavri | Boston University 2020 22 • Multi-tenancy • several queries • when applications analyze data streams from a small set of sources • Operator elimination • remove a no-op, e.g. a projection that keeps all attributes • remove idempotent operations

Identifier Scopes §33. Expression Evaluation Orders §34. Value Copy Costs in Go §35. Bounds Check Elimination Concurrent Programming §36. Concurrency Synchronization Overview §37. Channel Use Cases §38 more information about these games. Hope you enjoy them.) §35. Bounds Check Elimination 384 Bounds Check Elimination Go is a memory safe language. In array/slice element indexing and subslice operations helps Go compilers effectively use optimizations like BCE ? (bounds check elimination) and CSE ? (common subexpression elimination). BCE can avoid some unnecessary bounds checks, and CSE can avoid some

STACKFRAME Skip stackframes. PEEPHOLE Peephole optimizations. ASMCSE Use common subexpression elimination at the assembler level. LOOPUNROLL Unroll loops TAILREC change tail recursion to regular while math operations REMOVEEMPTYPROCS remove calls to empty procedures. CSE Use common subexpression elimination DFA Use DFA (Data Flow Analysis). AUTOINLINE Try to automatically inline procedures where appropriate the common subexpression elimination (formerly called the "reloading optimizer") 5. Uncertain optimizations (-OoUNCERTAIN): With this switch, the common subexpression elimination algorithm can be forced

to finding a plan that exploited dynamic partition elimination (DPE) and sometimes ignoring cases where both static and dynamic partition elimination would improve plan performance. This was done to prevent plan. To avoid generating sub-optimal plans, the query optimizer now generates both partition elimination options but only for the greedy algorithm, regardless of the join order chosen. This helps to GPORCA operates with an emphasis on generating join orders that are suitable for dynamic partition elimination. This often results in faster optimization times and/or better execution plans, especially when