Realizing arithmetical formulæ PDF
Preview Realizing arithmetical formulæ
Classicalrealizability Realizabilitygame Introduction Zoology Genderequality Realizing arithmetical formulæ E´tienne Miquey JointworkwithMauricioGuillermo February 4, 2013 E´tienneMiquey Realizingarithmeticalformulæ Classicalrealizability Realizabilitygame Introduction Zoology Genderequality Curry-Howard Proof/programm correspondence Proof theory Functional programming Proposition Data types Deduction rule Typing rule A⇒ B A→ B Γ⊢ A ⇒ B Γ⊢ A Γ⊢ t :A → B Γ⊢ u : A Γ ⊢B Γ⊢ (t)u : B Correct (for the execution) program might be untypable : let stupid n = . if n=n+1 then 27 else true E´tienneMiquey Realizingarithmeticalformulæ Classicalrealizability Realizabilitygame Introduction Zoology Genderequality Curry-Howard Proof/programm correspondence Proof theory Functional programming Proposition Data types Deduction rule Typing rule A⇒ B A→ B Γ⊢ A ⇒ B Γ⊢ A Γ⊢ t :A → B Γ⊢ u : A Γ ⊢B Γ⊢ (t)u : B Correct (for the execution) program might be untypable : let stupid n = . if n=n+1 then 27 else true E´tienneMiquey Realizingarithmeticalformulæ Classicalrealizability Realizabilitygame Introduction Zoology Genderequality Curry-Howard Proof/programm correspondence Proof theory Functional programming Proposition Data types Deduction rule Typing rule A⇒ B A→ B Γ⊢ A ⇒ B Γ⊢ A Γ⊢ t :A → B Γ⊢ u : A Γ ⊢B Γ⊢ (t)u : B Correct (for the execution) program might be untypable : let stupid n = . if n=n+1 then 27 else true E´tienneMiquey Realizingarithmeticalformulæ Classicalrealizability Realizabilitygame Introduction Zoology Genderequality Curry-Howard Proof/programm correspondence Proof theory Functional programming Proposition Data types Deduction rule Typing rule A⇒ B A→ B Γ⊢ A ⇒ B Γ⊢ A Γ⊢ t :A → B Γ⊢ u : A Γ ⊢B Γ⊢ (t)u : B Correct (for the execution) program might be untypable : let stupid n = . if n=n+1 then 27 else true E´tienneMiquey Realizingarithmeticalformulæ Classicalrealizability Realizabilitygame Introduction Zoology Genderequality Curry-Howard Proof/programm correspondence Proof theory Functional programming Proposition Data types Deduction rule Typing rule A⇒ B A→ B Γ⊢ A ⇒ B Γ⊢ A Γ⊢ t :A → B Γ⊢ u : A Γ ⊢B Γ⊢ (t)u : B Correct (for the execution) program might be untypable : let stupid n = . if n=n+1 then 27 else true E´tienneMiquey Realizingarithmeticalformulæ Classicalrealizability Realizabilitygame Introduction Zoology Genderequality Curry-Howard Proof/programm correspondence Proof theory Functional programming Proposition Data types Deduction rule Typing rule A⇒ B A→ B Γ⊢ A ⇒ B Γ⊢ A Γ⊢ t :A → B Γ⊢ u : A Γ ⊢B Γ⊢ (t)u : B Correct (for the execution) program might be untypable : let stupid n = . if n=n+1 then 27 else true E´tienneMiquey Realizingarithmeticalformulæ Classicalrealizability Realizabilitygame Introduction Zoology Genderequality Realizability Introduced by Kleene, relaxation of the previous correspondence Formula A realizers |A| |A| of programs sharing the same computational behavior ... but intrinsically limited to intuitionnistic logic E´tienneMiquey Realizingarithmeticalformulæ Classicalrealizability Realizabilitygame Introduction Zoology Genderequality Realizability Introduced by Kleene, relaxation of the previous correspondence Formula A realizers |A| |A| of programs sharing the same computational behavior ... but intrinsically limited to intuitionnistic logic E´tienneMiquey Realizingarithmeticalformulæ Classicalrealizability Realizabilitygame Introduction Zoology Genderequality Realizability Introduced by Kleene, relaxation of the previous correspondence Formula A realizers |A| |A| of programs sharing the same computational behavior ... but intrinsically limited to intuitionnistic logic E´tienneMiquey Realizingarithmeticalformulæ
Description:The list of books you might like
