rule — matching intermediate values . . . . . . . . . . . . . . . . . . . . . . . . . . 39 9 Theorem Proving 41 9.1 Equality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a ghci style interface which allows evaluation of, as well as type checking of, expressions; theorem proving, compilation; editing; and various other operations. The command :? gives a list of supported Definitions to complete the definition of parity. 40 Chapter 8. Views and the “with” rule CHAPTER 9 Theorem Proving 9.1 Equality Idris allows propositional equalities to be declared, allowing theorems about

Idris Packages 35 8 Example: The Well-Typed Interpreter 37 9 Views and the “with” rule 41 10 Theorem Proving 43 11 Provisional Definitions 47 12 Interactive Editing 51 13 Syntax Extensions 55 14 Miscellany a ghci style interface which allows evaluation of, as well as type checking of, expressions; theorem proving, compilation; editing; and various other operations. The command :? gives a list of supported to complete the definition of parity. 42 Chapter 9. Views and the “with” rule CHAPTER 10 Theorem Proving 10.1 Equality Idris allows propositional equalities to be declared, allowing theorems about

rule — matching intermediate values . . . . . . . . . . . . . . . . . . . . . . . . . . 41 10 Theorem Proving 43 10.1 Equality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a ghci style interface which allows evaluation of, as well as type checking of, expressions; theorem proving, compilation; editing; and various other operations. The command :? gives a list of supported to complete the definition of parity. 42 Chapter 9. Views and the “with” rule CHAPTER 10 Theorem Proving 10.1 Equality Idris allows propositional equalities to be declared, allowing theorems about

11 The Idris Community May 18, 2016 Contents 1 Type Providers in Idris 3 2 The Interactive Theorem Prover 7 i ii Idris Tutorial Series, Release 0.11 Tutorials submitted by community members. CHAPTER 2 The Interactive Theorem Prover This short guide contributed by a community member illustrates how to prove associativity of addition on Nat using the interactive theorem prover. First we define hole 2 } { hole 1 } { hole 0 } ---------- Assumptions: ---------- 8 Chapter 2. The Interactive Theorem Prover Idris Tutorial Series, Release 0.11 n : Nat m : Nat o : Nat ---------- Goal: ----------

12 The Idris Community July 26, 2016 Contents 1 Type Providers in Idris 3 2 The Interactive Theorem Prover 7 i ii Idris Tutorial Series, Release 0.12 Tutorials submitted by community members. CHAPTER 2 The Interactive Theorem Prover This short guide contributed by a community member illustrates how to prove associativity of addition on Nat using the interactive theorem prover. First we define hole 2 } { hole 1 } { hole 0 } ---------- Assumptions: ---------- 8 Chapter 2. The Interactive Theorem Prover Idris Tutorial Series, Release 0.12 n : Nat m : Nat o : Nat ---------- Goal: ----------

The Idris Community September 18, 2016 Contents 1 Type Providers in Idris 3 2 The Interactive Theorem Prover 7 i ii Idris Tutorial Series, Release 0.12.3 Tutorials submitted by community members CHAPTER 2 The Interactive Theorem Prover This short guide contributed by a community member illustrates how to prove associativity of addition on Nat using the interactive theorem prover. First we define hole 2 } { hole 1 } { hole 0 } ---------- Assumptions: ---------- 8 Chapter 2. The Interactive Theorem Prover Idris Tutorial Series, Release 0.12.3 n : Nat m : Nat o : Nat ---------- Goal: ----------

11 The Idris Community May 02, 2016 Contents 1 Type Providers in Idris 3 2 The Interactive Theorem Prover 7 i ii Idris Tutorial Series, Release 0.11 Tutorials submitted by community members. CHAPTER 2 The Interactive Theorem Prover This short guide contributed by a community member illustrates how to prove associativity of addition on Nat using the interactive theorem prover. First we define hole 2 } { hole 1 } { hole 0 } ---------- Assumptions: ---------- 8 Chapter 2. The Interactive Theorem Prover Idris Tutorial Series, Release 0.11 n : Nat m : Nat o : Nat ---------- Goal: ----------

12 The Idris Community July 26, 2016 Contents 1 Type Providers in Idris 3 2 The Interactive Theorem Prover 7 i ii Idris Tutorial Series, Release 0.12 Tutorials submitted by community members. CHAPTER 2 The Interactive Theorem Prover This short guide contributed by a community member illustrates how to prove associativity of addition on Nat using the interactive theorem prover. First we define hole 2 } { hole 1 } { hole 0 } ---------- Assumptions: ---------- 8 Chapter 2. The Interactive Theorem Prover Idris Tutorial Series, Release 0.12 n : Nat m : Nat o : Nat ---------- Goal: ----------

2 The Idris Community March 19, 2016 Contents 1 Type Providers in Idris 3 2 The Interactive Theorem Prover 7 i ii Idris Tutorial Series, Release 0.10.2 Tutorials submitted by community members CHAPTER 2 The Interactive Theorem Prover This short guide contributed by a community member illustrates how to prove associativity of addition on Nat using the interactive theorem prover. First we define hole 2 } { hole 1 } { hole 0 } ---------- Assumptions: ---------- 8 Chapter 2. The Interactive Theorem Prover Idris Tutorial Series, Release 0.10.2 n : Nat m : Nat o : Nat ---------- Goal: ----------