CONSTRUCTING GENERIC CONSTRUCTING GENERIC ALGORITHMS ALGORITHMS BEN DEANE / BEN DEANE / 16TH SEPTEMBER 2020 16TH SEPTEMBER 2020 @ben_deane @ben_deane 1WHAT WE'LL COVER WHAT WE'LL COVER Preliminaries:

nd) Register storage duration is automatic plus compiler hints (until C++17) // ... Bar b; constructing destructing Object Lifetime Lifetime ends when destructor call starts Lifetime begins when behavior (“bugs”) may occur when accessing an object outside its lifetime // ... Bar b; constructing destructing Object Lifetime Lifetime ends when destructor call starts Lifetime begins when behavior (“bugs”) may occur when accessing an object outside its lifetime // ... Bar b; constructing destructing Object Lifetime Lifetime ends when destructor call starts Lifetime begins when

just in time Avoiding unnecessary overhead is crucial for fast compilation. In many compilers, constructing an intermediate representation (IR) of a method is a standard process. When compiling from Java just in time Avoiding unnecessary overhead is crucial for fast compilation. In many compilers, constructing an intermediate representation (IR) of a method is a standard process. When compiling from Java just in time Avoiding unnecessary overhead is crucial for fast compilation. In many compilers, constructing an intermediate representation (IR) of a method is a standard process. When compiling from Java

pragmas Postulates Postulated built-ins Pragmas Index of pragmas Record Types Declaring, constructing and decomposing records Record modules Eta-expansion Recursive records Instance fields Reflection expression e explicitly for y without giving a value for x we can write subst C {y = e} eq cx When constructing implicit function spaces the implicit argument can be omitted, so both expressions below are valid "DEPRECATED: Use `id` instead of `λx→x`" #-} Record Types Declaring, constructing and decomposing records Declarating record types Constructing record values Decomposing record values Record update Record modules

pragmas Postulates Postulated built-ins Pragmas Index of pragmas Record Types Declaring, constructing and decomposing records Record modules Eta-expansion Recursive records Instance fields Reflection expression e explicitly for y without giving a value for x we can write subst C {y = e} eq cx When constructing implicit function spaces the implicit argument can be omitted, so both expressions below are valid "DEPRECATED: Use `id` instead of `λx→x`" #-} Record Types Declaring, constructing and decomposing records Declarating record types Constructing record values Decomposing record values Record update Record modules

pragmas Postulates Postulated built-ins Pragmas Index of pragmas Record Types Declaring, constructing and decomposing records Record modules Eta-expansion Recursive records Instance fields Reflection expression e explicitly for y without giving a value for x we can write subst C {y = e} eq cx When constructing implicit function spaces the implicit argument can be omitted, so both expressions below are valid "DEPRECATED: Use `id` instead of `λx→x`" #-} Record Types Declaring, constructing and decomposing records Declarating record types Constructing record values Decomposing record values Record update Record modules

predicative hierarchy of Prop The propositional squash type Limitations Record Types Declaring, constructing and decomposing records Record modules Eta-expansion Recursive records Instance fields Reflection p i In the drawing the direction i goes left-to-right and j goes bottom-to-top. As we are constructing a path from x to z along i we have i : I in the context already and we put p i as bottom. The repeated in this example: const : {A = X : Set} {B = Y : Set} → A → B → A const x y = x When constructing implicit function spaces the implicit argument can be omitted, so both expressions below are valid

predicative hierarchy of Prop The propositional squash type Limitations Record Types Declaring, constructing and decomposing records Record modules Eta-expansion Recursive records Instance fields Reflection p i In the drawing the direction i goes left-to-right and j goes bottom-to-top. As we are constructing a path from x to z along i we have i : I in the context already and we put p i as bottom. The repeated in this example: const : {A = X : Set} {B = Y : Set} → A → B → A const x y = x When constructing implicit function spaces the implicit argument can be omitted, so both expressions below are valid

expression e explicitly for y without giving a value for x we can write subst C {y = e} eq cx When constructing implicit function spaces the implicit argument can be omitted, so both expressions below are valid `id` instead of `?x→x`" #-} 3.24 Record Types • Declaring, constructing and decomposing records – Declarating record types – Constructing record values – Decomposing record values – Record update behave much like single constructor datatypes (but see Eta-expansion below). 3.24.1 Declaring, constructing and decomposing records Declarating record types The general form of a record declaration is

expression e explicitly for y without giving a value for x we can write subst C {y = e} eq cx When constructing implicit function spaces the implicit argument can be omitted, so both expressions below are valid `id` instead of `?x→x`" #-} 3.24 Record Types • Declaring, constructing and decomposing records – Declarating record types – Constructing record values – Decomposing record values – Record update behave much like single constructor datatypes (but see Eta-expansion below). 3.24.1 Declaring, constructing and decomposing records Declarating record types The general form of a record declaration is