LSTS is a proof assistant and maybe a programming language.
Proofs in LSTS are built by connecting type definitions to quantified statements. Types are logic at rest. Statements are logic in motion. A Type knows what it is. A Statement shows what it is.
Type definitions define logical statements that are then attached to Terms. All valid Terms have at least one Type. Some Terms may have more than one Type. Types may define invariant properties. These invariant properties impose preconditions and postconditions on what values may occupy that Type. Values going into a Type must satisfy that Type's preconditions. Values coming out of a Term are then known to have satisfied each Types' invariants.
lsts
type Even: Integer
where self % 2 | 0;
type Odd: Integer
where self % 2 | 1;
Statements connect logic to form conclusions. Each Statement has a Term part and a Type part. A Statement may optionally have a label so it can be referenced directly later. Statements, when applied, provide new information to the Type of a Term. When a Statement is applied, it must match the pattern of its application context. An application context consists of a Term and a Type, which is then compared to the Term and Type of the Statement. These Term x Type relations form the basis of strict reasoning for LSTS.
```lsts forall @incodd x: Odd. Even = x + 1; forall @decodd x: Odd. Even = x - 1; forall @inceven x: Even. Odd = x + 1; forall @deceven x: Even. Odd = x - 1;
((x: Even) + 1) @inc_even : Odd ```
For further information there is a tutorial and reference documentation.